Dissertation Defense, 05/18/20051 Measurement of the hadronic photon structure function F 2 γ with...

Dissertation Defense, 05/18/2005 1

Measurement of the hadronic photon structure Measurement of the hadronic photon structure

function Ffunction F22

γγ with L3 detector at LEP with L3 detector at LEP

GyGyööngyi Baksayngyi BaksayFlorida Institute of Technology

Advisors:Advisors:

Dr. Marcus Hohlmann, Florida Institute of TechnologyDr. Marcus Hohlmann, Florida Institute of Technology

Dr. Maria Kienzle-Focacci, University of Geneva (advisor at CERN)Dr. Maria Kienzle-Focacci, University of Geneva (advisor at CERN)

Dissertation defense: April 18, 2005Dissertation defense: April 18, 2005


Topics of DiscussionTopics of Discussion

Theoretical considerationsTheoretical considerations

KinematicsKinematics

The L3 detectorThe L3 detector

Analysis methodAnalysis method

ResultsResults

Summary and conclusionsSummary and conclusions

Dissertation defense: April 18, 2005Dissertation defense: April 18, 2005GyGyöngyi Baksayöngyi Baksay


QED: photon mediator =>structureless: ““direct/bare” photondirect/bare” photon

Free photonFree photon:: zero rest mass m=0

Virtual photonVirtual photon:: “off-mass shell” m0

* emitted and reabsorbed: t ħ/ E

* violates conservation of energy, * ff

fermion or anti-fermion further interacts=> parton content resolved

photon extended object (charged fermions+gluons):

””resolved” photonresolved” photon

Another dual nature of photon: direct or resolved

One possible description: Photon Structure FunctionPhoton Structure Function

Different appearances of the photonDifferent appearances of the photon

Virtual photon cloud:Virtual photon cloud:

Vacuum polarization:Vacuum polarization:


Kinematics (eKinematics (e++ee--**((**) ) e e++ee-- hadrons) hadrons)

4-momentum transfer:4-momentum transfer:

22

2γ

2

γ

22

21

2γ

2

γ

21

'222

'111

mqEq

mqEq

kkq

kkq

*2

*2

*1

*1

4-momentum fraction:4-momentum fraction:

22γγ

2

2

21

2

PWQ

Q

q2q

Qx

““Virtuality”Virtuality”

22

22

21

21

Qq

Qq

Virtual photon 4-momenta:Virtual photon 4-momenta:

)q,(Eq

)q,(Eq

*2

*2

*1

*1

γγ2

γγ1

)cosθ(1E2EqQ

)cosθ(1E2EqQ

2'22

22

22

1'11

21

21

:Wγγ h h2γγ

2h

2h

2vis W)p()E( WCenter-of-mass energy;

h=particle measured in the detector

2γγ

2

22

WQ

Q

q2p

Qx

)cosθ(1E2EqQ tag'tagbeam

21

2

0θ)cos/E(E1p)p)/(k(qy tag2

beamtag

0Pq

0Qq22

221

)Q(x,Fy)Q(x,F)y)(1(1xQ

α 2π

dxdQ

)Q(x,dσ 2γL

22γ2

24

2

2

2eXeγ

Four momentum fraction:Four momentum fraction: - process:- process:

0


Contributions to the two-photon cross sectionContributions to the two-photon cross section

QCDQPMVMDγγσσσσ (*)*

x

F2(VDM)gluons

FF22//

quarks

)Q(x,FQ

α 4π)Q(x,σ 2γ

22

22

γγ (*)*

(a)

(c)

(b)

f

k

n

1k

2224q2

2

cQPM logQ x)(1x xeQ

α 4πN σ

fn

1i

2i

2i

2i

γ2 )]Q(x,q)Q(x,[qexF

(b) Pointlike couplingPointlike coupling fully calculable QED process; Large quark density at large x and logarithmic rise with Q2.

2dxdQ

qg)γq( )σQ(x,f)qqg )σQ(x,fσ

q

2γq

2γg

QCD γ(

(c) QCD corrections (hard interaction) QCD corrections (hard interaction) DGLAP evolution equation; presence of quark & gluon density. Large corrections in NLO PDF’s do not converge; must be measured at a certain value of Q2.

(c) (a) (b)

(a) non-perturbative VDM (soft interactions)non-perturbative VDM (soft interactions) : superposition of ρ, ω, and φ. Ignoring gluon emission the VDM structure function (electron-nucleon scattering) shows Bjorken scaling. Increasing Q2: more momentum goes into radiated gluons; shift to lower x.

