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Specific ionization in a drift chamber filled with

helium-isobut ane

Marko Milek

Department of Physics, McGill University

Montréal, Québec, Canada

A Thesis submitted to the

Facdty of Graduate Studies and Research

in partial fulfillrnent of the requirements for the degree of

Master of Science

@Mark0 Milek, Mar& 1998

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Abstract

This thesis discusses the measmement of the d E / d x resolution of the B a h r

drift chamber. The study waa performed on the data obtained with a small scale

prototype drift chamber (built at LAPP, Annecy, Rance) during test beam m e

at CERN (PS) and Zurich (PSI). Drift chamber simulations were performed in

o d e t to study the urpected performance. Good tradcing, necessary in the analysis

of the PS m s but unnecessary in the PSI NIU, was obtained by perfoming a

x2 minimisation of the space residuah, yielding a time to distance fnnction. An

average trading nsolution of 350pm w u aehieved. The nsolution result for

seven energy loss samplings per event was scaled up to 40 samples p u event which

will be available in the B a h r chamber. The expected d E / d x resolution of the

BaBar chamber, as obtained fiom the PS runs, is: (7.3 k 0.1 f 0.5) %. The result

fiom the PSI runs is: (6.9 f 0.4 f 0.5) %.

Résumé

Cette thèae discute les mesures de la rtisolution en dEldx de la chambre à

dérive du détecteur Bahr . Cette étude a été effectuée avec les données obtenues

avec un prototype a petite gamme de la chambn à dérive (construite à LAPP, à

Annecy en France) dans le faisceau de test au CERN (PS) et a Zurich (PSI). Des

simulation^ des chambres à daives on été effectuée pour étudier la performance.

Une bonne reconsturction, nécémire pour l'analyse des test PS mai8 démodée

pour les tests PSI, a été obtenue en faisant une minhsation en x2 des "space

reaiduals" donnant une fonction qui relit le temps et la distance. Une résolution

de recon~tuction de 350prn a été achevée. Le rCsdt at de la résolution pour sept

maures de l'énergie perdue par événement a été extrapoié jusqu'à 40 mesures (ce

qui sera disponible dans la chambre à derive du détectem Bahr) . La résolution

en dE/dz attendue de la chambre BaBar, obtenue des tests PS est: (7.3 f 0.1 k

0.5) %. Le résultat des tests PSI eat: (6.9 I 0.4 Jt 0.5) 1.

Contents

1 Introduction

2 Theoretical Background 4

. . . . . . . . . . . . . . . . . . . . . . . . . 2.1 ThestandadModel 4

. . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Discrete Spmmetries 7

2.3 CPViolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

. . . . . . . . . . . . 2.3.1 CP Violation in the Standasd Modd 10

. . . . . . . . . 2.3.2 The Cabibbo-Kobayashi-Mmkawa Matrix 11

. . . . . . . . . . . . . . 2.3.3 CPmolaüoninNeutrdBDecays 13

. . . . . . . . . . . . . 2.3.4 CP Violation in Chazged B Decayr 17

. . . . . . . . . . . . . . . . . 2.3.5 Beyond the Standard Mode1 18

. . . . . . . . . . . . . . . . . . . . . . 2.4 SpcàticIonbation.dE/& 19

2.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

ii

CONTENTS

2.4.2 Applications of d E / d x to Partide Identification in Drift

Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 B a k r Experiment 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Motivation 27

. . . . . . . . . . . . . . . . . . . . . . . 3.2 The Experimental Setup 29

. . . . . . . . . . . . . . . . . . . . . . 3.3 Gu Choice and Properties 33

4 Small Scale Drift Chamber 36

. . . . . . . . . . . . . . . . 4.1 Prototype Drift Chamber Description 36

. . . . . . . . . . . . . . . . . . . . 4.2 The Truacated Mean Method 41

4.3 GEANT Detector Description and Simulation Tool . . . . . . . . 45

. . . 4.3.1 GEANT Simulation of the Prototype Drift Chamber 46

. . . . . . . 4.3.2 Thuncation of the GEANT dE/& Distribution 48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 TheI'rackFit 53

. . . . . . . 4.4.1 GARFIELD Simulation of the Drift Chamber 54

. . . . . . . 4.4.2 Tirne-to-Distance hinction and Track Fitting 58

. . . . . . . . . . . . . . . . . . . 4.4.3 Cuts and Evtnt Sekction 69

. . . . . . . . . . . . . . . . . . . . 4.4.4 Fial TtadMg R d t s 72

4.5 dE/& Caldation and Results . . . . . . . . . . . B . . . . . . . 74

iv

5 Conclusion

CONTENTS

82

A The Pedestal Run 84

B Ttack Fita Using MINUIT 88

B.l Negative Signed Momentum Rune . . . . . . . . . . . . . . . . . . 88

B.2 Positive Signed Momentum Runs . . . . . . . . . . . . . . . . . . 94

Bibliography 86

List of Figures

The unitanty triangle.

Constrsiats on the position of the vertex, A, of the unitMty triangle

following fiom IVdl, B-mixing and e. A possible unitarity triangle

is shown with A in the preferred region. . . . . . . . . . . . . . . .

Feynman diagrsrne responsible for Bo - Bo mixing. . . . . . . . .

Feynman diagram, tree (left) and penguin (right) for the B: +

r f r - d e c a y . . . . . . . . . . . . . . . . .

Energy 108s rate in coppu as a function of of incident pi-

ons [WN96]. . . . . . . . . . . . . . . . . . . . . @ . . . . . . . . . Energy loss rate for wrious materials and several partide species

as a function of incident parti& momentum [WN96]. . . . . . . .

Landau distribution for the ionization energy loss of 250MeV elec-

t n > ~ h h l of g ~ e 0 t l s âXF;On. . . . . . . , . . . . . . + . . .

Specific ionization of h n s and pion8 in copper, aa a function of

theirmomentam. . . . . . . . . . . . . . . . . . . . . . . . . . . .

3D view of the BaBar detector. . . . . . . . . . . . . . . . . . .

LIST OF FIGURES

Calculated and mesllured drift velocities as a function of electric

. . . . . . . . . . . . . . . . . . field for a zero magnetic field. . .

Spatial tesolution for wrious gasses fiom the prototype drift cham-

. . . . . . . . . . . . ber (points) and fiom other studies ( m e s ) .

. . . . . 2D geometry of the small scale drift chamber prototype.

. . . . . . . . Expvimental setup in the Tl0 test srea at CERN.

. . . . . . . . . . . . Schematica of the Data Acqaisition System.

Landau Distribution and the corresponding tnuicated means for

1000 simulated 'events'. The percentage of hits used in cdculation

isindicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Landau Distribution and the comzsponding truncated mesna for

10,000 simulated 'events'. The percentage of hits used in cdculation

isindicated. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Lengt hs traversed in each cd (mm). Two possible paths are shown.

Flat chtribution verifies that the cell illumination is uniform. . . .

Energy loss distribution for a 3 GeV eiectron in Argon as &en by

standard GEANT. The width of the Iayerir is gioai in centimetas.

Taken from [Sof94]. . . . . . . . . . . . . . . . . . . . . . . . .

dE/& distribution for 3GeV/c incident protons. 'Ihncated means

. . . . . . . . . . . for various tniacation fiactioru are &O shonn.

dE/& diskibution for 3GeV/c incident pions. Trnncated meam

for various tntacation fiactione are also shown. . . . . . . . .

LIST OF FIGURES vii

4.10 A single track paasing through c e b 1-7. Cirdes are distances the

ionbation electrons travded to the sense wire. . . . . . . . . . . .

4.11 Chamber lsyout (lelt) and electron M-lines for particle ttaversing

. . . . . . . . . . . . . . . . . . . . . . . . . . . . c& 1-7 (right).

4.12 Equipotential contours for the whole chamber (ldt) and c d 4 only

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( r i g h t ) . .

4.13 Time-to-Distance (TD) fnnction for c d 1 (top left), c d 2 (top

right), c d 3 (bottom lefi) and cd 4 (bottom right). . . . . . . . .

4.14 Polynomial fits to time-to-distance functions for c d s 1-4. . . . . .

4.15 ATC readouts for the two sets of mu. The -3GeV/c nuis (top)

show a 'deanct' beam partide content than the +3GeV/c nuur

(bottom). Responses £rom both ATCe are shoan: n=1.03 (le&)

. * * * . . . . . . . . . . . . * . . . . . . and n=1.05 (right). . .

4.16 Two dimensional projection of the Cerenkov cone (left). For /3 < l /n theie is no const~ctive intederence and Cerenkov light ie not

. . . . . . . . . . . . . . . . . . . . . . . . . . . emmited (right).

4.17 Raw time spectra (TDC readouts) for celb 1-4. Both sets of ninr

. . . . . . . . . . . . . . . . (-3GeV/c and +3GeV/c) were ueed..

4.1% The upected time spectrom, d o m c d illumination assumed. .

4.19 Exponential fits to ‘the aaos' for c d s 1 and 2. Both sets of m s

. . . . . . . . . . . . . . . . . . . . . . . . . . . . with were used.

LIST OF FIGURES

Anticodation of times in cella 1 and 2 (Mt) and correlations of

times in cells 1 snd 3 (Rght) before the time cut (top) and after

. . . . . . . . . . . . . . . . . . . . . . . . the timecut (bottom).

Three different time-to-distaoce fnnctions: a GARFIELD predic-

tion and fits to each of the nin sets (top). A Merence between

GARFIELD and the average of the fitted TD funetions (bottom).

d E / d z resolutions obtained from both negative and positive signed

momentum runs. Different &actions (10% to 100%) of hits wue

. . . . . . . . . . . . . . . . . . . . . . . . . uscd in caldations.

dE/dz resolutions obtained from the PSI runs. DXerent fiactions

. . . . . . . . . . (10% to 100%) of hits were used in caldations.

ATC readouts fiom both counters. Gaussian fit8 to pedestal distri-

. . . . . . . . . . . . . . . . . . . . . . . . bution are also shown,

TDC readouts for d l 0 cells. The noise levd is s m d as the TDCs

. . . . . . . . . . . . . . . . . . . . overflow for almost aJl events,

ADC readouts for d l 0 cells. Gaussian fits to pedestal distribution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . are&oshown*

Cdculated and fitted distances to the wite in cell 1. Negative eigned

. . . . . . . . . . . . . . . . . . . . . momentwnnuiswereused.

Spatiai residuab in d d a with a drift-time eut applied. Negative

aigned moment- ru.ns were used. . . . . . . . . . . . . . . . . . .

Spatial reeiduals in all c e l l ~ withont a dtift-time cat applied. 10,000

evaita fiom negative signed momentnm rans were ased. . . . . . .

LIST OF FIGURES

B.4 Time-to-distance hctions obtained £rom fits to dat with and with-

out the drift time cut, and from GARFIELD prediction. . . . . . 93

B.5 Spatial residuals in d cells with a drift-tirne cut applied. Positive

signed momentam runs were used. . . . . . . . . . . . . . . . . . . 95

List of Tables

2.1 Four fundamental forces and theh mediators . . . . . . . . . . . . . 6

2.2 Elementsry partide content of the Standard Mode1 . . . . . . . . . 7

. . . . . . . . . . . . . . . . . 2.3 Cf asymmetries in Bd and B. decays 16

3.1 The BsBar detector O parametet somm ary. . . . . . . . . . . . . . 30

3.2 Ptoperties of various gas mixtures at atmospheric pressure and 20°C . 33

3.3 K / r separation for wrious gas mixtures . . . . . . . . . . . . . . . 33

4.1 Experimental setop at T10. sumxnary of the component character-

istics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Confidence level of the Gaussian fit as a fanetion of the percentage

ofhifeused . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Fit parameters and theoretical values for dE/& diatributions (LM-

dan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4 Fit parameters of the truncated mean di~tributions for several tnin-

cation fiactions (percentagcs of hits wed in the caldation of the

meam) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

LIST OF TABLES

Summary of the parameters for polynomid fits to TD fwictions in

. . . . . . . . . . . . . c& 1-4. Confidence levels are also shown. 61

Threshold momenta aad the Cuenkov angles for protons and pions

inbothATCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

T i e seros for al l 10 cells, as obtained from the exponential fit

(both sets of runs were used). The correction centering the spatial

. . . . . . . . . . . . . . . . . . . . . . residuals was dso applied. 68

Cuts and their efficiencies for both sets of runs. . . . 72

Tie-to-distance funetion parameters, and parameters of Gaussian

fits to residual distributions. . . . . . . . . . . . . . . . . . . 74

4.10 Different nuis used in dE /& calculation. . . . . . . . . . . . . . . 75

4.1 1 Gaussian fit parameters and the conesponding dE l d x resolutions

for various fractions of hits used. Statistical errors aie &O shown. 77

4.12 Gaussian fit paxameters and the corresponding dE/dz resolutions

for vatious fxactions of hits used. Statistical errors axe &O shown. 80

A.2 Mems and widths of Gaussian fits to pedestal ADC distributions.

Arbitrsty a a i t s are used. . . . . . . . . . . . . . . . . . . . . . . . 85

B.l Means and widths of Gans~ian fita to space residuals (pm), p =

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +3GeVc-'. 90

B.2 Means and widtha of Gaussian fita to space residuah (pm), p =

+3GeVc-'. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Aknowledgements

1 would like to express my deepest gratitude to the members of the BaBar group

at LAPP: Yannis Karyotakis, Dominique Boutigny, Andrea Jeremie, Isabelle De

Bonis and Abdel Boncham for giving me the opportunity to work with them on

what has proven to be an interesting and ehallenging ptoject. I also thank my

aupervisor, Prof. Popat Patel, for his help in finding a suitable project and in

writing of this thesia. This research was partially finandally sponsored by the

Alexander McFee Foundation.

My time at McGill was made enjoyable and interesting, both intellectudy and

eocially, primarily by my office buddies: Shem, Claude, Kost-, Wai and Rainer,

who wese both helpfal and supportive.

1 must &O thank Marko for getting us here, or, at least, helping us dong the

way and my parents for unconditionally believing in me.

Fin* 1 thank Jelena for being thue, bearing with me and providing the

necesssly strength and stability.

Chapter 1

Introduction

The physics of Elernentary Partides is a vast and anuent field, with a very smbi-

tious goal: a fundamental description of the nature of both matter and energy* At

thii point, it is a vexy mature and well developed field, with a body of theory and

a language that constitutes what are ptobably the most accurate theonea known

to modern science. This language is called Quantum Field Theory (QFT) and it

is a (some sceptics would say forced) mixture of several theories:

a Quantum Mechdcs - the laws that describe the processes at atomic distance

SC&, whue the classical laws of Newton and his successors break down and

where the traditional notions of reality are challenged.

a Special Relativity - Einstein's diseove y of the relationships between space

and time on one hand, and matter and enetgy on the othet.

