What Does A Drift Chamber Do?

❂ Basic principle

� Charged particle in matter loses energy by ionization

� Matter in drift chamber is gas

� Ionization is our source of information

❂ Tracking

� Ionization along path : Timing➪ Reconstruct picture of track

� Track of charged particle bent in magnetic �eld

➪ Momentum

� Can also provide global timing information (t0)❂ Particle identi�cation (PID)

❂ Amount of ionization along path

➪ With momentum, gives PID

The BaBar Drift Chamber

IP1618

469236

324 681015 1749

551 973

17.1920235

❂ cylindrical, 40-layer design

� 7104 drift cells, hexagonal �eld wire pattern

� 80,120 �m Gold-plated Al �eld wires

� 20 �m gold-plated tungsten-rhenium sense wires

❂ Features dictated by multiple-scattering limit

� Low Z gas mixture (80:20 helium:isobutane)

� Al �eld wires, endplates

� Be inner core

❂ Features dictated by boost

� All electronics on rear endplate

� Forward endplate thinner in region of acceptance

Expected Performance

❂ Position Resolution

� 130 �m single-cell resolution

❂ Momentum Resolution

� Care about charged particles with pt between 100 MeV/C and 2.5 Gev/C

� Only just starting to get real idea of performance

❂ Particle ID

❂ dE/dX resolution of 7 percent

❂ `Good' �=K separation up to 700 MeV

✎ Electronics not to degrade intrinsic performance by more than 10 percent.

Tracking: Signal

❂ Creation of signal

❂ Charged particle collides with gas molecules

� Primary ionization: liberate electron

� Secondary ionization: electrons collide with gas molecules

❂ Drift, proportional ampli�cation

❂ Collection of signal

❂ electrons attracted to sense wires

❂ TDC readout

❂ Interpretation of signal : Tracks

Proportional Wire

❂ Basics of avalanche

� Electron drifts and collides with gas molecules

� Picks up energy from E �eld between collisions

� If enough, ionizes gas molecule, liberates electrons

➦ ...and photons

❂ Important quantities

� Mean free path between collisions

� Size of E �eld near wire

✎ thinner wire means larger �eld gradient

➪ want thinnest wire that won't snap

The Wire Continued

❂ Proportionality

� Signal proportional to number of primary electrons produced

� Condition: number of electrons in avalanche negligible w.r.t. linear charge

density of wire❂ Issues

❂ Space Charge

� Electrons collected, ions left behind

� Slowly move toward cathode (�eld wire)

� Meanwhile, reduces ampli�cation❂ Breakdown and Quenching

� ionization also produces photons

� photons can also spark new avalanches

� photons travelling on average further than avalanche length gives break-

down.

� quench gas absorbs photons, prevents breakdown.

The Cell

❂ Need position information from the signal

❂ Ideally, surround anode with cylindrical cathode

� circular cell

� circles of equal drift time

✎ too much material

� In practice, �eld wires approximate ideal cell shape

✎ surfaces of equal drift time called isochrones

The BaBar DCH Cell

❂ Typical cell size: 1.2 by 1.8 cm squared

❂ Typical shape:❂ Field wires in a hexagonal pattern

� Held at ground

� Sense wires at 1960V (1900V)

� 50n isochrones in 1.5 T magnetic �eld

HEX2 - Wire 168 Isocrones every 50 ns

BaBar DCH Cell Continued

❂ Position of hit within a cell

✎ Actually measure drift time, not distance

� conversion done by t-to-d calibration

� Iterative process

� right and left sides of cell �tted separately

-1

-0.5

0

0.5

1

0 100 200 300 400 500 600

Drift Time (ns)

Sig

ned

Dis

tanc

e to

wire

(cm

)

PEP-II / BaBar

d(t) layer 31

Resolution within the Cell

0

0.005

0.01

0.015

0.02

0.025

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Mean 125 µm

Signed distance from wire (cm)R

esol

utio

n (c

m)

❂ x-axis: signed radial position within cell

❂ y-axis : residual

� Di�erence between �tted track doca and drift time

❂ Leaves us with questions

➪ What do we mean by a track?

➪ What are track parameters? (like doca)

➪ How is tracking done?

What is a Track?

❂ For us, a reconstructed quantity

✎ Made of hits (cell signals)

➦ We'll leave the how for later

❂ A helix (�t assuming uniform B)

❂ Relevant parameters

❂ Space Point: d0, �, z

❂ Shape: curvature (!), dip angle (�)

� Relation to cell: doca, entrance angle, ambiguity

� Quality of reconstruction

� Global timing information (T0)

✎ Parameter of track �t

✎ Source of event time

➪ Leave last two for other talks

Track Parameters� Doca (distance of closest approach)

� Entrance Angle: �track � �hit

� Wire Ambiguity

� Relating drift time to position not always unique

� Resolve ambiguity with pattern-recognition methods

� Becomes a signed label

❂ This picture is 2d, but we have 3d information

✎ Our picture is incomplete

➪ It is time to complete it

The Larger Picture

❂ Stringing pattern of chamber

❂ layers organized into superlayers

� 40 layers, 10 superlayers

� Guard wires (340V)