),(QF,0,0)(Wσ0)Q,Q,(Wσ 2

1GVDMγγVMDγγ

22

21γγ

GVDMγγ

φω,ρ,V20

222V

2

2V

2

V2

GVDM mQ1

0.22

mQ1

4mQ1r)(QF

i

1i2i2 (x)2xF(x)xfe(x)F


CERN, LEP, and the L3 detector CERN, LEP, and the L3 detector

highest cm. energy reached: 209 GeV

L3L3

CERNCERN

LEPLEP


Data setsData sets and and ccrossross-s-sectionsections

Present data analysisPresent data analysis 700 pb700 pb-1-1

LEP2 at dominanthadronseeee

LEP2


Analysis MethodAnalysis Method

Monte Carlo Programs:Monte Carlo Programs: PHOJET, PYTHIA, TWOGAM

Triggers and Selection:Triggers and Selection: select single-tagtwo-photon events

Unfolding:Unfolding: xvis distorted, hadrons partially detected, obtain xtrue distribution using Bayes Theorem

Determine measured cross sectionDetermine measured cross section using unfolded data

Extract FExtract F22(x,Q(x,Q2 2 )/)/ using analytical calculations (GALUGA)

Study x and QStudy x and Q2 2 dependencedependence of F2(x,Q2)/

Compare resultsCompare results with theoretical predictions and previous experimental results


Monte Carlo ProgramsMonte Carlo ProgramsPHOJET(1.05c):PHOJET(1.05c): hadron-hadron,photon-hadron,photon-photon collisionsDual Parton Model (soft and hard processessoft and hard processes) with QCD QCD improvedimproved parton model.Two-photon luminosity calculated from the flux of transversely polarized photons.

PYTHIA(6.203):PYTHIA(6.203): general purpose MC, (LO) hard-scattering processes, elastic, diffractive and low pt events.Classification according to photon interactions: direct, resolved, VDMdirect, resolved, VDM and hard scaleshard scales: photon virtualities and parton pt.

TWOGAM(1.71):TWOGAM(1.71): direct, resolved, VDMdirect, resolved, VDM processes separately generated3 cross sections adjusted to fit x distribution of the data.Photon flux: exact (LO) formula

Detector simulation:Detector simulation: GEANT and GEISHA

Background:Background: PYTHIA and DIAGγ)qqZγe(e )ττeee(e --

stat. MC >5 x stat. data; MC’s reconstructed the same way as data

ΔLσdWdPdQLσdWdPdQ σΓNΔσ (*)*(*)*(*)*(*) γγ

22TTγγ

22

γγTγee


How do we see it in the detector?How do we see it in the detector?

tag >> 0 electron observed inside the detectorantitag 0 other electron undetected

ee++

ee--

*(*) interaction

“Single-tag” process

HADRONSHADRONS

Triggers and selectionTriggers and selection

ee+ + not not detecteddetected

Triggers:

Single-tag triggerSingle-tag trigger

70% Ebeam deposited in ECAL or LUMI, in coincidence with 1 track in the central tracking chambers

TEC triggerTEC trigger

Outer TEC trigger: 2 tracks back-to-back in the transverse plane within 60O, pt>150 MeV

Inner TEC trigger: complementary; at least two tracks in the internal chambers with any configuration of tracks.

trig trig 97% 97%

LUMI-tag conditionLUMI-tag condition

Highest energy cluster; shape e.m. shower

Etag/Ebeam>0.7

LUMI polar angle

Anti-tag conditionAnti-tag condition

To ensure low virtuality of the target photon

Emax/Ebeam<0.2

(rad) 0.0637θ(rad) 0.0325 tag

ee- - tagged tagged in LUMIin LUMI


SelectionSelection

Background rejection forBackground rejection for ee++ee-- Z Zqqqq

events: low energy in the central detectorsevents: low energy in the central detectors

EECAL+HCAL<0.4

misidentified as the tagged electron.misidentified as the tagged electron.

s

Hadronic channelHadronic channel (ee++ee-- e e++ee-- hadrons hadrons):

Hadrons in the final state contain several:

At least 4 additional particles

Ntracks + N 4

Track (chambers): pt>100 MeV, <10 mm

Photon (BGO): E>100 MeV, not assoc. with charged track

Ntracks=2: e+e- e+e-l+l- (l=leptons) excluded

0π,π

Exclude low WExclude low Wvisvis

Exclude resonances and low efficiency region

Wvis>4 GeV


Selected eventsSelected events

well measured

QQgengen22

QQvisvi

s22

UnfoldingUnfolding

Energy of the target photon is not known (second electron undetected)

Reconstruct events using information from eetagtag and final state hadronsfinal state hadrons

Boost of system hadrons partially detectedhadrons partially detected

Observed xxvisvis distribution is distorted compared to the x distribution is distorted compared to the x truetrue distribution

Multidimensional method based on Bayes Theorem

Correction with MC’s: Pythia,Twogam (compare x-shapes)

2γγ

2

2

WQ

Qx


UnfoldingUnfolding

Number of unfolded events assignable to each of the causes:

Correlation, i.e. “Smearing matrix”:

For Sji=1 each observed event xvis must come from one of the causes xgen.