Field Theory - origindy devdoped by Faraday and MaxtlpeIl to desaibe elec-

tricity and magnetism and now extendcd to describing drong interactions,

weak interactions and gravitation.

Symmetry Principles - the application of the mathematical Theory of Groups

to describe a set of transformations that can be applied to physical systems

and have them unchanged are now b&g used to dassify and enurnerate

those systems.

The importance of CP violation, especidy in the early univeree formation, cas

not be overestimated. If indeed d the matter and energy of the Universe were

created out of the gravitational potential energy of the Big Bang, the symmetry

with respect tu charge conjugation would have ensured that equal srnounta of

matter and antimatter were produced. But, this is dearly no longer the case, as

the Universe we observe is constructed b o a t entirely of matter with very little

antimatter. Ba& in 1967 Andrei Sakharov established that thee requirements

must be met in order to produce thie mettez-antirnatter asymmetry [Sak67]:

O a stage in the evolution of the Universe which was far fiom equilibriam - this was ca ta idy tnie in the first moments of Universe creation when the

expansion waa rapid.

a proton decay - modem Grand Unified Theories aU predict that protons in-

deed do decay [GG74] (even though proton decay hm yet not been observed,

itil Metirne is believed to be many otders of magnitude larger than the age

of the Univuse [WN96]).

O CP violation - obirerved in the kaon system in 1964. [CCFT64]

B e h g in mind the fact that CP violation in B murons îs a lot stronger than

in K mesons, one wodd not be mong in saying that the comprehensive study of

the CP violation in B d e c q , perfomed of ta B factoty, is one of the psiorities for

High Enezgy Physics in the foUowing decade. This study is the primary physics

god of the BaBar quiment. [Co1951

Chapter 2

Theoret ical Background

2.1 The Standard Model

Over the last few decades a theory has emerged that desaibes all of the honni

elementarg partîde interactions ucept gravity (and as fat as we c m tell, gavity

is far too weak to play an important role in dementary partide processes). This

theory (or rather a collection of related theories) which, in addition to theories

mentioned in the previous chapter, also incorporates quantum electrodynamics,

the theory of electroweak procesaes and quantum chromodynamics haa become

hown as Mc Standard ModeL Even though no one pretends that the Standad

Model is the definitive description of nature it ha an attractive aesthetic feature:

all of the fiindamental intetactions ate derived h m very few general principles.

Those teqtiirementi on any candidate physicd thcory are the following: wiatarity

- e m e r the conservation of probability, mmimcawoliPy - physicai observab1es

mut be separately measurable at dinaent positions and equd timer, and locality

- the amplitudes for spatidy aeparated physicd processe mu& faetoriae and be

pmerved under time evolution (ptovided that no signais piopagate h m one point

2.1. THE STANDARD MODEL 5

to the othu), invariance under Lorentz trunsjonnations und t ra~lat ionr - by the

Noether9s Theorun implies the existence of the conesponding conserved quantities

(like four-momentum and angular momentum), stobility - ensures existence of the

lowest enugy state and nnomalisobtlity - the physics at s m d energy scale is

lazgdy insensitive to the physics at high energy scale (if Q < A then contributions

of order Q/ A, where A is the large ecde energy faetor and Q measuns the s m d

energy scale, c m be neglected). [Bu1971

The strong, weak and electromagnetic interadions are understood aa arising

due to the exchange of various spin-l bosons amongst spin-112 paxticles that

make up matter. Th& properties can be summarized as being partides that are

assodated with the generators of the dgebra:

The eight spin-i pattides associated with the factor SU,(3) ('c' is meant to denote

color, which is a quantum numbu carried by strongly interacting partides) are

callcd gluons and are thought to be massless. The four spin-l bosons associated

with the factor SUL(2) x Uy(l) ('L' is meant to indicate that only left-handed

fermions carry this quantum number, 'Y' distinguiahes the gmup associated with

the weak hyperdisrge fiom the U,(1), the electromagnetic goup) are reiated to

the physicd bosoncl W*, Zo and the photon.

Table 2.1 shows the four fundamental forces governing the interactions between

both mattn and energy. Masses of the gauge bosons are drom [WN96]. Gravity,

mediated by a hypothetical spin-2 graviton, being difEcult to quantiae, is exduded

fiom the Standard Model.

Apart fiom spin-1 psrtides there ase a number of fundamental spin-112 parti-

des, called fermions, and the chuacter of th& interactions con be a ~ ~ a r i z e d by

@vhg th& transformation propaties with respect to the SU,(3) x SUc(2) x Uy(l)

CHAPTER 2. THEORETICAl; BACKGROUND

Table 2.1: Four fimdamental forces and th& mediators.

gauge group. Fermions traneform in a fairly compiicated way as t h e sppear to

be tkee f d e s of partides, with each family coupling identically to d gauge

bosons. Leptons are, by definition, those spin-112 partides which do not takepart

in strong intuactions. Six leptons are known up to date. Hadronr, on the other

hand, are defined as partides which do take psit in strong interactions. The spec-

tnun of known hadrons ia rich but they can be accounted for as the bound states

of five quarks (a, d, c, s and b). Table 2.2 is a summaq of the Standard Model

partide content. The masses were taken fiom [WN96]. Both quarks and leptons

are grouped into three families. Corresponding antipattides are not shown. The

v masses are uppa limits with a 90% confidence level. The u, d and u quark

maases are estimates of 'cument-quark masses' in a mase independent subt raetion

scheme, the c and b quark muses ate estimated fiom eharmonium, bottomonium,

D and B masses, the t quark maar is from a CDF observation of top candidate

t ~ d 8 .

h

Once the most genaal renomdisable Lagangian built out of the fields cor-

reqonding to the expected particle content ii diagonalid, .II the boaon and

fcnaion massa can be read OR and are identicdy zao ! The vaaishing of the

Range

[ml

Force

Gravity infinite Graviton

Electromagnetism infinite Photon 5 6 x 1 0 ~ ' ~ 5 5 x

Mediator

Strong

Mass Elec t ric

[MeV/c2] Charge [el

O

Z"

Gluons

91187 O

O O

Lepton 1 Mass Electric Quark I I I M a a s Electnc

Table 2.2: Elementary partide content of the Standard Model.

&

masses is the consequence of the SU,(3) x SUL(2) x Uu(l) inwriance of the theory

and can be avoided only if this symmetry is spontaneously broken by the ground

state. The simplest way to do so is to add to the theory a weakly-coupled spin-0

partide with a potentiai which is minimiged for a non-zero field. This partide

which is 'artificially' added to the Standard Model is the Higgs boson, which is

yet to be experimentally observed, and its foudations axe much weaker than the

test of the theory. In a way, the Higgdoublet parametrises most of our ignorance

of the Standard Model. [Bu971

2.2 Discrete Symmetries

[MeV] Charge

515 IO-'' O

As we have seen, symmetries play a crucial role in the Standard Model as they

gave us the conserved quantitics. Spmmetries with the turpect to the gauge goup

(SU#) x SUc(2) x Uy(l)) and to electromagnetiw (U,(l)) are continuous, they

represent invariance of the physical qumtities under transformations govemed by

one or mon continuous parameters (such aa poaition in space or an* oricn-

u

[MeV/c2] Charge [el

2-8 213

8 CHAPTER 2. T H E 0 ~ T I C A . L BACKGROUND

tation). There are, in addition, symmetries associated with discrete parameters

aad t kee of thun are particularly useful: pority inversion (P) - the inversion of

the thee spatial coordinates through an atbitrary origin converting a Ieft-handed

~ystem into a right-handed, t h e nuersal (T) - effectively the reversal of the tem-

poral coordinate and charge conjugation (C) - a change in the sign of ail intemal

degrees of fieedom (electric charge, baryon number, lepton number, strangeness,

charm, beauty, truth but not masa, four rnomentum and spin) of all partides in

the system converting partides into antipartides.

Until 1956 it was believed that the physical laws were ambidextrous, inverting

parity on any physicd procese muet rcsult in anothet possible process. The evi-

dence of parity violation in weak decays (original experiment was made on Com

beta decay) was k s t detected by C. S. Wu e t d. who found that moet of the dec-

ttons were emitted in the ditection of the nudeai spin. [W+57] Anothu evidence

of P violation is the fact that al1 neutrinos are left-handed and d antheutrinos

are right-handed, as measured in T* -, + v,(üp). Charge conjugation is &O

not a symmetry of the weak interactions as applying it to a left-handed neutrino

produces a left-haaded antheutrino, which doesn't exist ! Time reversal is a lot

harder to test as no particles are eigenstates of T so we can not just look at

whether a given reaction presemes the eigendues of the tirne reversal operator,

or whether the rates of T even and T odd reactions are the same. The most direct

way to test the conservation of T is to messure the rates of a candidate teac-

tion (such as B + p * d + 7) si we run it both waya under the same conditions.

As atated by the 'principle of detaücd bdmce' those rata should be the ilame.

No evidence of T ~iolation waa found in strong and electromagnetic interactions,

which is hardly surprishg considering that both Csnd P were violated urcltlsively

in weak decays. Unfortunately, inverse-reaction experinientr are hard to do in the

weak interactions. Consider a t y p i d weak decay A -, p+ +r-. The inverse reac-

tion is p+ +r- -r A (allowed only if the energîes of p+ and n- are lsrge enough to

produce A), but we d l never see such a reaction because a strong interaction of a

proton and a pion will always dominate over the wesk one. [GriB?] In practice the

critical test of T inmuiance involves measurementa of quantities which should be

uractly equal to a n o if T is a perfect symmetry. The best known experiment to

date is Ramsey's upper limit on the electnc dipole moment of a neutron. [Ram82]

Nevertheless, there is a compelling answer as to why time reversd cannot be

a perfect symmetry of nature. Based on the most general assumptions - Lorentz

invariance, quantum mechanics and the idea that interactions are c d e d by fields

- the TCP Theonm states that the combined operation of t h e reversd, charge

conjugation and paxity inversion, in any order, is an exact symmetry of any in-

tcraction. [Lue571 It is not possible to construct a quantum field theory in which

TCP is violated. If, aa wil l be presented soon, CP is violated then there must be

a compensating violation of T.

2.3 CP Violation

Some temporary relief to the 'problem' of C and P violation was ptovided by

the discovery that the Univesse ia made of only left-handed partides and nght-

handed antipaxtides. This means that the combined CP symmetry trmsforms the

red physical states into each other. With the discovery of the CP violation in the

kaon eystun the sanctity of discrete symmetries was pushed badc again. The most

obvious CP violating scemrio is when two CP conjugate processes have different

amplitudes. The general approach to the exphnation of the CP violation, when

CP conjugste amplitudes a n the same, is via the interfaence of two amplitudes

that have a noms0 physid phase cliffisence in a mdtiamplitude process. CP

violation can be either: direct - the h o amplitudes that intedete with each other

contribute dUectIy to the decay of the B meson (there bQng C O & ~ ~ U ~ ~ O M fiom

10 CIIAPTER 2. THEORETICAL BACKGROUND

both tree and pengnin diagrams) and indzred - due to d g , the intuference

between X -, f and X -+ W -* f (aaauming that both X and X decay into s CP

eigenstate f ) @es rise to CP violation. If for a process we have M = Mi + e * ~ ~

then for a rate and a CP conjugate rate

we get P - PCp + O. The three family Standard Model does provide the necessary

CP violating phaee through the CKM matriz.

Evidently, the long lived neutral Laon is not a perfect eigenstate of CP. Vio-

lation in Ki - Ki mixing is desdbed by a single parameter r = 2.3 x 10%

IKO >= (1 + e)lKo > +(1- E ) ~ K " >

CP violation in the semi-leptonic kaon decayi has also b e n obsemed. It iii

parametrized by the foilowing quantity (charge asymmetry in leptonic decays):

The experimentally measured d u e of 6 (averaged £rom electron and muon chan-

nels) is: 6 = (0.327 & 0.012)%. [WN96] Thiii asymmetry provides an absolute

distinction between mattet and antimat ter and an unambiguous, convention free

definition of positive charge as the charge of a lepton preferentially produced in

the decay of a long-Iived neutral kaon.

2.3.1 CP Violation in the Standard Model

The following sections are a summary of the several pablished works on the subject

of CP violation in and beyond the Standard ModeL The full diacusrion is given

2.3. CF VIOLATION

in: [NQ92], [Gro96], [Lon961 and [Kay96].

A Lagrangian is CP conserving if all the coupling and mass terms cm be made

teal by an appropriate set of field redefinitions. In the Standatd Model, the most

general theory with only two quark generations and a single Higgs multiplet is of

that type. However, when a tbVd quark generation ie added then the most general

quark m a s mat& does d o w CP violation. The three generation S t andmd Model

with a single Higgs multiplet has only a single non-mro phase and it appesrs in

the mat& which relates weak ugeastates to mase eigenstates. This is commonly

known as the CKM (Cabibbo-Kobayashi-Maskawa) matrix, [KM731 which ie a

generslization of the four quark mixhg m a t h parametriaed by a single (Cabibbo)

sngIe. [Cab631

2.3.2 The Cabibbo-Kobayashi-Maskawa Matrix

By convention, the t h charge 213 quarks (u,c and t) are uamixed, and aU the

mixhg is utpressed in krms of a 3 x 3 unitary matrix V operating on the charge

-113 quatks (d , s and b):

The d u e s of individual mat* elemcnts can in principle aU be d e t e h e d fiom

weak decays of relevant quarks or from deep inelastic neutrino scattering. Using

the unitarity constraht and assiiming ody tkee quark generation~, the 90% con-

fidaace b i t s on the magnitudes of the eltments of the CKMmatrk are: [GKR97]

12 CHAPTER 2. THEORETICAL BACKGROUND

There aie severd parametrizations of the CKM matrix. One proposed by Chaa

and Keung [CK84] (c, = COS 0;; and sij = 8ij, with i and j bang the generation

labels, and a single phase O 5 5 2 4 :

The unitarity of the CKM matrix leads to relations such as:

The unitority triangle is s geometrical representation of this relation in the com-

Figue 2.1: The Mitarity triangle.

plex plane: the t h complut quantities, V&V;, VdVd uid V&V; should form

a tria*, as rihonm in Fig. 2.1. The unituity triangle gives a rektionrhip be-

tween the two moat poody detumined entries of the CKM mat&, Vd and VM.

2.3. CP VIOLATION 13

It is thus convenient to present constraintg on the CKM p a t d e r s as bounds on

the coordinates of the vertex A of the unitarity triangle, ss in Fig. 2.2. [GKR97]

The top qusrk mas6 evaluated at the relevant scale for the Ba - B: misng is

mt = 166 f 5GeVc-l. Note a difierent scale with respect to the unitarity triangle

in Fig. 2.1.

Figare 2.2: Constraints on the position of the vertex, A, of the unitdty trimgle

following fiom (Vdl, 8-mixing and c. A possible nnitaxity triangle is shown with

A in the preferred region.

