David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Experimental Tests of QCD...

David Milstead – Experimental Tests of QCDITEP06 Winter School, Moscow

Experimental Tests of QCD at Colliders: Part 1

David MilsteadStockholm University

ITEP 2006 Winter School, Moscow.


What do we mean by ”testing QCD” ?

Quantum Chromodynamics is established as the theory of the strong force

S is the least constrained coupling constant of the fundamental forces.

Difficulty calculating beyond NNLO.

To test pQCD -> measurements devised to suppress higher orders

To develop pQCD -> measurements devised to enhance higher orders


High precision is vital!


Themes of part 1Precision tests of perturbative QCD using ’clean’ jet, event shapes and structure functions.

The capabilities of different collision environments

Extraction of s and parton densities.

Important theoretical and experimental errors to consider!

What have we done and what more can we do ?

Are tests limited by experiment/theory/both ?

Part 2 – particle production + non-perturbative QCD


lepton- hPdf (h, ISR FSR

h-h pdf (h) ISR FSR

Collision environments and experiments

scattering

e+e- annihilationPdf ISR FSR

q

q


Understanding Particle Collisions

Jets, particle

production, energy

flow, correlations

(1) Partonic structure into nucleon pdf

(3) ME-based pQCD

(2) Higher ordersvia parton showering,leading log resummation

Hadronisation – String, cluster, power corrections,LPHD{ }

QCD factorisation to separate out long and short distance interactions

Eg. DIS


Proton structure and pdfsDeep-Inelastic Scattering – Reminder!

Q2 /

GeV

2

x

22

2

2

22

1 massInvariant

ty Inelastici

)'.(2 riableBjorken va

)'(tuality Photon vir

pmx

xQW

xs

Qy

llp

Qx

llQ

HERA

i

i xxqexF )()( 22


Collinear factorisation and parton densities

Factorise long and short range interactions and neglect virtuality of interacting parton.

DGLAP equations describe evolution of quark and gluon densities with F

Below a factorization scale F emissions are absorbed into a universal parton density/distribution function (pdf)


F2 from HERA-1

Range in x:0.00001-1 Q2: 1-30000 GeV2

Directly sensitive to sum of all quarks and anti-quarks

Indirectly sensitive to gluonsthrough scaling violations

)()ln( 2

2 xxgQd

dFs

NLO DGLAPfit

pQCD describes the data well over 4 orders of magnitude in Q2


Determination of s

NLO QCD fits to structure function data provide most precise determination from DIS data.

Large theoreticalerror outsanding .


The work of HERA in determining proton structure


Nucleon Structure with BFKL

LO BFKL fithep-ph/9605389H.Navelet et al.

Difficult to disentangle BFKL/DLGAP/CCFM from F2


DGLAP-model underestimates hard emissions in gluon ’ladder’.CCFM model describes data well + heavy quarks in ep,ppBut, large uncertainties!


Structure Functions at the LHC

x

Expand phase space

First measurements to include Drell-Yan, multi-jet, prompt photons to determine pdfs.

Problem… How do we know SUSY/UED/? Backgrounds.

Require precision from pre-discovery colliders –

High x gluon may inhibit discoveries

Low x evolution must be well modelled


T. Carli,(proc. DIS 2004)


Lessons for using pdfsIs DGLAP appropriate at low x ?Is your measurement likely to be sensitive to effects from non-ordered emissions ?

How do you decide on a pdf uncertainty ? Compare several ? But then one compares only central values. CTEQ prescription (J.Pumplin et al., JHEP0207).

Pdfs can be derived at LO, NLO, NNLO.Order of pdf should be matched to scale of matrix element in fixed order program which is used (coming soon).


Disentangling perturbative QCD from the hadronic final state.

Fixed order perturbative QCD calculations forjet cross-sections, leading particles, event shapes, charged particle scaling violations.

Into the Hadronic Final State…


An incomplete list of QCD Models for the hadronic Final State

Leading order multi-purpose event generators

-QCD Matrix Element + parton showering+ hadronisation model (string, cluster – lecture 2): PYTHIA, HERWIG, ARIADNE (CDM), PHOJET….

Next-to-leading order models calculating specific 2-4 jet processes. Can be combined with resummed logarithms - JETRAD, JETVIP, MEPJET…..

See http://www.desy.de/~heramc/mclist.html


QCD uncertainties- Renormalisation

These are lectures about data not QCD calculations…

To test QCD we must understand QCD uncertainties.