Comparison of the reconstructed xxvis and generated value xgen

MCgen

MCvis /NNε

After unfolding, the events are corrected for detector acceptance and efficiency:

Causes: xgen,j

Effects: xvis,i

cn

1llgen,

0lgen,

MCivis,

jgen,0

jgen,MC

ivis,MCivis,jgen,

0ji

)(x)Px|P(x

)(x)Px|P(x)x|P(xS

En

1i'j

jgen,visivis,

MCivis,jgen,'

jjgen,unf ε

)x|N(x))N(xx|P(x

ε

1)x|N(x

Unfolded eventsUnfolded events Experimentaly observed eventsExperimentaly observed events

Correlation between generated and measured MC eventsCorrelation between generated and measured MC events

Probabilities that the effects measured in bin “i” are originating from the causes in bins “j”.


Extraction of FExtraction of F22

efficiency triggeracceptanceL

NNΔσ backgroundunfolded

meas

hadrons)eee(eΔσ

hadrons)eee(eΔσα)Q(x,[F

Galuga

meas2γ2

meas]

To obtain F2

GALUGA cross section calculated in the given Q2 and x range

Target photon fluxTarget photon flux

)Q(x,Fy)Q(x,F)y)(1(1xQ

α 2π

dxdQ

)Q(x,dσ 2γL

22γ2

24

2

2

2eXeγ

2eγ

2γ

22ee

dxdQ

dσ

dzdP

dN

dzdPdxdQ

dσ (*)

eeGaluga ΔσΔσ

value ysmall to due (1%) small oncontributi QPM, to set F

reference, as used output GALUGA 1FγL

γ2

2% Δσ on yuncertaint factors, form pole ρ and GVMD using calculated GeV 0.07~P Galuga2

dWdPσΓdσ 2

γγTeγ (*)*

Radiative corrections:Radiative corrections:

RADCOR [Nucl. Phys. B 253 (1985) 421; Comp. Phys. Comm. 40 (1986) 271 ]

Calculates initial and final state radiation for

Corrections mainly due to initial state radiation from the electron scattered at large angle.

Final state radiation detected together with the “tagged electron”

Radiation from other “electron” negligible

μμeeee

tot

radnon

Δσ

ΔσR meas

2γ2corrrad

2γ2 ]α)Q(x,[FR]α)Q(x,[F


Comparison: PYTHIA & TWOGAMComparison: PYTHIA & TWOGAM


Evolution of FEvolution of F22 with xwith x

ffPLPL perturbatively calculable perturbatively calculable. For

fhad use approximate similarity of

the vector meson and the pion is used.

Starting distributionStarting distribution hadron-likehadron-like (based on VDM)

)Q(x,ff

α 4πκgqq f 2

0π2ρ

γγγγ

ba x)(1x ~)Q(x,f 20π

GRVGRV**

*GRV[M. Glück, E. Reya, and A. Vogt, Photonic Parton Distributions, Phys. Rev. D 46, (1992) 1973 .]

γhad

γPL

γ fff

Galuga calculation: GVDM to a form factor comparison: 2%.

Estimation of the radiative corrections 2%


Q2 evolution of F2

44% CL

71% CL

fit:


Comparison with other LEP experiments and GRV-set1

Comparison has its limits ! Each experiment uses Each experiment uses different methodsdifferent methods.. Other experiments: expectations of a MC generated with a well defined PDFPresent L3 measurements: analytical calculations (GALUGA)Radiative corrections: present L3 measurements and OPAL

MC’s predict different shapes for x

Differences between MC’s larger than differences between different experiments [LEP working group: Eur. Phys. J. C 23 (2002) 201.]


Kinematical range:LEP2Kinematical range:LEP2

ALEPH Eur. Phys. J. C. 30 (2003) 145

DELPHI Bejing Conference (preliminary) 2004

L3 Phys. Lett. B 447 (1999) 147 and

This analysis: L3 preprint, CERN-PH-EP/2005-004,

February 15, 2005. L3 preprint 295, submitted to Phys. Lett. B.

OPAL Phys. Lett. B. 533 (2002) 207

LUMI Q2 range


e+e- colliders are an ideal testing ground for two-photon physics studies.

At LEP2 the cross section dominates by 2 orders of magnitude.

L3 has excellent resolution for photons and charged hadrons.

The hadronic final state depends on the chosen model, which needs to be tuned to mach the data distribution.

High energy data with high statistics allowed precision measurements of the photon structure function testing QCD and QED predictions in the kinematical range: x 0.006-0.556, and Q2 11-34 GeV2.

The data are best reproduced by the higher-order parton density function GRV. Due to the high energy obtained with the LEP accelerator, it was possible to measure in addition to the 3 light quarks the effect of the heavier charm quark.

Summary and conclusionsSummary and conclusions


Thank you!

Dissertation Defense, 05/18/20051 Measurement of the hadronic photon structure function F 2 γ with...

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