The Standard Mode1 predictions for the CP asymmetries in nentral B decays

into catain CP eigenstates are M y determined by the d u e s of the three angles,

a, /3 and 7, of the unitîuity triangle.

2.3.3 CP Violation in Neutra1 B Decays

Whcn we consider a neutrd meson Bo and its antipartide Ëo the two masa eigen-

states are BL and Ba (meaning Jight and heavy, nspectivcly):

CEAPTER 2. TEEORETICAL BACKGROUND

The eigendue equation is:

Hue M (the mass matrix) and I' (which descnbes the exponentiai decay of the

system) are 2 x 2 Herrnitian matrices. The difierence between rH and rc is produced by channels with branching ration 0(10-3) which contribute with alter-

nating signs and it is safe to set I' = r6 = rH. Aleo, we dehe M = (Mc + M H ) / 2

and AM = Mg - ML. As r12 < MI2 gives Iplql = 1 the proper t h e evolution

of states which at tirne t=O were either pure Bo or pure Bo is &en by:

Since we are interested in the decay of neutral B mesons into a CP eiguistate,

which we denote by fCP, we define the folloming amplitudes:

The time-dependent rates for initidy pure Bo or BO states to decsy into CP

ugenst ates are:

The time-dependent CP asymmetry, which is dehed as:

2.3. CP VIOLATION

ie given by:

The quantity 1 . which can be extracted fiom afep( t ) can be directly related to

the CKM mat& elements in the Standard Model. In the general case:

b W- d b u c t d

Figure 2.3: Feynman diagrams responôible for Bo - Bo mhthg.

where A, are red, & are CKM phases and 6i are strong phases. If ail amplitudes

that contribute to the direct decay have the same CKM phase, such that AIA =

e-w~ and if q / p = e-'*, where 4M is the CKM phase in the B - B m i M g

(the relevant Feynman diagrsms are shom in Fig. 2.3), then Eq. 2.13 simplifies

considerably :

CP m~mmetries in Bo -, f, provide a way to meaaurt the angles of the unitarity

triangle, which are defhed by:

CEAPTER 2. TEEORETICAL BACKGROUND

The aim is to 4overdetermine' the unitaiity triangle, to make enough independent

measurements of the sides and the angles and thus check the validity of the Stan-

dard Model. Table 2.3 [NQ92] liats CP asymmetries for various channeh in Bd

(Ieft) and B. (nght) decays. One possible hadmnic final state is listed for each

ape&c quark decay. Standard Model predictions for the parameter TmA (in terms

of the unitatity triangle angles) are given in the last columns.

Table 2.3: CP aaymmetries in B . and B, decays.

Figure 2.4: Feynman diagrams, tree (lefi) and pengnin (right) for the Bi -, n+n-

decay.

It is important that only one weak amplitude contributes to a decay if one is

to cleady extract the CP phsses ushg indirect CP violation. A problem arises

since many B decays have more than one such contribution. In addition to tree

diagrams, penguin diagrarns are oRen present. This is the case in the decay

B: -r a+i- (both Feynman diagram for tbis decay are shown in Fig 2.4), which

is one of the interesting CP eigenstates. Eere, the tree diagram has the weak

phase VzVd, while that of the penguin diagram is &&. Therefore, for this

decay, in addition to indirect CP violation, direct CP violation is present due to

the interference between two types of diagrams. This spoils the deanliness of the

measurement of the CP asymmetries, hence the term 'penguin pollution'. Thus,

the measurement of CP asymmetry in this mode does not give sin 2a, as advertised

before, but sin(2a + O + - ) , where O+- depends on weak and strong phases of the

tree and penguin diagrams as well as on their rcktive &es. It should be noted

that this problem does not hi le in all modes. For example, in Bd -, PK; both

tree and penguin diagtams have the same weak phases 80 there is no interference,

and in B, -r Df K T there are no penguin contributions.

2.3.4 CP Violation in Charged B Decays

In charged B decays one may look for the CP violating asymmetries of the fotm:

where f i e any final state and f is its CP conjugate. Although CPT thecxem

reqnlles that the total B+ and B- decay widths are the rame, speciiic ehmels

or sums over channels can contribute to the above asymmetry. For this to happm

there must be intederence between two separate amplitudes that contribute to

the decay with Metent weak phoses, & # A, and with difterent strong phase

shifts, 61 # 62. In that caae:

18 CHAPTER 2. THEORETICAL BACKGROUND

It was recognized [BSS79] that, within the Standard Model, these conditions can

be readily met in three types of B decays: (à) CKM suppressed decays where

t m amplitudes can intedere with penguin type amplitudes, (ii) CKM forbidden

decays, which have no tree contributions but thue c m be inteduence of penguin

contributions with different charge 213 quatks in the loop, and (à$ Radiative

decays, similéu to (iz) bat the leading contribution is an electromagnetic pengiiin

(the gluons are replaced by a single photon line).

2.3.5 Beyond the Standard Model

The above discussion assumes that the only source of CP violation is the phase

of the CKM rnatrix. Models beyond the Standard Model involve other phases

and, consequenttly, the measuremente of the CP asymmetries may violate the

constrainta of the unitarity triangle. Even in the absence of new CP violrting

phases the sides of the triangle may be aected by new contributions. In certain

models, such as four-genetation model and modela involving 2-mediated flavot-

changing neutral currents, the unitarity triangle turns into a quadrangle.

Through a messurement of the CP aciymmetries, the presence of new physics

cm be detected in sevaal ways: (i) the relation a + P + 7 = T is violated, (ii)

evai if a + @ + y = r value for the CP phase can be outside of the Standsrd

Modd predictions, (iii) the CP angles are consistent with the Standard Model

predictions but are inconsistent with the measured sides of the nnitaxity triande.

Any additional information on the CP violation in and beyond the Standard

Model can be foand in a myriad of books and review publications on theoretical

particle phydca. The ones used in the prepruation of thia intmducto ry chapter

are: (NQ921, [Gro96], [Lon96], [Kay96], (WN96] and [Bur97].

2.4. SPECIFIC IONIZATION - DE IDX

2.4 Specific Ionization - d E / d x

2.4.1 Theory

This section is a summary of the theoretical description of the partide energy

loss in matter. It was taken from Introduction to EtpeRrnental Particle Physzcs,

by R.C.Fernow [Fer86], Particle Detectors, b y C.Grupen [Gm96], and Review of

Purticle Phystcs, published by The Amencan Physical Society [WN96].

Charged partides passing through mmstter loae kinetic energy by excitation of

bound electrons and by ionkation. The later process ie of greater importance

aa the atomic electrona are liberated from the atom and can be eubsequently

detected.

Given the momentum of the incident partide p = -ym& (where 7 is the

Lorentz factor, pc = v and mo is the rest mass of the partide) the m h u m

energy that might be transferred to an atomic electron (mase m.) in a medium is

given by [Ros52]:

where the kinetic energy Ekm is related to the total according to Ek,, = E -moc2.

If one neglects the quadratic term in Eq. 2.19, which is a good approximation for

d incident partides othet than electrons, it follows that: a

For relativistic partides EKn a E zs pc and the m h u m trd'able energy

becomes :

F = E2

macl ' E+*

20 CHAPTER 2. THEORETICAL BACKGROUND

If the incident partide is an electron, these approximations are no longer valid.

In this case Eq. 2.19 nduces to:

which is expected for a central collision of two classical paxticles of equal mass.

The average energy loss dE pet 'length' dx for 'heavy' partides in semi-classkal

approximation is given by Bethe-Bloch formuta (Bet30, Bet32, Blo331:

w here

z - charge of the incident partide in units of elementary charge

2, A - atomic number and atomic weight of the absorber

me - electron mass l e = r. - dassical electron radius (te = S;;o -cg)

NA - Avogadzo number (6.022 x 10~~rnol-')

I - ionbation energy of the absorber material which can be approlrimated by

I = 16Zo-9eV for Z > 1

6 - a parameter which describes how much the extended tranaverse electric field

of incident relativistic partides ie ecreened by the effective chatge denaity of the

atomic electrons. For enagetic partidcs 6 2ln7 + (, where < is a material

dependent constant . The energy loscr is usady given in uni ts of .S. The length unit g is

commonly u d because the energy 108s per d a c e mus denaity (which is dx as

d&ed above) ia lstgely independent of the proputies of the material. Eq. 2.23

is an approximation which is p r e c i ~ 60 the Ievel of a few percent up to enugies

of eevual hnndred GeV, but it cannot be wed for dow particles which move with

veloaties comparable to, or lem than, those of atomic electrons.

Radiative effects become important

o. 1 1.0 10 100 1000 10000 By = plMc

Figure 2.5: Energy loss rate in copper as a function of @y of inadent pions [WN96].

Muon momentum (GeVfc)

Pion momentum (GeV/c)

F i g w 2.6: Enmgy 108s rate for d o u s mataiah and severai paxticle speaea as a

fanction of incident partide momentum [WN96].

22 CHAPTER 2. THEORETICAL BACKGROUND

Figure 2.5 [WN96] shows the enugy loss rate as calculated for an incident

pion passing through copper. (Note the difference in energy notation between the

figure and the t u t : T,, E C" and Td n Emt). In the low energy domain

the energy loss decreases like P-Q where q ranges between 2/3 and 3. It reaches

a bzoad minimum of ionization at p7 z 3.5. Relativistic partidea which have

an uiergy loscl in this region are cded bminimum-ionizing particles'. The energy

los8 increases again because of the logarithmic term in the bradsets of Eq. 2.23.

This equation only describes energy losses due to ionization and excitation of the

atomic electrons in the medium.

Figure 2.6 [WN96] shows the energy loss rate for several spicies of inadent

partides, as a function of the incident partide momentum, passing through liquid

hydrogen, gaseous helium, catbon, aluminum, tin and lead.

At high energies radiation losses, which are not induded in the Bethe-Bloch

formula, become mote and more important, as the rate of energy los8 due to

bremsstrahlung [Rot1521 :

begins to dominate the total rate of energy loss at very hi& energies (EilTeV for

partide more massive than the electron).

Equation 2.23 gives only the average energy 108s of eharged pattides. For thin

absorbas, i.e., mainly in gases, strong fluctuations around the average energy

108s exist. The enugy loss disthbution for thin absorbas is strongly asymmetric

and can be paramettieed by a Landau distribution, see Fig. 2.7. A reasonable

approximation of the Landau diatribation is givcn by [B+84]:

whue A is the deviation fiom the most probable energy loss:

AE - actual energy loss in a layer of a given thidmess,

AEw - most probable energy 108s in the same layer,

p - density of the traversed material in g cm-3

x - thickness of the material in cm.

re - the daasical electron radius in cm.

The Landau fluctuations of the energy loss are related to a lorge extent to very high

energy transfers to atomic electrons, which dow escape and are cded 6 or bock-

on electrons. The strong fluctuations of the energy loss are quite frequently not

observed by a detector, as detectors only measure the energy which ie deposited

in th& sensitive volume, and this energy may not be the same as the energy lost

by the partide. Some of the 6 electrons may leave the sensitive volume before

depositing all of th& energy. Therefore, it is quite ofien of practical interest

to consider only the energy loss with energy transfers E smaller than some cut-

off d u e Est. The 'mead for this truncated energy loss distribution is given

by [WN96]:

The trancrted energy loss distribution does not show as pronounced Landau tail

as distribution of Eq. 2.23. Because of the density efEéct , upressed by 6, the mean

energy loss of the truncated distribution approaches a constant at high mergies,

which L d e d the Fermi plateau.

So far, only the energy los6 of the 'heavy' partides waa dismsed. Electrons,

as the incident particles requin specid treatment as: (i) even at low energies,

24 CHAPTER 2. THl3ORETKAL BACKGRO UND

the energlr los8 is iduenced by bremsstrahlung, and (ii) the mass of the incident

psrtide and the target electron are the same. The eqaiwlent of Eq. 2.23 for elec-

trons, which &O takes into consideration the kincmatics of the election-electron

collisions and the semning effects, is [MRRS88]:

The ionization energy 108s of a 250MeV electron in a lem gaseous argon layer is

shown in Fig. 2.7, where we have used: AEw = 2.4keV and ( = 0.125keV [Gru96].

- - Landau Distrlbutlon

Energy toss [keV]

Figure 2.7: Landau distribution for the ionization energy loss of 250MeV electrons

in lcm of gac~ous atgon.

F i n e , the enugy 108s in s compound of vatious elcments i is given by:

when fi is the mascl fiaction of the i-th dement and *Ii the average en- 108s

rate in that dement. Corrections to this relation due to the dependence of the

ionkation constant on the molecular structure can be safely neglected, provided

that one does not have p $ IOœ2 - IO-^.

2.4.2 Applications of d E / d x to Particle Identification in

Drift Chambers

It ehodd be realized that the spedic energg Ioss rate, Eq. 2.23, depends on the

incident particle's electric charge and velocity, but not on its masse Thezefore, if

one is able to simultanconaly measure curvature of the tradc and the deposited

ionkation energy associated with the tradr, the incident partide can be identified

in the folIowing way. The corvatue of the tradc, as obtained fiom the fit of the

drift diamber hits, yields the momentum of the partide, as well as the sign of its

electric charge. If the path a partide has traversed in the drift chamber is known

(and it is, alter the track fit is done) the measntement~ of the 'totd' energy loss

of the particle give the rate of energy loss ( d E / d x ) and, findy, the partide's

velocity. The momentum and the velocity of a given partide are s&cient to

iinambiguonsly d e t e d e its mus, thexefoxe, the incident particle is identüied.

Figure 2.8 shows the specific ionization eneqy loss rate for incident kaons and

pions in copper. Note the expanded vertical scde compwd to Fige 2.5. The

horizontal axie is the moment- rather than factor of Fig. 2.5. The incident

particle momentum ranges between O and 3GeVc-l. dE/& was caldated using

Eq. 2.23 with the ionization energy of copper Ic, = 322eV [WN96]. AU the

'density effects' (the 6 term) were neglected. Note that the two ciuves cnws at

the momentum of zs O.9GeVc-'.

A tandamental problem of this procedure &ses h m the fact that, beyond

certain momenta, energy loss rates of diffetent pattide species, pions and b u s for

example (Fig. 2.8), o v d p due to instramantal resolution. Partide identification

Pion

Part ic le momentum [GeV/c]

Figure 2.8: S p e d c ionization of kaons and pions in Coppet, as a function of their

moment um.

using the dEldx method becomes impossible in that mornentum range.

Chapter 3

BaBar Experiment

This chapter is a brief review of the B a h r Technical Demgn Report [Co195]. Other

references are quoted where necessary.