Renormalisation scaleContribution to cross-section from loops.Divergent as Regularise cross-section with introduction of cut-off – new scale R

PP

Observable R should be independentof choice of scale – renormalisation group equation


Renormalisation Scale Uncertainty

pQCD calculations contain an assumption for the value of the renormalisation scale – it is arbitrary but related to a hard scale in the event (eg b-mass, jet pt, Q2 )-Variation of this scale is often the largest theoretical uncertainty.- Scale uncertainty reduces with higher orders

A question to ask anyone who shows a QCD calculation is ”what is the scale and what is the scale uncertainty?”


Scale uncertainty and k-factors

Choices of renormalisation scale

K-factors for inclusive jet production in DIS

Variation in value of scale(0.5to 2)(customary)

{

{K-factors


NLO – LO cross-section Scale Dependence

Scale uncertainity reflects contribution of higher orders.

Reduced scale uncertainty for NLO

Dijets in DIS with kt-algorithm


Jets and Partons

Differences between e+e- and hh S. Chekanov,”jet algorithms A mini-review”, (hep-ph/0211298)


Gluino pair production at the LHC

Quantification of discovery of any particle with colour requires pQCD calculations

scale uncertainty


Jet Physics

’Reconstruct’ pQCD process with a jet of hadrons - s

Jet clustering algorithms used to measure cross-sections.Requirements:(1)Infrared and collinear stability-jet cross-section must not change if the original parton radiates a soft parton or splits into 2 collinear partons.(2)Close correlation with parton direction(3) Small hadronisation corrections(3) Small renormalisation scale uncertainty(4) Suppression of contributions from beam remnants.

e+ e-

q q

Hadronisation

jet

S


Reduce experimental (energy scale) error by studying angular properties


4-Jet Rate from ALEPH-LEP

Based on NLO+ resummed NLL

s=0.1170+-0.0001+-0.0013


Jets at HERA

Ratio of 3-2 jets – cancel theoretical uncertainties


2005

The evolution of the strong coupling constant with time!


Event Shape Variables

Thrust

2

2

2

2

i

i

E

pM

ij ji

ij ijji

pp

ppC

2

sin3 2

Thrust: longitudinal momentum sum

Broadening: transverse momentum sum

Measured with n set to the thrust axis, and photon axis

Jet Mass and C parameter: correlations of pairs of particles

Infra-red safe and excellent probe of pQCD – use current region of Breit-frame in ep.

n for TT axis

i i

i ki

nk p

npT

k

ˆ

maxˆ

i

i

p

npB


e+e- & ep : Breit Frame

02 qxP

DIS event

La

b F

ram

eB

reit

Fra

me

Bre

it F

ram

e

Breit Frame definition:

“Brick wall frame” incoming quark scatters off photon and returns along same axis.

Current region of Breit Frame is analogous to e+e-.

Scale Q in DIS equivalent to sqrt(s) in e+e-

PT PL

2s

2s

e+e- event


E Event Shapes at LEP

Consistent s from 6 different variables

Running

sqrt(s)

vari

ab

les


Power corrections: an analytical approach

Power correction is used to calculate hadronization corrections for any infrared safe event shape variable, F

Mean event shape variables are sum of perturbative and non-perturbative (power correction) parts

The power correction depends on two parameters, α0 and αs

0 “non-perturbative universal parameter”

)()1(ln

2)()(ln

3

16 2

0

00 Q

KQQ

Q

QaF s

IsI

I

PIFpow

correctionpowerveperturbatiFFF

Used to determine the hadronization corrections

-(Dokshitzer, Webber Phys. Lett. B 352(1995)451)


Power corrections in e+e- and DIS

Consistent picture over full space range.

Many experients single experiment

e+e-ep


Simultaneous extraction of s of 0

Reasonably good agreement over manydifferent variables


SummaryPrecision tests of perturbative QCD using ’clean’ jet signals and structure functions.No sign of failure of pQCD or new physicsThe capabilities of different collision environmentsComplementary precision work at e+e-,hh,lhExtraction of s and parton densities.Both extracted to high precision – high x pdf uncertainties - low x evolution in questionImportant theoretical and experimental errors to consider!Renormalisation scale uncertainties and energy scale uncertainties are some present limitationsWhat have we done and what more can we do ?Higher orders needed. Optimal calibration. New variablesAre tests limited by experiment/theory/both ?Both


Collision environments and experiments

e+e- annihilationPdf ISR FSR

lepton- hPdf (h, ISR FSR

h-h pdf (h) ISR FSR

scattering

Pdf(

ISR

FSR


Photon Structure at LEP


SM or BSM ? Precision limited by experimental and theoretical errorsOptimal to determine pdfs at HERA and then test at the Tevatron.

David Milstead – Experimental Tests of QCD ITEP06 Winter School, Moscow Experimental Tests of QCD...

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