� Axial superlayers|wires strung along axis

✎ 4 axial superlayers

� U and V stereo layers|wires are tilted✎ 6 stereo superlayers (3 of each)

✎ 40 mrad to 70 mrad (need larger radius for larger angle)

✎ U and V wires tilt in opposite directions

✎ Superlayers correspond to track segments

✎ Axial segments used in L1 trigger

The Larger Picture Continued

Using Stereo Information

❂ Axial layers do not provide z information

� Corresponds to projection of track onto rear endplate

➦ Technically can extract z information from charged separation

� Poor in practice

� Need electronics at both ends of chamber

� Axial track info forms a circle (!, �, d0)

➪ Stretch in Z, forms a cylinder

❂ Take stereo segment (i.e. U superlayer segment)

� Projection on endplate displaced

� Move in z until aligns with track

� \slice" cylinder

❂ One stereo segment isn't enough

� Need two z-related parameters (z, dip angle)➪ Need two independent lines

� Could use adjacent wires in superlayer

✎ Doesn't work well

� Use wire from other stereo avor (i.e. V for U)

A SampleEvent

From the Large to the Small

❂ Cell shape variations

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161162� Guard wires

� Field distortion across superlayer boundaries distort cell shape in outer layers

❂ Lorentz Angle

� Tracking accuracy best when electron drift at right angles to track

� B �eld a�ects drift: E�B

� Lorentz angle : angle between drift direction and E❂ Crosstalk

� Ions attracted to �eld wires

➪ Induce pulse on neighboring sense wire

Gas Choice

❂ 20 percent Isobutane, 80 percent Helium

❂ Why Helium?

� Multiple scattering (low momentum tracks in BaBar)

� He low Z

❂ Isobutane provides 80 percent of ionization

➪ Isobutane determines resolution✎ More Isobutane and multiple scattering worsens resolution

Gas Z A Density [g/l] dE/dx [kev/cm] W [ev]

Helium 2 4.003 0.178 0.32 41

Argon 18 39.95 1.78 2.44 26

Isobutane 34 58.12 2.67 4.50 23

Carbon Dioxide 22 44.00 1.98 3.01 33

Wire Choice

❂ Issues

❂ Mechanical Strength

� 20 micron sense wires: tradeo� with cell size, �eld gradient

� 80, 120 micron �eld wires

❂ Multiple Scattering

� Al low Z

❂ Resistivity

✎ Sense wire primary source of noise in readout circuit

� Tungsten, gold plating

❂ Surface Quality

✎ Sharp �eld gradients : sparking

� Rhenium in sense wire alloy

Electronics and Timing

❂ Sense wire dominant source of noise

❂ 4-channel ampli�er discriminator chip

❂ Di�erential output of amp. channel goes to discriminator

✎ Time over threshhold plus 40 nsec➪ goes to 6-bit TDC

� 1ns resolution

❂ FEX

❂ Keep up to 11 TDC hits for event

Particle ID and dE/dX

❂ Bethe-Bloch distribution

❂ Basic principle of PID with dE/dX❂ Mechanics of dE/dX

❂ BaBar Performance

The Bethe-Bloch Distribution

Muon momentum

1

10

100

Sto

ppin

g po

wer

[M

eV c

m2 /

g]

Lin

dhar

d-S

char

ff

Bethe-Bloch

Radiativeeffects

reach 1%

µ+ on Cu

Without δ

Radiativelosses

βγ0.001 0.01 0.1 1 10 100

1001010.1

1000 104 105 106

[MeV/c]100101

[GeV/c]100101

[TeV/c]

Anderson-Ziegler

Minimumionization

Eµc

Nuclearlosses

µ−

1

2

3

4

5 6

8

10

1.0 10 100 1000 10 0000.1

Pion momentum (GeV/c)

Proton momentum (GeV/c)

1.0 10 100 10000.1

1.0 10 100 10000.1

1.0 10 100 1000 10 0000.1

−d

E/

dx

(MeV

g−1

cm2 )

βγ = p/Mc

Muon momentum (GeV/c)

H2 liquid

He gas

CAl

FeSn

Pb

❂ Models energy loss in material of a relativistic particle

� dE/dx (energy lost per unit path length)

� vs. � or momentum

❂ Form� Minimal dependence on particle type; for practical purposes function of �

� Signi�cant material dependence

dEdx=4�Ne4

mc2

1�2Z2[ln(p

2mc2Emax�

I

)��2

2�

�(�)2

]

❂ Restricted energy loss formula

� Doesn't include high-energy transfers that do not contribute to a track

� Universal validity

Bethe-Bloch Continued

❂ Relativistic rise

� Corresponds to logarithmic term

� Density dependence

� Physical origins

� In time behavior of electromagnetic �eld of travelling particle

� Maximal energy transfer increases with �

❂ Fermi plateau

� �(�) curtails relativistic rise

� Complete cancellation of dependence as � ! 1

❂ Minimum

� At around � = 4

❂ Characterize curve

� Usually look at ratio of dE/dx on plateau to dE/dx at minimum

� R `amount of relativistic rise'