3.1 Motivation

While it has been understood for several Yeats that the measurement of CP violat-

ing asymmetries in Bo decaye could lead to important tests of the CKM matrix,

the urpehents seemed beyond nach. The discove y of a suiprîsingly long b quark

lüetime together with a luge Bo - Bo mixing made it poilsible to contemplate

such uperimcnts. It soon becsme dear that the moat straightforward apptoach

involved experiments at a vatiety of e+e- machines, Qther in the T(4S) region

(1Oa58GeV), in the PEP/PETRA continuum region, or at the Zo pole (91.19GeV).

The most favorable e+e- uperimental situation, which h the one produchg

the arndcst statiatieal enor with the Ieast integzated ltrminosity, is the asymmetric

storage ring f i a t proposed by Oddone. [Odd87] This machine would boost the

decaying Bo mesons in the laboratory £rame, allowing existing vertex measuring

technology to measure the time order of Bo - B decay paits (remember that in

order to uttract the CP violating psrameter I m A from the meaaured ssymmetry,

see Eq. 2.15, one needs to knon the time t between the two Bo decays) even with

the short B meson fiight distance.

PEP-II couder, at Stanfozd Linesr Accelerator Center (SLAC), in S tanford,

California, promises to provide the required liiminosity, initially 3 x 10JJcm-2e-',

ultiniately IO=, with asymmetric 'Y'(4S) production at a 87 = 0.56) (9GeV elec-

trons on 3JGeV positrons). The BB production rate will be 3H3 at the initial

luminosity, rising to 10Hz. The experimentai challenge is then to provide high

eficiency, high tesolution exclusive state reconstruction in a situation new to the

e+e- coUider world: a center of msas in motion in the laboratory.

The primary goal of the B a h r experiment is the systematic study of CP

viohtion in neutral B decays, as discussed in the previous chapter. The secondaiy

pals are to explore the wide range of other B physics, ch- physics, T physics,

two-photon physics and T physics that becomes a d a b l e with the high luminosity

of PEP-II.

The critical urperimental objectives to achieve the reqtlired sensitivity for CP

messurement s are: [Co1951

O To monstnict the decaps of Bo mesons into a wide varîety of exclusive bal

atates with high efficiency and low background.

r To tsg the flavor of the other B meson in the ment with high efficiency and

parit y.

O To messure the relative decay time of the two B meuwr.

3.2. THE EXPEMMENTAL SETUP

3.2 The Experimental Setup

Figure 3.1: 3D view of the BaBar detector.

The BaBat urpehentd design is ahown in Fig. 3.1 and a aummasy of the

iridividual dctectot components is givui in Table 3.1. It consists of a a c o n vertu

detector, a dtift chamba, a pattide identification ciyrtem, a Cd electromagnetic

c d o h e t a , and a magnet with an instrumented flux tetum. The superconducting

solenoid is dtsigned for a magnetic field of 1.5T, and the f l iu t e tm is instramented

fot muon identification and coarse hadron calorimetrp. All of thoae deteetors

30 CHAPTER 3. BABAR EXPERTMENT

Detector Technology

SVT Doublesided

Silicon S trip

1 Drift Chamber

P D DIRC

11 MAG 1 Superconducting

Dimensions 1 Performance

. -

40 Layers

r = 22.5 - 80.0cm

-1llcm < z < 166cm -

1.75 x 3.5cm2 quarts

-0.84 < COS 0 < 0.90

16-17 Layers cp > 90%

for p, > 0.8GeVc-'

Table 3.1: The BaBar detector - psrameter sommary.

opaate with good performance for laboratory polar angles between 17' and 150°,

corresponding to the range -0.95 < cos 0, < 0.87 (due to the Lorentz boost, the

centu of mass ftame does not coincide with the laboratory fiame).

The detector coordinate system is dehed with +z in the boost (high enexgy

beam) direction. The origin is the nominal collision point, which is ofEset in the

-z direction fiom the geometncal center of the detector magnet.

The traclring system in B d u consists of the vertex detector and a drift ch-

ber. The vertex detector is u ~ d to precwly meastire both impact patameters for

charged tr.cke ( z and r - 4). Theee measwments are used to detumine the

diAerence in decay t k of two Bo mesons. Charged partides with transverse

momentum (pe) between h. 40MeV/c and - 100MeV/c are tradced only with the

vertex detector, which must therefore provide good pattern recognition.

The drift chamber (extending from 22.5cm in radius to 80cm) is used prima-

ily to achieve excellent momentnm resolution and pattem recognition for charged

partides with pr > 100MeV/c. It also supplies information for the charged track

trigger and a measurement of dE/dz for partide identification. The optimum

reaolution is achieved by having a continuous tradDng volume with a minimum

amount of material to cause multiple scattering. By using helium-based gas mix-

tare with low mase w i r e s and a magnetic field of 1.5T very good momentum

resolution can be obtained. The chamber is designed to minimise the amount

of material in front of the paztide identification and calorimeter systems in the

heavily popdated forward direction. The readout electronics are mounted only

on the backwazd end of the chamber.

Two primary goals for the partide identification system are to identify kaons

for tagging beyond the momentum range in which dE/& separation works w d ,

and to identify pions from few body decays such as Bo -, *+rd and Bo -, p r .

A new detector techn010gy t needed to meet these goals and in the b s m l region

a DIRC (Detector of Interndy Reflected Cerenkov radiation) is used. Cerenkov

light produced in quartz bars is tranefened by total interna1 reflection to a large

water tank outside of the backward end of the magnet. The light is observed by an

M a y of photomultiplier tubes, where images govemed by the Cerenkov angle are

fotmed. This mangement provides at leaat 4 standard deviation n / K sepuation

op to aknost the kiaematic limit for partides fiom B decays.

The dectromagnetic dorimeter must have ciuperb en- reaolation down to

very low photon enagiea. This is provided by a fully projective Cd(Ti) aystal

calorimeter. The barrd calorimeter contains 5880 trapezoidal mals; the endcap

c a l o h e t u c o n t h 900 crystals. The crystal length varies £tom 17.5Xo (Xo is

the radiation length) in the fomasd endcap to 16Xo in the backwatd part of the

barrel. Electronic noise and besm related backgrounds dominate the resolution at

low photon energies, while ehower leskage fiom the rem of the crystals dominates

at higher energies.

To achieve v u y good momentum resolution at 'high' momenta without in-

creasing the tracking volume, and therefore the dorimeter cost, it is necessary

to have a field of 1.5T. The magnet is therefore of superconducting design. The

magnet is similar to many operathg detector magnets, so the engineering and

fabrication should be straightfornatd. The segmentation of the iron for an Instni-

mented Flax Retum (ER), and the need for the DIRC readout in the bahvard

region cause some design complications.

The IFR ie designed to identify muons with momentum around O.SGev/c and

to detect neutrd hadrons (0uch as Kir). The magnet flux tetuni is divided into

layers between which are gaps with Resistive Plate Chambers (RPC), which serve

as active detectors. The RPCs represent a proven technology which adapts w d

to the B a h r geometry.

The high data rate at PEP-II requkes a data acquisition system which is more

admced than those used at pment ef e- experimente. The rate of procesees to be

ncorded at the design luminosity of 3 x 10S5cm-2s-1 is about 100Eiz (the bnnch

aossing paiod is 4.2ns), ucept for Bhabha evente which have to be 'icaled'.

Simulations of machine backgrounds ahow hit rates of about 100kEz pet layer in

the inna region of the drift chamber and about 140MEb in the h s t Silicon laya.

The goal ie to operate with nefigible dead time even if the backgrounds are 10

times hi&= than present estimates, WU might happa e d y in the H e of the

expairnent .

3.3. CAS CHOICE AND PROPERTIES

3.3 Gas Choice and Properties

The choice of gas for the dri£t ch& is driven pr imdy by the iieeds to reduce

the total amount of the material, minimize multiple scattering for low momentum

tracks, and to operate efficiently in a 1.53" magnetic field.

Table 3.2: Propedies of various gas mixtures at atmospheric pressure and 20°C.

Gas Mixture

Ar : CO2 : CH4(89:10:1)

Table 3.3: K/r sepatation for muiour gas mixtane.

Xo

(4 124

Gas Mixture

AT : Ca : CE4(89:10:1)

These requinmentir ate w d satisfied by mixtures of helium and hydrocarbons.

Mixtures with 10-30% of d o u s hydrocatbons dord a smdl Lorentz angle (the

angle between dectron drift velocity and the dectnc field), good resolution and

Ions

(cm-1)

23.6

p for 347 (MeV/c)

665

# ofu at 2.6GeV/c

2-4

vd

( 1 r m l 4

49

OL

(deg)

52

Resol.

(%)

7.3

CHAPTER 3. BABAR EXPERllMENT

Electric field (kV/cm)

Figure 3.2: Calculated and measured drift velocities as a function of electnc field

for a zero magnetic field.

low multiple scattering. Tables 3.2 and 3.3 show the properties of gases which

have been considered for the B a h r drift chamber.

The dRtt velocities and Lorentz angles are d e t e d e d with the Boltmnann in-

tegration code [Bia89] and the dE /dz caldations were performed with a modified

version of a program by Va'vra [VRFC82]. Note that the helium mixtures have a

radiation length more than five times latger than that of AT : CO2 : CE4(89:10:1),

a commody used argon-based mixtare.

Fig. 3.2 shows the calculated drift vdocity vs. electric field for fou gases in the

table. The results an fkom [PBES92] (He : C4Hio), [BBB92] (He : C G : C4Hio

and AT : Ca : CH4), [C+91] (He : DME). The h&um based mixttuea lead to

bettu performance than typicd atgon d u c s since the smdler Lorents angle

r d t a in a more d o m distance-tirne relation.

The nmlt~ for the spatial tesolution w nunmarised in Fig. 3.3. Points rep-

3.3. GAS CHOICE AND PROPERTIES 35

resent the data from prototype chambu while a m e s are results of other stud-

ies. [PBES92, C+91, U+93] The He : C4Hio(80:20) mixture was chosen for the

B a h r drift chamber bssed on the measured spatial resolution and simulated

d E / d z resolution. The aghg studies were performed with a small proportional

counter and an Fes6 source, and the isobutane mixture showed negligible aging.

Long term aging studies are undet way.

2 4 6 8 10 Drut Distance ter^)

Figure 3.3: SpeW resolution for various gasses from the prototype drift chambu

(points) and from other atudies ( m e s ) .

Chapter 4

Srnall Scale Drifk Charnber

A e m d d e drift chamber prototype was buih by members of the B a h r group

at Laboratoire d'Annecy-le-Vieux de Physique des Partides (LAPP), Annecy-le-

Vieux, Frmce. This chamber waa used for snbseqnent test-beam experiments at

the Proton Synchrotron (PS), CERN (Augast 1997) and at PSI, Zurich (Octobes

1997). The goal was to diidy the spe&c ionization (dE/dx) of the Helium-

Isobntane gas mixture (80%Ee 20%G4Hio) which is to be used in the actual

B a k r drift chamber.

4.1 Prototype Drift Chamber Description

The prototype drift chamber is a cylinder of radius c5.5cm and of length a17.5cm.

It consists of 34 hexagonal cells (each c d b a right hexagonal prism of length

17.5 an). This geometry closely resembler the mid layezs of the BaBar drift

chsmba. Sense aires (gold pkted tmgsten, 20 &on diametet) are cmtered at

the middles of eaeh cell and are kept at a potential of positive 1650 Volts. Field

wires (berylium, 100 miaon diameter) positioned at the vertices of hatagons are

kept at a constant potential of O Volt8 thus creating sn electric field at tracting the

deposited electric charge toward the sense +es. Fig. 4.1 shows a two dimensional

(a-x plane, with +r behg along the incident beam direction, note that thii does

not correspond to the B d a r coordinate system) view of the s m d d e drift

chamba prototype.

Annecy BaBar Test Chamber

F i y n 4.1: 2D geometry of the s m d scaie drift chamber prototype.

For the events passing the common threshold, needed information was obtained

in the following way. The times at which the signal arrived at sense wires in ceb

1-10 weze recorded by TDCsl while the chaige collected on each sense wire wail

recorded by ADCs.' Signal duration was limited to a 2ps gate. In addition, cells

1-7 were also recorded by FADCsO3 Only 200 samples were made at the rate of

100lih. Other 24 cella were not read. An Fes6 radioactive source is mounted

on the inner w d of the chamber. Fess transforms via the capture of an electron

fiom one of its atomic orbitals: e- + p -, n + v. A hole in the atomic shell is

filled by another atomic electron giving rise to the emission of a characteristic

x-ray (231keV, with a half-Me of 2.73 years [WPF88]). Electrons fiom this decay

cause ionbation the same way the beam partides do. Every 5 minutes 500 of

these 'source' events axe recorded. These were used for calibration purposes. The

lifetime of this iron isotope is large enough eo that the probability of one beam

and one source events overlapping is negligible.

Four scintillators4 and two ATCe6 were mounted in fiont of the chamber and

used with beam events. The coincidence of fonr scintillators wsa used as a trigget.

ATC readouts were used to distinyish whethu the ionimng partide waa a proton

'TimFteDigitd Convuter: TDC giver a timc i n t d measurement in digital fom. Triggu

sf arts a d e r which coants pulses fiom a constant fit~uency oscillator. At the arrivai of the

aignai t h t d a is gated off to pield a namber proportional to the time between trigget and the

usl. [Le~e'r] aAnalog-to-~igîtal Converter: ADC is a device which converts an analog signal to an quiva-

lent digital fom. The signai charges a capacitor which is then àischarged st a constant cunent.

Digitireci signal amplitude ir propoitiond to discharge time. [Ledlfl ' ~ l u h Anaiog-teDigitd Converter: FADC is an AM: which sampla the signal at a tirai

mk thus digithg both the shape and the magnitude of the signal. [Le0871 4Scintilktor is a psrficle detector utüiiing a p~opat). of mme materi& which anit a flash

o f &ght when struck by a particie (chargai or neutd). ' A C T O ~ ~ ~ cetenkov Theshoid Counter: ATC ptoduces a signal whcn ita medium istraverscd

by a parti& rhich emits benkov taàiation. This happeni if the the puticle mores fiutes than

4.1. PROTOTYPE DRIFT CHAMBER DESCIUPTlON 39

or a pion. Minimum (threshold) momentum at which a given partide will emit

Çerenkov light ie:

whexe mo is the particle's rest mass and n is the index of refiaction of the ATC

medium. For out two ATCs (n=1.03 and n=1.05) threshold momenta for pions

and protons axe: pth,(potm, 1.03) = 3.8GeV/c, pthr(proton, 1.05) = 2.9GeV/c,

pthp(pia, 1.03) = 0.57GeV/c, pthp(lnm, 1.05) = 0.44GeV/c. Thuefore, a combi-

nation of these two ATCs d o w s us to diatinguish pions from protons up to the

1 momentum of 3.8GeV/c. Fig. 4.2 ahows the schematics of the experirnent d

Figare 4.2: Experimentd setup in

setup uaed for the beam teeting at CERN.

the Tl0 test area at CERN.

Recording of a beam event starts whui a triggu signal is sent to FADC, ADC

and TDC. This happens when scintillators SLS4 are hit, the beam is on and the

cornputer is ready to take new data. Trigger for the soarce events is provided

by the drift chamber s ipa l paasing a set threshold and a ready sipal from the

cornputer.

The output8 of the chamber (pulses fiom seme prkes) arc split, attenuated to

1.5V for the FADC and 400mV for the TDC/ADC and time delayed not to precede

the trigger. A Fan out6 unit is aeed to split the signais going to TDCs/ADCs.

"Fan out: PO in .a active device WU d o r s distribution of one signal to s e v d puta of

the syrtem by 'diirding' the input into severai identicul signais of the same h-t and shape.

It Ihouid be distin@hed fiom the passive splitta which divides sigd'i ampiitude

J( 4 Tirne Delay Time Delay

FADC FO A

L

Attenuator 1.5 V

1 Discriminator / Discriminator 1

1 -

I

l e

Attenuator I

Beam Cornputer Coincidence Scintillators

Splitter

F i p 4.3: Schematics of the Data Acquisition System.

L

Attenuator a 400 rnV

component

Magnet

Drift Chamber

Scintillators S4,S3,S2

Aerogel Threshold Counter ATC3

Auogel Threshold Counter ATC5

Scintillator S 1

Beam Pipe

Description

Bma=1.2T, gap = 22cm

radius = 5.55an, Iength = 17.5cm

cross section = 27mmx27mm

n=1.03, read by an ADC

n=1.05, read by an ADC

cross section = 100mm x 100mm,

read by an ADC

T* ,P* p=lGev/c -, 5Gev/c

Table 4.1: Expaimental setup at T10, summary of the component chaxacteristics.

ADC @al is then attenuated to 80mV, and the signal pcis&g the threshold

stops the TDC. Set Fig. 4.3.

4.2 The Truncated Mean Method

The dE/& resolution is caldated using a tnincation technique. Only a fraction

of the hits ( d E / d x measurements fiom each of the cells) are used in the energy

loiri calculation. The hits are ordered according to the pulire heights, fiom s m d

to large, and a certain percentage of hits are remooed fkom the high end. The

meanri of the remaining dE/dx meawementr are histogramed. This technique

shodd convert a Landau spectnun of dE Jdz into a Gaussian-like spectmm of the

trancated meanr [GDKKgG]. The resolution is then d&ed sil the ratio of the

width of the Gausman to the pedeatd subtraeted peak [GDKK96]. k c a t i o n

method yielde symmetriea enon on dE/& (this wodd not be true for enors

derived from the original, asymmetric, Landau distribution) which CM then be

CEAPTER 4. SMALL SCALE DMFT CHAMBER

easily propagated.

It WU be shown that this method works w d for low statistics, but fails for a

large number of events, as the truncated distribution systematicdy m e r s from a

Gaussian. This is e d y undustood knowing that the relative uncertainty of the

counta in each bin equak: = &. Therefore, a histogram with lower statistics

will give a bettu fit, even if the fit function does not M y correspond to the fitted

distribution.

Two sets of randorn numbers (N=42,000 and N=420,000, which are statistics

conesponding to 1000 and 10,000 events with 42 hits p a event) were generated

according to the Landau distribution pealting at 100 with the width of 10 (arbi-

trsry anits). 42 consecutive numbers were linked into an 'event' and truncation

mean method was applied. A number of highest hits were cut fiom each 'event'

and the tmcated distributions are plotted in Figs. 4.4 (1000 'events') and 4.5

(10,000 'events').

Each of the tmcated distributions was fitted to a Gausaian and a confidence

level WU caldated for the obtained x2 and a given number of degrees of freedom.

When the number of degees of &dom (n) is large the confidence level is ap-

proximated by [BC84]:

The confidence levels of the Gaussian fits to the s m d Landau 'data' set are

dependent on the number of truncated hits ( s a Table 4.2). The best fit is obtained

?c.L. in the ptobsbility that a rrndom mput of a given expuiment wodd lead to a greater

Xa, d g the mode1 L comrt. It L used as a memut of the fit quality.

4.2. TEIE TRUNCATED M W M E T H O

O 200 400 600 arbitrary units

L u d u Distribution

80 1 O0 120 140 arbitmry units

Tmncuted ntean, 50%

arbitrary units

T'ncuted mm, 70%

80 1 O0 120 140 arbitrary unics

Tmncared mean, 40%

orûitrary units

80 1 O0 1 20 140 orbitrary unib

Tmncated mean. &O%

Figure 4.4: Landau Distibution and the corresponding truncated means for LOO0

simulated 'eventr '. The pucentage of hit s tued in cddation is indicated.

arbitrary units

80 1 O0 1 20 140 orbitrary units

- 80 100 120 f 40

arbihry units

Tmncated mean, 70%

arbitrary unib

Tmcuted man, 40%

80 1 O0 120 140 arbitrary units

Truncated mean, 60%

80 100 1 20 140 orbittory unit9

Tmcuted nuon, 80%

Fi- 4.5: Landau Distribution and the correspondhg tnuicated mema for

10,000 sixnulated 'events'. The percentage of hits oeed in caldation is indiuted.

4.3. GEANT DETECTOR DESCRTPTlON AND Sl'MULATION TOOL 45

Table 4.2: Confidence level of the Gsuesian fit as a hct ion of the percentage of

hits used.

Fiaction of the hitr used

Confidence level J

when only 40% of the sampled hits are avuaged. There is a tradeoff of the quality

of the Gsussian fit and the tesolution obtained, dependent on the truncation

fraction, that wi l l have to be exsmiaed when the data is analyzed. It should

be noted that the mean of the Gaussian corresponds to the peak position of the

underlying Landau distribution. A a m d shift in the peak is obaerved and wil l be

corrected for.

When the rame truncation method is applied to the big 'data7 set (10,000

'events7) distribution that is obtained is no longer a Gaussian. Regardless of the

truncation fraction confidence levels of the Gaussian fits are identicdy O. Trun-

cated distributions systematicdy diffa froom a Gauiisian. A s m d asymmetry in

the p e a h (elongated high end is the consequence of the original Landau diiltri-

bution) can be neglected and, thereiixe, we are able to define the resolution of

the ionbation enugy 108s aa the ratio of the width ta the mean of the Gaussian

(tnincated) distribution.

40%

31.6%

4.3 GEANT Detector Description and Simula-

tion Tool

GEANT [Sof94] is a i y d m i of deteetot description and simulation tools which help

in deGg, optimioation, derelopment and testing of reconstruction program, and

50%

5.45%

60%

0.35%

70%

0.29%

80%

0.03% [ -

46 CEAPTER 4. SMALL SCALE DRIFT CHAMBER

interpretation of expeximental data from High Energy Physics uperiments.

4.3.1 GEANT Simulation of the Prototype Drift Chamber

GEANT was used to simulate the M t chamber response and see what d E / d x

resolution is to be expected. Both the geometry of the chamber and the proper-

ties of the HJiam-Isobutane gas were taken into acconnt. GEANT uses Monte

CarIo techniques to simulate passage of partides through different detector com-

ponents taking into consideration properties of the simulated psrtide (its type

and momentum), traveraed materials and any extaal factors (such aa electnc

and magnetic fields O). For each simulated event we know the exact length the

paxticle traveled in each c d of the drift chamber, as well ae the amount of ionisa-

tion energy depoaited in esch cd. GEANT assumes that the charge coileetion at

the sense wire is 100% efficient. In simulating ionbation energy lois GEANT uses

two corrections to Landau model. Vavilov (Vav571 theory removes the restriction

that the typical energy los8 is s m d compared to the maximum energy Loss in a

single collision. If typical energy losses are comparable to the binding energies, as

is true for gaseous detectors, more sophisticated approach ia necessary [Ta1791 to

simulate data distributions.

Therefore, dE/& resolution obtained from GEANT does not indude any ex-

perimentd uncertainties and it is a messure of the intrinsic width of the ionization

distribution,

10,000 pions (r-) and 10,000 protons, at momentum of 3.0GeV, were aeated

and th& behavior in the prototype drift chamber was obsetved. To avoid

'For the dPtt eb.mbu gua mixture (80%He, 20%C4Hio) A=5.222g/mol, ik2.626, p = 8.4 x

10-~g/-a. %orne ri~nr with an extemil mgnetic field picsent rue taken at CERN. A dudy dteored

in thir th&, however, ia bsrcd d iu ive ly on B = O m m .

4.3. G E U T DETECTOR DESCRIPTION AND SIMULATXON TOOL 47

" <mm, x - Zowrr cdlr

Figure 4.6: Lengths traversed in each ce11 (mm). Two possible paths are shown.

Flat distribution verifies that the c d illumination is aniform.

fluctuation8 in dEldx resulting fiom a short distance travezaed in a given c d

only the events for which thie distance lies in a 8mm-15.72- range 'O were

sdected. This cut removed apptoximately 40% of eventr, with roughly a hall of

the remaining evente passing through lowa 7 cella (marked 1,2,3,4,5,6,7 in Fig. 4.1)

and a half passing tkough ripper 7 celle (marked 1,8,3,9,5,10,7 in Fig. 4.1) See

Fig. 4.6. These are the only two possible paths because each test-beam partide will

be nquired to have at lemt 7 hits, and only celle 1-10 are read by the electronics.

Figs. 4.8 and 4.9 show simulated dE/dx (ionization enetgy deposited in each

c d , divided by the Iength traversed through that 4) for the drift chamber pro-

totype, dong with the comsponding tmcated distributions. Incident partides

are pions and protons at 3GeV/c momentum. Fits to the Landau distribution

(in tems of the universal Landau [KS84] fundion) are &O shown. The fit for

thra independent paxametus (Pl - integratçd ares of the distribution, P2 - the

loDeknnined by the cbambcz geometry, comrponding to psrticles which do not pur close

to field 8nd seme Wires.

peak of the distribution, and P3 - the width of the distribution) was done using

PAW [Sof95]. The fit function is:

with X being the measrved dE/dz . The peak of the distribution, corresponds

to the average ionization p a unit length of pions (protons) in the He-Isobutane

gaa (as given by Bethe-Bloch formula, Eq. 2.23), while the width of the dE/dx

distribution is given by: a = ( l x , with ( bang the width of the ionisation distri-

bution (dE, not d E / d x ) , as defined in Eq. 2.27. Using the fundamental constants,

properties of the incident partides (type aad momentum) and the puameters (A,

Z and p) of the drift diamber gaa we can calculate the theoretical prediction of

the width of the Landau distribution. Results are shown in Table 4.3. Note that

the theoretical positions of the peaks are too hi&. This is due to the 6 = O

approximation which ovetestirnates the speafic ionization. See Fig. 2.5.

4.3.2 Duncation of the GEANT d E / d x Distribution

Table 4.3: Fit puametus and theoretical valuer for dE/& distribations (Landau).

4.3. GEANT DETECTOR DESCRlPTION A N D SIMULATION TOOL 49

dE/dx distributions of both protons and pions were obtained fiom GEANT.

We ree geat agieement betweea theoretical d u e s and the fit parameters in case

of protons. Pion distributions, on the other hand, seem to be too wide, fit d u e s

are an overestimate of the expected ones. More importantly, it can be seen that

the pion diatribution is not Landau. This is because another regime defmed by the

contribution of the collisions with low energy tramfer nad8 to be considered when

(1 I < 50 (this is the iimit to Landau theory in GEANT). Below t his limit, as it is

Figure 4.7: Enagy 108s distribution for a 3 GeV electron in Argon as given by stan-

dard GEANT. The width of the layers is given in centimeters. Talcen fiom [Sof94].

tme in our case where = 70.73eV, &,, = 64.71eV and I = 38.51eV speaal

modeh talriag into acconnt the atomic structure of the material are used. The

U r b b Model [Sof94] compotes restricted energy losses with 6-ray production and

can be u~ed for thin layers and gmses. Approaching the limit of of the validity of

Landau theory, the energy loss pndickd by the Urbk Model spproaches smoothly

the Landau distribution, as seen in Fig. 4.7. It is assumed that the atoms have two

energy levels and that partichatom interaction nül be either excitation energy

loss or an ionbation energy losa. As the excitation cross sections depend on the

mass of the incoming partidee this correction is visible in the pion spectnun but

not in the proton spectnim,

protons

pions

Table 4.4: Fit parameters of the tnincated mean distributions for severd trunca-

tion fractions (percentages of hits ueed in the calculation of the means).

%cation method was applied to d E / d z distributions of both protons and

pions. Fitr are shown in Figs. 4.8 and 4.9 and the obtaIned parsmetus are s m -

merized in Table 4.4. It was shown before that the truncation method does not

yield a true Gaussian for hi& statistiu, 80 high X'S p u degree of ficedom of

the fits to the tmcated distributions were expected. The widths of these diatri-

butions are a measure of the intwic width of the original Landau distribution.

The actual dE/& resohition (defined as o/p of the tmcated means diatribution)

which will be meamred fiom the data hu two contributions: the intrinsic width

4.3. GEANT DETECTOR DESCRIPTION AND SIMULATION TOOL 51

II) Y

C

3 3000

2000

d E I h (proton) - al1 ceUs dE/dx (ke~/rnm)

Truncated mean, 40%

Figure 4.8: dE/& distribution for 3GeV/c incident protons. k c a t e d means

for various tmncation fractions an also cihom.

O. 1 0.2 0.3 dE/dx (keV/mm)

dEIdn (pion) - aU c e h

t

0.08 0.09 0.1 0.1 1 O. 12 dE/dx (ke~/mm)

Tmncated mean. &O%

Figure 4.9: dE/& didnbution for tGeV/c incident pions. h c a t e d means for

various traneation fiaetions are also rhoan.

4.4 THE TRACK FIT

of the dE/dx distribution and the width due to experimental uncertaintiea.

4.4 The Track Fit

To measure specific ionization ( d E / d z ) in the drift chamber prototype one needs to

know the amount of ionbation energy deposited in each c d , as well as the length

the partide traveled in a given c d . To obtain the later, the exact trajectory of the

partide (the track) needs to be reconstructed. The only information available is

the TDC readouts (or the timing as deduced fiom the FADCs) which correspond

to the transport time of the ionization electrons from the trads to the sense wire.

To convert t his time information int O distance the time-to-distance relationship

(TD is genvally a £unetion of the distance to the sense wke) needs to be known.

Even the knowledge of the right TD does not uniqudy determine the track, as

the direction fiom which the charge hm driftcd to the sense wire is unknown.