� � x-coordinate of plateau

� Depend on gas, density(T,P), sample length

Bethe-Block and Babar

❂ Distribution material and conditions dependent

❂ Using direct formula impossible

� Can't calculate all constants from �rst principles

➪ Parametrized �t to data instead

� BaBar DCH: 5-parameter �t

dE/dx and PID

❂ Remember energy loss results in ionization

� Will speak interchangeably of dE/dx and I

(measure of ionization strength along track)

❂ Theoretically

� Measured ionization ! particle mass

� Measured momentum

v =

pc2

pp2c2 +m2c4

➪ Particle ID

❂ To elaborate

� I � Z2Fg(v)

� Divide by minimal value at vmin ! normalized curve

❂ In practice

� Fg(v) not monotonic

� No closed form m = m(I; p)

➪ Plot Fg(v) curves for di�erent particles instead

Principles ContinueddE/dx vs momentum

10 3

10 4

10-1

1 10Track momentum (GeV/c)

80%

trun

cate

d m

ean

(arb

itrar

y un

its)

eµ

π

K

p dBABAR

❂ Above are curves for pions, kaons, electrons, muons, and protons

� Identical shape

� Displaced (on log scale) by logs of particle mass ratios

� Point on diagram: (Momentum, Ionization (dE/dx)

❂ PID not perfect or unique

� Curves overlap

� Ionization measurement has �nite accuracy

❂ Accuracy of ionization measurement (dE/dx resolution) obviously crucial

➪ Factors in accuracy? Measurement technique?

Statistics of Ionization

❂ Remember particle = track

❂ One track

� Approx. 40 hits➪ approx 40 ionization/charge measurements

✎ Average of all measurements bad estimator

� Mean energy loss dEdx�x has large uctuations

� Distribution skews towards high values (Landau tail)

❂ Solutions:

� Fit to shape of measured distribution

� Theoretically better

� Truncated mean method

� Take subsample, exclude high values

� Simple, similar performance in practice

dE/dx Resolution in BaBar

❂ Resolution rms width of dE/dx distribution

dedx/BB -1IDEntriesMeanRMSUDFLWOVFLWALLCHAN

130 2458 0.6094E-02 0.7721E-01

0. 0.

2458. 25.74 / 26

Constant 256.7Mean 0.5125E-02Sigma 0.7561E-01

99/08/31 18.07

Electron

IDEntriesMeanRMSUDFLWOVFLWALLCHAN

230 721

-0.4397E-02 0.7888E-01

0. 0.

721.0 13.74 / 22

Constant 73.13Mean -0.6906E-02Sigma 0.7753E-01

MuonIDEntriesMeanRMSUDFLWOVFLWALLCHAN

330 1802 0.3774E-02 0.7568E-01

0. 0.

1802. 49.53 / 18

Constant 185.1Mean 0.4962E-02Sigma 0.7642E-01

Pion

IDEntriesMeanRMSUDFLWOVFLWALLCHAN

430 177

-0.1678E-01 0.9047E-01

0. 0.

177.0 17.90 / 22

Constant 15.28Mean -0.8338E-02Sigma 0.8335E-01

KaonIDEntriesMeanRMSUDFLWOVFLWALLCHAN

530 19817-0.7998E-03 0.8709E-01

0. 0.

0.1982E+05 181.2 / 27

Constant 1837.Mean -0.1596E-02Sigma 0.8533E-01

Proton

IDEntriesMeanRMSUDFLWOVFLWALLCHAN

630 1792 0.4542E-02

0.1002 0. 0.

1792. 48.69 / 27

Constant 145.0Mean 0.8299E-02Sigma 0.9612E-01

Deuteron

0

100

200

300

-0.5 0 0.50

20406080

-0.5 0 0.5

050

100150200

-0.5 0 0.505

101520

-0.5 0 0.5

0500

100015002000

-0.5 0 0.50

50

100

150

-0.5 0 0.5

❂ 80 percent truncated mean

❂ Better than 2� �=K separation up to 700 MeV

Electronics and dE/dx

❂ Pulse

� Slow shaping

� Digitization: 15 Mhz FADC

� Interleaved with TDC hits

➪ Holes (Interpolation)

❂ Charge

� Integrated area of pulse

� Calibrated

❂ FEX output

� Charge

� Some shape information

Omissions

❂ Many important issues

� Not enough time to discuss them all

❂ DCH as Trigger❂ DCH and Event Time❂ Systematics and Corrections

❂ In tracking, dE/dx

❂ e.g. crosstalk, charge screening, entrance angle

❂ System Details

� Electronics

� Gas

� Mechanical

� Controls

❂ Aging

� Hydrocarbons can be a problem

� Current di�culties