This leaves us with a set of &des centaed at aense wires with radii representing

Figure 4.10: A single track pusing through cells t7. Ckdes are distances the

ionkation electrons traveled to the sense wire.

the drift distance in each d. S a Fig. 4.10. The track is findy determined by

minimising the following 2 fit:

54 CHAPTER 4. SMALA SCALE DRIFT CHAMBER

where XTD - XFIT aze the space residuals (difference in the distance from the

sense wire obtained from the TD and the didance of the track). Due to the

qu imen ta l error in the drüt-the measurement and the uncertainty in the TD

function these residuats WU be nomero. The track, which is our best estimate

of the actual particle trajectory, is a curve (a helix which in the absence of the

magnetic field flattens into a line) passing through points XFIT which minimise

the normabed sum of the squated residuals.

4.4.1 GARFIELD Simulation of the Drift Chamber

GARFIELD [Vee96] is a cornputer program origindy written for the detailed

simulation of two-dimensional drift chambers. The input parsmeters indude the

chamber geometry, voltages on the field wires and the properties of the drift

chamber gas. The two-dimensionality is, in oar case, not a serious constraint as the

beam partides traverse the drift chamber perpendiculm to the wires which dowa

us to treat the chamber as a 2D object. The ptogram can, for instance, calculate

the following: field mrps and contour plots, plots of electron and ion drift lines,

x(t ) (tirne-to-distance) relations, drift t h e tables and a m d time distributions.

Our main goals were to check the u d o d t y of the cells by looking at equipotential

contours and the drift lines, and to obtain a firat ordes TD fonction. In Fig. 4.11 we

see the layout of the c d with the field wires represented by crosses and sense *es

by &des. Note the 90' rotation with respect to Figs. 4.1 and 4.10 which makes the

besm direction vertical. Drift line plot (describing the trajectories of the ionhation

deettons M i n g toward the sense wires) is ehown for the incident partide passing

throngh celle 1-7. The asymmetry in the drift lines is caused by slightly diBesent

electne potentids in different cells. This is underatandable bearing in mind that

the potentid at each point in the drift chamber is a superposition of potentisls

due to each of the 8 e ~ e &es (each sense wke h kept at the constant 1650 Volts).

LAYOUT OF THE CELL

1

- E I . . - sk S . . U1

O

i 1 . - m . rn

W . 4' a . a . . . . . i

L. 4 I m . . . . 1

I 0 . 0 . . . . . . S .

t 1 ;

a . . . . * ' . . . 4 . . .

a b a * . * 0 * O S . * . . .

- 1 ; . . . s

* . Q . .

I . . . - 2 .

a

-3C . . . . . . . .

O .

-4 i . . . -3 ;

4 . . I .

-6f

TRACK-ORIFT LINE PLOT

Figure 4.11: Chamber layout (left ) and electron drift-hes for particle travershg

CA 1-7 (right).

The configuration of surroundhg wiies changes as we move towud the edges of

the chamber, and so does the electric potential, thus changing the drift pattern.

This does not pose a serious concern to us, as the timing information ie obtained

by the &st ionization electrons reaching the sense wire. These dzB dong the line

of dosest approach of the tradc to the sense aire and are, therefore, not affected

by the asymmetties which are limited to the edges of the cells.

Equipotentid contours for the whole chamber, and for ce11 4 only, are ais0

shown. We can se that the c d has a nice Stculat symmet~y dose to the sense

wire. This symmetry ie broken as ne move toward the edgea of the hexagonal c d .

It will be shown that the potential configuration close to the edges of the cells

prevents the ionisation elaetrons ueated in that region fiom reaching the sense

wire in a teasonable tirne,

The mort important information obtained h m the Garfield ptogram is the

fkst otder approximation of the time-to-distance funetion. TD fandion can, in

principle, be different for diEttent drift ehamba cella (ody the cells nit h readout s,

CONTOURS OF V L . . . + !

Figure 4.12: Equipotential contours for the whole chamber (left) and c d 4 only

(right ).

numbered 1-10 in Fig. 4.1 are relevant). Due to the symmetry of the chamber,

only TD functions for cells 1-4 were examined. Partides moving along the beam

direction (along the positive z ais) were created and the axrival times of the

ionkation electrons to the sense wires in dl of the hit cells were calculated by

GARFIELD. By ParJring the distance of closest approach of the track to the senae

wires " and cdcdating the srrival time for eaeh distance a TD tanction is ob-

tained. Plots of the TD functions for c& 1-4 sre shonn in Fig. 4.13. Dashed

lines teptesent the estimated uncertaintie in the drift times. For the distances

larger than EJ 7.6mm (depending on the c d ) GARFIELD calculation of the TD

function did not converge properly. In theee regions TD ftinction was not plotted,

but the values wcre s t ü l calcdated asd will be ased later,

"Nok t b t due to the s p d c beam direction the distances of cl& a p p x d of the track

to renie wixer 1, 3, 6 and 7 rhould be about the rame. The rame ia tme for the distances to

wkes 2,4 and 6.

4.4. THE TRACK FIT

-3 x(t)-Carrelation plot -J x(t)-Correlation olot 00- 30- * I O ~ m + ~ ~ u l ~ ~ ~ m & S % ' v ~ ~ (m4 . + 8 1 0 ~ : M 1 ~ ~ Z U 1 0 S T ~ & ~ y ~ 1 ! ~ . ( q t l ) , t l

I . . . . ' . ' . l

42@ 1 , , W C 't

uoi l, /

foo b i t

t

34 \, , . J20 t \

1

.8

I I O b c o m * - 0 1 . J

x-Distance from the Wire km1 x-Distance f rom the Wire [cm]

Figure 4.13: Time-to-Distance (TD) bction for c d 1 (top left), d 2 (top iight ),

c d 3 (bottom l a ) and c d 4 (bottom tight).

58 CaAPTER 4. SMALL SCALE DRXFT CEAMBER

4.4.2 Time-to-Distance hnction and Track Fitting

The time-tedistance function was extracted from the data l2 in the following way:

a An analytical function giving a good approximation to the expected TD

funetion, as calcdated by GARFIELD, was found.

r For each event in a given data set drift distances in every c d were calculated

from drift times using a carrent estimate of the drift function.

a A linear fit to the points of dosest approach to sense wires (assirming that

the fiist chsrge arriving to the wise was propagating perpendicular to the

track) waa made.

a Space residuals, the difference between the distance to the wire calcdated

fiom the drift function and the distance of the track to the wire: RES =

XTD - XFIT, were calculated for each c d that was hit.

r A new estimate of the drift funetion was obtained by minimising the sum l3

of the squw of the tesidusle. This minimization was done using MI-

NUIT [Jam94] fanetion minimisation and error analysis tool.

a A proper convergence of this procedure gave us the best approximation of

the drift function for our drift chamber.

The &ce of the most suitable analytical function to parunetEae the tirne-

tedistance function was not simple. The BaBar reconatroction sofiware team

"Pot each event we tecordecl the timing imfommtion for each c d (the time the signai ptop

agated to the wnse w k ) and the charge depositd in each c d (whieh is not relevant for track

fitting).

"The mm waa perhmed ovet d ceiia and d events in the data set,

4.4. THE TRACK FIT 59

snggested the me of a piecewise linw function 14. This did not work too weii

due to a fairly large number of parametas (one parameter is needed for each

time bin because, if continuity of the TD function is imposed, the ofiets are not

independent of the slopes). This made MINUIT minimization long and somewhat

umeliable because foc a large number of parameters (between 7 and 15 time bins

were used) and a very big number of points that were fitted (7 c d s in z 10,000

events per data set) the minimiration cm converge at a local, as opposed to the

global, minimum. Also, a big dependence of the calcdated minimum on the input

parameters was observed.

The nurt logical choice for the parametrization of the drift function was a

polynomial. To satisfy the basic property of the drift function that zero drift

time conesponds to zero distance, the h a parameter of this polynomial must

equal zero. Another issue was the optimum degsee of the polpomial. Clearly,

the degm rhould be aa s m d as possible, resdting in the smdest number of

patametets needed to describe the drift function, which is crucial for a good

MINUIT m;nimi.xation. AIso, as discnssed before, the drift fanetions are not

exactly the same in aU of the cells but, as the differences are rather smd, one

wodd stilI like to use a unique dRft function. Finally, the choice was the smdest

degm for which the parameters of the drift funetions for cells 1-4 agreed to within

1 standard deviation. This, in a way, justifies the use of a single drift function for

all the cells. The degm chosen was 3, and the parametrhation of the the-to-

distance function is:

Fig. 4.14 shows fitir to the GARFIELD predictions of TD fanctions for ceils 1-4.

"The thne iuir is dinded hto a nomba of Km. TD nuiction in ucb bi i E hm, but the dopes and o h t s me difftrtllt in dXéxent bina. The conrtraint is the continuity on bin

borindlui~~.

T (micro sec) TD - Cell 1

T (micro sec) TD - Ceii 3

- - - - -

O O.? 0.2 0.3 0.4 T (micro sec)

TD - Celi 2

T (micro sec) TD - Cell 4

Figaie 4.14: Polynomial fits to time-to-distance functions for cells 1-4.

4.4. THE TRACK FIT 61

Points (*) axe the drift times cdculated for the diatances of dosest approach of the

track to the sense aire ransyig from Ocm to .92cm, 6 t h a step of 0.02cm. Lines

an fits to the polynomial function of Eq. 4.6. Fit puameters (Pl, P2 and P3), as

well as the correspondhg x2 are ahown. They are ale0 summhed in Table 4.5.

The mean d u e s of the parsmeters and their uncutainties were calculated as the

weighted axerage over the cells (due to the symmetry, TD function is the same in

ceb 1 & 7, 2 & 6, 3 & 5, with ce11 4 being unique):

It is clear that the proposed parametrization of the drift function satisfies ail

Table 4.5: Summary of the parsmeters for polynomid fits to TD functions in cells

1-4. Confidence levels are also shom.

the requirements mentioned before. The number of fiee parameters is small, fits

to the expected time-to-distance fanetions are good (dl the confidence levels axe

above 9996, and the paxameters for TD fonctions in different c& are within one

standard deviation of each other which allows us to treat the TD fanction as

independent of the c d n d e r .

The focusing magnets in the Tl0 test m a dowed as to set the dped momen-

tum (the product of the magnitude of the momentam and the electric charge of

62 CHAPTER 4. SMALL S C U E DRIFT CRAMBER

a given particle) of the incoming paxticles. The test beam nins that will be stud-

ied are divided into two classes: runs with the particle momentum of +3GeV/c

(240,000 events More cuti, incoming partides are positively chatged) and nuis

with the particle momentum of -3GeV/c (204,880 events before cuts, incoming

partides are negatively charged). The main diffeience is that for the nuis with

a positive aigned momentum the beam contains mostly pions, protons and some

kaons, whereaii the negative signed momentum beam does not contain antipro-

tons. This Merence can be seen by looking at the ATC response '' for the two

sets of mil. ATC responees are shown in Fig. 4.15. Two different types of

particles triggering '' the ATC CM, statisticdy, be distinguished by the number

of Cerenkov photons produced. The number of photons produced by a partide

with charge ze per unit path length and per unit energy i n t e r d of the emitted

photons is [WN96]:

whae 6, = arccoi( i /n~) a Jm is the half angle of the Cexenkov cone

for a partide with velocity v = Be. For practicd use, Eq. 4.8 must be integrated

over the region for which pn(E) > 1. From the information in Table 4.6 we see

that both protons and pions at 3GeV/c will produce Cerenkov light in the ATC3,

but only pions will trigger the ATC5. Electrons and hone trigger both ATCe.

h o , we sa that pions travezsing the ATC counters will produce more photons

as they yield laqer Cerenkov ande. This is tnie undu the sasuxnption that the

energy ranges over which Eq. 4.8 has to be integrated are similar for both types

of partides (or if the integration range for pions is larger). Given the actoal ps, the iategration range for pions is: n(E) > 1.002, and the integration range for

" ~ e m t m b a t w opr e t ~ p ATC c ~ p n t a (~=I.os and n=1.03) ~ O W S ei ta dttiiiwh

protons fiom pions at 3GeV/c momentum. " P d g t h g h the dctcctor with IL momentum k g e r than the t h h o i d momcnttun, u

d&ed by Eq. 4.1.

4.4. THE TRACK FIT 63

arbitrory units arbitrary units

ATC3 ATCJ

" O 500 1000 1500 2000 arbitrary units

ATC3

O 500 1000 1500 2000 arôitrary units

ATCS

Figure 4.15: ATC readouts for the two sets of m. The -3GeV/c m r (top) show

a 'deana' beam particle content than the +3GeV/c runs (bottom). bponses

h m both ATCs are shonni: n=1.03 (Mt) and n=1.05 (right).

Figure 4.16: Two dimensional projection of the Cerenkov cone (left). For P < l /n

thue is no constructive interference and Cerenkov light is not emmited (right ).

protons ici: n(E) > 1.048, which v d e s the conclusion that pions wili produce

more ~erenkov light . Looking at Fig. 4.15(bottom), we set a single peak produced

by piona (as only pions an over the threshold momentum) in ATC3 and two peaks

(lower-piotons, highu-piona) in ATCS. The positions of peaks dong the x axis

are a relative measan of the number of Ce~enkov photons produced (asauxhg

that the detection probability is the same for the light produced by either type

of incoming pattides). The relative positions of pion and proton peaks in ATCS

show that pions producc approximately 3 timea more light than protons. This is

in agreement with Eq. 4.8 with a factor of two comming fiom the ratio of sin2 0,s

and the refit being due to the Latger integration range for pions. The top two

graphs have only a single, pion peak. This is the verification of the fact that the

beam with the negative aped momentam does not contain antiprotons.

4.4. THE TMCK FIT 65

Table 4.6: Threshold momenta and the Cerenkov angles for protons and pions in

both ATCs.

b'

Time Zero (TO)

The raw times measund are not equal to the ionbation electron propagation times

(drift time) needed for the traek reconstmction. TDC readout conesponds to

the tirne between the arriva1 of the tri- lgnd which starts the TDC recording

(common s t s t t ) and the signal pulse £rom a givui wire which s top a apecific

TDC ch~~lllel. This is different from the drift time due to the time delay of the

signal pulses (see Fig. 4 4 , the propagation times of the signal pulsa from the

chamber preampli6ez to the disaiminator and the vanous time delays due to the

electronics. For the track fitting purposes it is necessary to determine the time

zero (TO) which is a Merence between raw times and drift times. T h e zeros

can be different for different channcls (correspondhg to different sense wires) and

wiU be deterxnined for each drift chambu c d sepuately. Figure 4.17 shows the

reeorded time spectra for the sense wires in cells 1-4. The highly popdated bin at

= 1200ns is the TDC ovedow, which is reeotded when the stop signal does not

Mive within a t h e gate set for one event. T h i ~ meam that the cd wu not hit in

a given event. The shape of the spectrum depends on the c d illumination and on

the drift function. As the drift velouty is not constant over the d, unifom c d

illumination does not r d t in a flat drift-time distribution. Since the ionbation

Partide

pion

proton

kaon

dectron

P 0.9978

0.9544

0.9736

0.9999

pth+03(GeV/c)

0.57

3.8

2.00

0.0021

sin2@c,1.03

O .O53

- 0.006

0.057

~th+,L06(GeV/c)

0.44

2.9

1.54

0.0016

8in2@c,1.06

0.088

0.042

0.043

0.092

Figure 4.17: Raw t h e spectra (TDC readouts) for cells 1-4. Both sets of nins

(-3GeV/c and +3GeV/c) w a e used.

C - 1 O 7 O0 8 4000 - En trias 1 00000 -

3500 - - 3000 - - 2500 - - 2000 - - 1500 - t O 0 0

Figure 4.18: The expected time spectruxn, d o r m d illumination asmmed.

4.4. TEE TRACK FIT 67

electrons drift fastes if the ionbation occurred dose to the sense wire, the drift-

time spectrum will be syatematicdy shifted towatd short drift-times, as seen in

the Fig. 4.18. This plot was made by h s t numericdy inverting the tirne-to-

distance function into the appropriate distance-to-the funetion. 100,000 random

nambets, with a flat distribution, th& values lying between O and 0.935, were

created thus simulating d o r m illumination of a hslf of a single drift c d . These

Ldistances' were then converted into the corresponding 'drifi times' which, when

plotted, represent the expected drift-the distribution. Note that the maximum

drift time is a 475ns.

In principle, no signal should arrive before the time TO has psssed. This is

not true in a real experiment M a signal larger than the threshold, which will stop

the TDC, cm be caused by electronic noise. Note that TDCl ovedows Iess than

TDC3 (due to the chamber design and the alignent with respect to the beam, the

number of hits shodd be about the same in c& 1 and 3) which is a consequace of

a highu noise level on TDC3, most likely cauaed by the preamplifias. Electronic

noise is boat exduively respon~ible for the drift time mismeaau~ement which,

dong with the nonuniformities in the ionization charge collection efiiaency as

a function of drift dietance, convertil the theoretical time spectnim of Fig. 4.18

in to the measured TDC response of Fig. 4.17. The sharp leadhg edge of the

distribution becomes a amooth, exponential-lüre increase. It is dear that the TO

for a given c d must lie between the lowest measured time and the first peak (at

about 2501~). The time zero is estimated as the point where the distribution

croclaes the half m&um mark (in the midde of the peak and baseline values).

Individual TOs are found by fittiiy the leading edge to the following q o n e n t i d

fanction:

with P2 b&g the tirne auo. When t = P2 the above function reaches a height

68 CHAPTER 4. SMALI; SCALE DRIFT CHAMBER

exact17 between the bsaeline (P4) and the maximum (Pl), P3 is the width over

which the function rises.. The fidl data set (both sets of nuis) was used

n r. q 2500 5 3500 8 3

3000 2000

2500 1500

2000

1500 1000

1000 500

500

O O 5 0 100 150 200 50 100 150 ZOO

T (4 r (nsl

m - C d l îü - Ceil 2

Figure 4.19: Exponential fits to ' t h e zeros' for cells 1 and 2. Both sets of runs

with were used.

Table 4.7: T î e zeroe f o ~ d 10 c&, sil obtsined fiom the exponentid fit (both

sets of runs w u e used). The correction centering the spatial tesiduals was also

applied.

in the TO determination. This malres sense considering that tirne eeros depend

only on the eiectronics and transmission delays and they aie desrly a property

of the -&enta setup, independent of the type or the chatge of the partide

travershg the chamber. The only comction to the fitted values was done in order

to center the spatial rtsidurk in every cell amund sero, aa niU be rhown later.

When dete- the correction only the negative signed momenttim niarr were

wed M it ia impractical to try fitting the whole data mt (becauae of a kger

4.4. THE TRACK FIT 69

nnmber of events the minimisation is not as successfUl) to adjust ail the tesiduab.

The results are presented in Table 4.7

4.4.3 Cuts and Event Selection

Before attempting any event reconlrtraction (track fitting) and further analpis

of the speeüic ionization, events satisfying certain criteria need to be selected.

This is donc in order to reduce the experimental background and thus obtain a

measurement with the lowest possible uncert ainty.

The first requirement imposed on <good9 evente is that the appropnate 7 ce&

(remember that thete an two poesible paths a partide can traverse, each passing

through 7 c&) m u t be hit. A signal must be recorded in each of the 7 TDGs

during a set interwl (mBJcimum drift time is a 476ns, as seen before) starting at

time zero. Additional requirement is that none of the nmaining 3 cells were hit.

These two cuts combined remove about 25% of the events.

Since the partide type determines the amount of deposited ionization at a fixed

partide momentum, it is erircial to utdude dl but one pattide type, in our case

pions. This is done by cutting on the ATC responses. A reasonable eut removes

protons fiom the data sample. The ATC nsponse of the p=-3GeV/c runs (sec

Fig. 4.15) was fitted to a Gaussian and the events within are accepted.

The cots, in t e m of arbitrary units of iight yield, are: 453 c ATC3 < 1488

and 579 < ATCS < 998. The lower limit is severe in order to eut protons fiom

the +3GeV/c rnnr as w d ar to ensure that the accepted mentir have the ATC

signal weil above the pedestal ducs . The analysis of the pedestal run is given in

AppendU A.

Another rtqnirement is that the ADC content of the 'hit' celb must be larga

70 CHAPTER 4. SMALL SCALE DRIFT CEAMBER

than a c d d a t e d thteshold value. This cut wi. discriminate against the events

h which one or more TDCs were triggered by noise. The mean ADC response

resdting fiom the electronic noise waa uctracted fiom the pedestd nui (Appendix

A). Gaussian fits provide both the mean and the width of the pedestal ADC

distributions. A 'good' event is required to have ail 7 ADC d u e s larger than

p + 5.00 of the pedestal due.

FinalIy, the cut which is essential to good trsdring involves times meaeured

in all hit cells. From the c d geometry and the known partide direction it is

dear that there should be a strong correlation between times measiued in c&

1, 3, 5 , 7 and in c d 2, 4, 6, or cells 8, 9, 10, as the tradt passing dong the

beam direction should be approximately equdy dietant fiom each c d in a given

goup. Sunilarly, there should be a etrong anticonelstion between the times in

different groups of ceils (remember that either cells 2, 4, 6 or c e b 8, 9, 10 axe

hit in a given event). F i y e 4.20 shows time correlations and anticondations

for a single 20,000 event run. Cutting on the time anticorrelation rather than the

t h e correlation between dXerent cells was psoven to be more efficient. Once a

scatter plot of anticorrelated times was made (as in Fig. 4.20) only events faJling

into a region of the plot bounded by two M e s (with centers at the 45' Une) were

accepted. This nit &O improves the correlation of the times measured in the cells

of the same group. The improvement of the tracking resolution achieved by this

cut is demonstrated in Appendix B.

Table 4.8 shows the &encies of the cnts used. In each of the foilowing table

rows (3 Ce& Not Hit, ATC Cut, ADC Cut and TDC Cut) only one eut was

applied but 7 good hits were alwsyr reqaired. The column muked %' gives the

efnaency cdculated ushg the number of events with 7 good hitr rather than all

of the eventa recorded. The final &ciency (4.5% fot ncgative liped momenttun

runs and 3.2% for positive signed momentum nus) is low. This t a consequace

4.4. TBE TRACK FIT

Figure 4.20: Anticorrelation of times in cells 1 and 2 (Mt) and correlations of

times in ceh 1 and 3 (right) before the time eut (top) and d e r the timc eut

(bottom).

CEAPTER 4. S M A U SCALE DRIFT CHAMBER

Event s

Total - - - - - - . -

7 C& Hit

3 Cells Not Hit

ATC Cut

ADC Cut

TDC Cut

All Cuts

Table 4.8: Cuts asd their efficiencies for both sets of m s .

of a rather high noise level in alI the readouts (TDC and ADC) but does not

senously limit o u study as the smount of data adable is very large.

4.4.4 Final Tracking Results

For a detailed discussion of individual track fits to both positive and negative

signed momentum trscks s a Appendix B.

It will be shown that the parametrizations of the TD funetion obtained by

minimising a X2 fit to uther sete of nuu, are consistent with each other and,

moreover, are in good agreement with the GARFIELD predictions. Fig. 4.21

(top) shows that the two fitted TD funetions (one obtahed fkom each of the run

aets) are vittnally indistinguishable which proves that the method of TD fanetion

estimation is d d and that the data is consistent. The difference between Gufield

estimate and the fitted TD, Fig. 4.21 (bottom), is neva larger than 30pm which

1 considerably amallu than the space reaidul and is, therefore, satisfactory.

4*4. THE TRACK FIT

--- . FIT(p=-3GeV/c)

.-.-.-- FIT (p= + 3 G e ~ / c )

- C

C

C - C

O 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 T (micro sec)

f (micro sec)

rn(GARFIEW) - TD(Fff)

Figure 4.21: Tkce cliffatnt time-to-distance fimctions: a GARFIELD ptediction

and 6ts to each of the nrn aetr (top). A Merence between GARFIELD and the

average of the fitted TD ftinctions (bottom).

74 CHAPTER 4. SMALL SCALE DRIFT CHAMBFR

A summsry of the TD function parameten, for three düterent cases is given in

Table 4.9. Aho quoted are the average values (a weighted average, taking into

Table 4.9: The-to-dist ance iunction parameters, and paramet ers of Gaussian fits

to residual distributions.

consideration that cella 1,3, 5, 7 are hit twice as much as the rest , was pedormed)

of the absolute values of the means of the residual distributions, and the widths

of the residual distributions. It cm be concluded that the space residuals are well

centered (as (pl < o) meaning that the fitted drift function is unbiased. Average

width of the sppace residual distributions b a measure of the tracking resolution

aehieved and, in out case, it equals a 350pm.

4.5 d E / d x Calculation and Results

Average

3.6854

-8.480

10.420

19

351

GARFIELD

3.840

-8.349

9.266

-

1

1

Once good tracking resolution is achieved uttracthg the d E / d x kiformation be-

cornes simple. The amount of energy deposited in each c d is proportional to

the chuge accumulated in the correspondhg ADC, after the pedestd was sub-

tracted. The length a particle travused in each c d is easily caldated for eaeh

tradr. Thaefote, dE/& is calcdated as the ratio of the pedestd subttacted ADC

d o u t to the WU-aossing length.

+

J

Pl

P2

P3

lr-sl (c") W s (P)

p = -3GeVc-'

3.6866

-8.4922

10.386

12

330

p = +3GeVc-'

3.6841

-8.4679

10.453

25

372

To make the truncation technique possible ail the peaks of the ADC distribn-

tionr must coincide. This adjnstment is made by fitting the pedestal subtracted

ACD spectra to Landau diatributions and correcting for different peak positions.

Since the unite of energy depositions messured are arbitrary (no calibration was

done to relate the ADC readout with the proper energy units) all the peaks will

be rescaled to 100.

II Date II Aiig 23 ( Aug 23 ( Aug 24 1 Au(: 24 1 24 11

' i

1) # of Events 11 44.88k 1 20k 1 6Ok 1 60k 1 60k 1)

D&

Time

# of Events

Time

Table 4.10: Different runs used in dE/& calculation.

Table 4.11 shows the calculated dE/dz resolution as a function of the per-

centage of hita used in the calculation. StaWical enors on the parametus of the

Gaussian fit8 (done by PAW) are propagated to give the utor in the meastind +axspidth resolution. The fitri w a e paformed in the mean-,,d region to minimi.e the

d e c t of the non4aussi.n tail at the high end, as suggested by [GDKK96].

Aug 22

16:lO

20k

19:OO

with w ~ ~ , and m w bting the width and the mean of the

(4.10)

Gaussian fit. The

20:33

-

Aug 22

16:SO

40k

- - - -

Aog 23

16:OO

20k

- - - - - -

Aug 23

16:30

60k

12:20

- p. - -.

Aug 23

17:48

60k

13:OO 14:35 I

76 CBAPTER 4. SMALL SCAJE D m T CHAMBER

n C

c u

0' 100 X 100 7.455

O O 20 40 60 80 arbitrory 100 units : 20 : 40 60 80 arûitrory 100 units 120

dedrl O dedrS0 ul Y

C 20; ;l i 100 7.107 $ 100 7.00s

O 40 60 80 100 120 40 60 80 100 120

orbitrory units orbitrory units

in u

t cl ol ü w n 101 $8 8 100 O

7.296 1 00 7.97

O 40 60 80 100 120 140 60 80 100 120 140

arbitrory units arbitrary units

dedxrO dedx60 cn Y

c 2 100 0 7.m "'ii :/ u a 8.746 1 17.11

O 60 80 100 120 140 160 80 100 120 140 160 180

orbitrary units orbitrorj units

dedr70 de&M cn C)

c Cl ; 5; ;1 z IO0 10.53 3 100 17.53

O 1 O0 150 200 100 150 200 250 300

arbitrary units orbitrary units

de &9û &hl00

Figure 4.22: dE/dz resolutions obtained fiom both negative and positive signed

mommtum rum. Diffaent fiactions (10% to 100%) of hits were ased in calcula-

4.5. DEI DX CALCULATION AND RESULTS

1 Hits used

10 %

20 96

30 %

40 %

50 %

60 %

70 %

80 %

90 %

100 %

widt ho,

Table 4.11: Gaussian fit parameters and the corresponding d E / d z resolutionci for

various fiactions of hits used. Statistical errors are &O shom.

resolution of dEldz meaeorement varies with the tmcation percentage and has

a broad minimum at = 7076, confinning a result stated by [GDKK96].

Theze ie a systematic error associated with the tmcation procedure, as the

resolution depends on the percentage of hits used to calculate the means. To esti-

mate this enor the standard deviation of the resolutions (for truncation fractions

of 30% to 90% 17) waa calculated yielding u,,t,,tic = 0.5 %. From Table 4.11 we

can condude that the optimum tmcation percentage (giving the smdest d E / d x

resolution while still having a symmetrical, Gaualan-Iike distribution) is 70%.

The measured resolution is then:

This rat& is in good agreement with u(dE/&) = (6.8 I 0.3 f 0.5)%, Bven - - --

L T ~ b t range ru ccnterd ~ u n d 60%, the tmcation pereentage most often 4.

78 C W T E R 4. SMALL SCALE DRIFT CHAMBER

by [Bli97]. Our mean value of the resolution is slightly higher, due to different

operating voltage; o u statisticd uncertainty is smder because of the larger num-

b u of events used; the systematic uncertainty estimates are the same. Another

measunment of the spedic ionization resolution in the helium-isobutane (a dif-

ferent chamber geometry was used) was presented by [GDKK96]. Their result,

o ( d E / d x ) ranging fiorn 6.25% to a 7.6%, dependhg on the operating voltage,

is, again, consistent with our measurement. The resolution cornes partly fiom the

intrinsic width of the Landau distribution. This contribution for the Truncated

Mean Method with 70% of hits used (incident partides axe pions), as estimated

by the GEANT simulation, ii 3.7%. The expexbnental uncertainty contribution

(resulting fiom both tracking and the ionization energy rneasuiement errors) to

the measured resolution is 3.6%.

The same tnuication procedure was applied to the data Lom the test beam

nui at PSI in Zurich (inadent partides are pions with momentum 0.405 GeV/c).

The chamber was rotated by 90' (about the y - azia) with respect to the CERN

setup. Agah, 10 innermost celle are read but only the readout fiom 4 central cells

was used in caldation (celb numbered 11, 9 ,4 and 12 in Fig. 4.1). The adwntage

of this chamber positionhg is simple. All of the pions paasing through the central

part of the cells (these an easily eelected by imposing a cut on the drift time)

traverse equd lengths in all four cells, thus completdy eliminating tracking fiom

the dE/dx cddation. The resolution expected should be bettes than previously

quoted (4.11). b o , we cm eatimate the 108s in the resolution caused by tracking

uncert ainties .

Gaussian fits to the tmncatcd mean distributions for these runs are shown in

Fig. 4.23 and the parameters, together with the cdculated dE/& nsolutions, u e

li~ted in Table 4.12. L a q t r statisticd errors are a consequence of a considerably

amaller data set u d . The optimum truncation percentage is again 70%, and

n ; 20 1 O 0 10

O 20 40 60 80 100 20 40 60 80 100 120

arbitrary units arûitmry units

dedx10 dedx20 m C

a C

S 20 5 20 O O

10 10

O O 40 60 80 100 120 40 60 80 100 120

arbitrary units orbitrary units

dedx30 d e M

40 60 80 100 120 140 arbitrary units

dedxSO

60 80 100 120 140 arbitrary units

d e M

80 100 120 140 160 180 arbitrary units

dedr80 m c,

UI 4

20 c 7 O

10 y 10

O O 100 150 200 100 150 200 250 300

arbitrary units arbitrary units

de- dedxlûû

Figure 4.23: dB/& resohtioncr obtained from the PSI runs. Different fiactions

(10% to 100%) of hits w a e uaed in calculations.

Table 4.12: Gauesian fit parameters and the conesponding dEldz resolutions for

1) Hita used

various fractions of hits used. Statistical errors are &O shown.

C

the syatematic error is estimated as u,,taatic = 0.5 %. The measured dE/&

resolution for the PSI nuis is then:

10 %

20 %

30 %

40 %

50 %

60 %

70 %

80 %

90 %

100 %

which is consistent with the result obtained from the CERN data. As traclting

was not used in this caldation we cm estimate the energy mismeastuexnent

contribution to the resoiution to be 3.2%. The contribution due to tracking is

1.6% (as the tao mors, added in quadratute, mut give 3.6%).

Both of the sbove reaults can be checked against the approxhate formula for

the dE/& rerolution [AC80]:

with n being the number of ionhation meainirements (in our case 40), C the same

as defincd in Eq. 2.27 and I the ionization potential. The factor of 112.35 cornes

4.5. DE/DX CALCULATION AND ReSULTS 81

£rom converthg FlVHM into a. This empirieal formula is well supported by

urperimentd data for argon, xenon and propane. It should be good to about

20% in the rmge 0.5 < ( II < 10. Ueing the relevant quantities calculated before

(1 = 38.51 eV and (+, = 64.71 eV) yields the resolution of: a (g) = (5.3f LI)%.

The error is eatimated bssed on 20% uncertainty of this empincal formula. This

tes& is consistent with o u measurements of the d E / d x resolution.

Chapter 5

Conclusion

Measurements of the dEldx resolution in the Helium-Isobutane gas (80%He,

20%C4Hio) which wil l be used in the BaBar drift chamber were made using a

s m d scale prototype drift chamber. Test-beam experiments were pedonned at

CERN (PS, proton and pion beam with a d a b l e momentum of 1 GeV/c to 5

GeV/c) and at Zurich (PSI, pion beam with a 0.405 GeV/c momentum).

Testing of the k c a t e d Mean Method verified that the Landau spectrum of

the spedc ionbation can be converted into a Gaussian-like. The qudity of the

Csussian fit, however, depends on the fraction of hits used in the caldation and

on the amount of statistics used.

A GEANT simulation was made in orda to study the chambu response in

absence of the utperimental uncertainties. The dE/& resolution caldated &er

applying the truncation method (70% of hits are used) to the pion specific ion-

hation spectnun is 3.7% and it is a measure of the inthsic width of the Landau

distribution.

A GARFIELD simulation of the drift &bu was done to obtain the ftst

order time- to-distance function and fmd it s suit able paramet hation for the sab-

sequent fitting to the data (a third order polynomial with a zero constant terxn

proved to be the best choice).

Ali of the selected events were required to have exactly 7 good hits with the

miva l t h e luges than time zero (tirne zeros were fitted to the t h e spectra in

each c d and adjusted to center the space residuals). Additional cuts were made on

ADC, TDC and ATC responses to eliminate events consistent with the pedestal.

After the track fit was performed by a x2 minimination the average spatial

resolation, as messured by the weighted averages of the space residuds in ail

cella, waa calcdated to be:

Obtained time-to-distance function is in good agreement with the GARFIELD

prediction.

The dEldz resolution, defined as the ratio of the width of the Gaussian dis-

tribution to the pedestal subtracted mean, was calcdated for both sets of runs.

Varions fractions of hits used were tested and the optimum was foand to be 70%.

Systematic uncertainty was estimated by varying the tnuieation fiaction. The

results are:

for the PS NIM, and:

for the PSI runs. The increase in the resolution with respect to the GEANT

ptediction eu i be explained in temu of the contribution due to the enors in

the ionbation energy messurement (3.2%) and the contribution due to impedkct

tracking (1.6%).

Appendix A

The Pedestal Run

A pedeetal nui with 4000 eventa was taken in ordu to study the system depen-

dent backgrounds. The tEgger signal was penodically created and the chambet

readouts were taken while the beam was tumed off.

- O 500 1000 1500 2000 - O 500 IO00 1500 2000 arbltroy unfts arbltmry unit8

ATC3 ATC'

Figare A.1: ATC teadouts fiom both counters. Gaussian fita to pedestal dirtri-

bution are &O shown.

The readouts from both threshold countear are shown in Fig. A.1. Gaussian

fita to the distributions yield the foUoning pedestai values (arbitrary units for the

ligh yield are uaed): ATC3 = 43 k 137 and ATC5 = 177 k 43.

By looking at the TDC readouts (Fig. A.2) it cm be reaiized that the noise

level is reasonably smd. The number of ovedows in each of the TDCs is dose to

4000 (which is the total number of events). Only c d 3 has a considerably highes

noise level. Table A.l lists the number of events in which a given TDC channel

did not overflow, which is a measure of the noise level.

Table A.l: Noise level in each of the TDC channels.

The pedestal d u e s of the ADC readouts were obtained by a Gaussian fit.

Even though the measand distributions an not Gaussian (ail can be seen in

Fig. A.3), these fits give us the information about the peak (conespondhg to the

mean of the fitted Gaussian) and the width of the pedestal ADC distributions.

This information is summbed in Table A.2.

Table A.2: Means and widths of Gaussian fits to pedestal ADC &stribations.

Arbitrary u n i t a are used.

APPENDIX A. THE PEDESTAL RUN

Figure A.2: TDC readouts for 9 10 ceils. The noise Ievel is amd as the TDCe

ovedow for alrnost all events,

< 1000

3 31 EntriCr ' "; ;! 8 500 200

O 50 75 100 125 150 50 75 100 125 150

arbitrory U ~ S arbitrary u d s

ADCI ADC2

u ; yjo ;;; O

250 O

25 50 75 IO0 125 150 175 200 225 250 arbitrory unils arbitrory units

ADC3 ADC4

f O 400 01 O y:: 200

O O 75 100 125 150 175 100 125 150 175 200

arbitmy units arbitrory units

ADCS ADC6 m d c Enairt Oh. ,' 500 0 500

O 25 50 75 100 125 75 100 125 150 175

arbitrory units arbitrory units

ADC7 ADC8

QI 4

L

5 400 b 200

O L"" 50 75 100 125 150 175 200 225 250 275

arbitrary units orûitrory U ~ S

ADC9 MC10

Figure A.3: ADC readouts for d 10 cells. Gaussian fits to pedestd distribution

are also shown.

Appendix B

Track Fits Using MINUIT

The track fits (with fit parameters being the coefficients of the paraznetrized time-

tedistance function) were done using MINUIT in data-driven mode [Jam94]. Ini-

tial d u e s of the parameters Pl, PZ and P3 are GARFIELD predictions.

B.l Negative Signed Momentum Runs

Once the trads fit converges (remember that a s u m ovet ail ce& hit in all eventa of

the squares of the spatial residuals is behg minimised) the optimum parameters

of the tirne-to-distance function are set. The quality of the fit can be veded

by plotting varioas quantities. Fig. B.1 shows distances to the wire in c d 1 as

calculated fiom the drift t h e (which is the TDC nadout afta TO subtraction)

using the time-to-distance function (top left, XI) and the distance of the track

(obtained £rom the fit) to the wite (top right, XFT1). If the knowledge of the

TD fanction and the time measiuements were pedect the two distances ahould

be the same. Due to arperimental mors there is a difference between the two

values, cded a space tesidiid: Rs = X - XFT. These will be dircturred in a

B . . NEGATIVE SIGNED MOMENTUM RUNS 89

moment. A scatter plot of the track distame vers- the calculated distance is

aho shown (bottom left). We can s a that there is a strong coaelation between

micro sec

XFTl VS TI

Figure B.1: Caldated and fitted distances to the wire in c d 1. Negative Gped

momentum runs were uscd.

the two for ail but v q small and very large distances. This is a com«1\1enec of

a i m d nomber of events talling in these regions, which compromises the qu&ty

of the fit t h a . The beet fit is obtained arotmd the middle of the ce8 where

the datirtics ia the highest. A plot of the tradr distance veraaci the drift-time

90 APPENDLX B. TRACK FITS USn\rG MINUIT

(bottom right) dosely resembles the TD funetion, as expected. Low statistic at

very short drift distances prevents us fiom verifjhg that fitted distances &O

approach zero for very short drift times. Spatial residuals measure the quality

of track reconstruction in a @ven chamber, as they correspond to the uncertainty

in the partide trajectory. Fig. B.2 shows spatial residuale in all 10 cells of our

prototype chamber and Table B.1 surnmsrizes the paxameters of the Gansaian

fit8 to residual distributions. All the residual distributions axe centered around

Table B.1: Means and widths of Gaussian fits to space residuals (pm), p =

+3GeVc-l.

aero (to within 30pm, which is luge compared to the widths) which means that

the track fit is not biaaed towatd distances either larger or smaller than those

calculated by the TD fanetion. The centering of the residual distributions was

done by adjusting the time-eexos, as mentioned before. Findy, the d u e s of the

fit parameters (P1=3.6866, P2=-8.4922, P3=10.386) do not M e r eignificantiy

fiom the GARFIELD predictions .

To show the efficiency of the drift time cut, as discussed in the Cuts and Event

Selection subsection, the track fitting will be attempted on the data set (negative

signed momentum) without the eut pdormed. To simulate the same smount of

statistics only 10,000 eventa entered the fit. As shown in Fig. B.3, space residuab

increase drasticdy ia the tirne cat ii not applied. In addition, they are neither

symmetzical nor cenkred at rao. The asymmetry of the residuals io a conseqtttnce

of the wrong TD fonetion (P1=6.2207, P2=-25.137, P3533.857) reaulting from

-0.1 O o. 1 cm

Residuals I

-0.1 O O. 1 cm

Residuals 7

Figwe B.2: Spatial residuab in all c&

Residuals 6

-0.1 O o. 1 cm

Residuals 8

with a drift-time cot applied. Negative

signed momentum runs wae nsed.

APPENDIX B. TRACK FITS USING MINUIT

-0.1 O o. 1 -O* 1 O O* 1 cm cm

Residuals I Residuals 2 m C

a CI

: 200 C

O O 2 U 100

O O -0.1 O O. 1 -0.1 O O* 1

cm cm

Residuals 3 Residuals 4 m C c 200 S 200 C

a 3

100 O 100

O O -0.1 O O* 1 -0.1 O 0.1

cm cm

Residuals 5 Residualr 6 a l r

8 200 U

O -0.1 O O. 1 -0.1 O O. 1

cm cm

Residwls 7 Residuals 6 0 O

-0.1 O o. 1 -0.1 O 0.1 cm cm

Residualr 9 Residualr 10

Fignre B.3: Spatial residuals in d cells without a drift-time cat applied. 10,000

events fiom negative signed momentum runs were used.

B.1. NEGATWE SIGNED MOMENTUM RUNS 93

t-g to fit uncut data. Dülerent TD functions axe shown in Fig. BA. The shifts

T (micro sec)

TD fincrions

Figure B.4: Time-to-distance functions obtained fiom fits to dat with and without

the drift tirne cut, and from GARFIELD prediction.

in the mean values of the residuals axe ptodaced by the ovuestimate of the TD

function for s m d times whenas the elongated tails at the opposite ends of the

distributions are caused by the undetestimate of the TD fanetion for large times.

Remember that all positions (X and XFT) are given with respect to the chamber

z axis (sa Fig. 4.1) and are, therefore, positive in cells 8, 9, 10 and negative in

celh 2, 4, 6. An overestimate of the TD fnnction makes (XFTI > 1x1 in all cells

resulting in negative mean space residuals in ceils 8, 9, 10 and in positive mean

spaee resîdul in cclls 2, 4, 6. Note that mean space residuals in ceb 1, 3, 5, 7

are either positive or negative, reaulting in a double p& seen in Fig. B.3.

94 APPENDLX B. TRACK FITS USlNG MINUIT

B.2 Positive Signed Momentum Runs

Fig. B.5 shows the space tesiduals after the fit to positive signed momenturn

nuis, with s drift time cut applied and Table B.2 summarizes the parameters of

the Gaussian fita to residual distributions. We can see that both the residual

distributions and the parameters of the TD hnction (P1=3.6841, P2=-8.4679,

P340.453) a g m with the values obtained fiom the h s t set of runs. The residuals

are not as well centered around zero because the correction to time zero8 was done

using ody the p = -3GeVcœ1 runs, as mentioned bdore.

Table B.2: Mesns and widths of Gaussian fits to space residuals (pm), p =

+3GeVc-'.

B.2. POSITM SIGNED MOMENTUM

-0.1 O O. 1 cm

Residuab 3

Residuals 5

Residuals 4

Residuals 6

cm

Residuals 8

Fi- B.5: Spatial residorlo in d c& with a drift-the cut applied. Positive

signed momentam mms wete wed.

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