Transcript Document

Measurement of the hadronic photon structure
function F2γ with L3 detector at LEP
Gyöngyi Baksay
Florida Institute of Technology
Advisors:
Dr. Marcus Hohlmann, Florida Institute of Technology
Dr. Maria Kienzle-Focacci, University of Geneva (advisor at CERN)
Dissertation defense: April 18, 2005
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Topics of Discussion
Theoretical considerations
Kinematics
The L3 detector
Analysis method
Results
Summary and conclusions
Gyöngyi Baksay
Dissertation Defense, 05/18/2005Dissertation defense: April 18, 2005
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Different appearances of the photon
QED: photon mediator =>structureless: “direct/bare”
photon
Virtual photon cloud:
Free photon: zero rest mass m=0
Virtual photon: “off-mass shell” m0
Vacuum polarization:
* 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” photon
Another dual nature of photon: direct or resolved
One possible description:
Photon Structure Function
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Kinematics (e+e-*(*)  e+e- hadrons)
Virtual photon 4-momenta:
 - process:
Four momentum fraction:
q1  (Eγ* , q γ*1 )
1
q 2  (Eγ* , q γ*2 )
2
4-momentum transfer:
q1  k 1  k 1'
q 2  k 2  k '2
q1  Eγ*  q γ*1  m12
2
2
2
1
q 2  Eγ*  q γ*2  m22
2
2
2
2
“Virtuality”
'
Q12 2 q12  2E1E
1
2 (1  cosθ1 )
'
Q


q

2E
E
Q  q  2E 1
E (1  cosθ beam
)
tag (1  cosθtag )
2
2
Wγγ :
2
2
q 
Q
P0
2
2
22
22
Q
Q
Q
Q
x
x 2q1  q2 Q2 2Wγγ2  P2 2
2p  q
Q  Wγγ
2
2
Wvis
 (h Eh )2  (h ph )2  Wγγ2
h=particle measured in the detector
dσeγeX (x,Q2 )
4-momentum fraction:
'
2
Center-of-mass energy;
 q12 
 Q12  0
2
2
2
dxdQ2
0

2π α2

(1  (1  y)2 )  F2γ (x,Q2 )  y 2FLγ (x,Q2 )
4
xQ

y  (q  p)/(k p)  1  (Etag /Ebeam )cos2θtag  0
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Contributions to the two-photon cross section
σ γ*γ( * )  σ VMD  σQPM  σQCD  σ γ γ (x,Q2 )  4π α2 F2γ (x,Q2 )
2
* (*)
Q
(b)
F2/
quarks
(c)
gluons
(a)
(b)
F2(VDM) (a)
(c)
x
(a) non-perturbative VDM (soft interactions) : superposition of ρ, ω, and φ. Ignoring gluon emission the
VDM structure function (electron-nucleon scattering) shows Bjorken scaling. F2 (x)   e i2xfi (x)  2xF1 (x)
i
Increasing Q2: more momentum goes into radiated gluons; shift to lower x.
σ
GVDM
γγ
(Wγγ , Q , Q  0)  σ
2
1
2
2
VMD
γγ
(Wγγ ,0,0) FGVDM (Q ), FGVDM (Q )   rV
2
1
2
V ρ, ω, φ
1  Q2 4m2V
1  Q
2
m2V 
2

0.22
1  Q2 m02
(b) Pointlike coupling  fully calculable QED process; Large quark density at large x and logarithmic
rise with Q2.
nf
2
nf


4π α 4
2
2
2
e
x
x

(1

x)
logQ
q
2
k
k 1 Q
σQPM  Nc 
 F2γ  x  e i2[q i (x, Q 2 )  q i (x, Q 2 )]
i 1
(c) 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.
 γ

QCD
2
γ
2
2
σ
   fg (x,Q )σ (γg  qq)   fq (x,Q )σ (γq  qg)dxdQ
q


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CERN, LEP, and the L3 detector
CERN
highest cm. energy reached: 209 GeV
L3
LEP
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Data sets and cross-sections
LEP2
Present data analysis 700 pb-1
ee  eehadrons
dominant at LEP2
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Analysis Method
Monte Carlo Programs: PHOJET, PYTHIA, TWOGAM
Triggers and Selection: select single-tag two-photon events
Unfolding: xvis distorted, hadrons partially detected, obtain
xtrue distribution using Bayes Theorem
Determine measured cross section using unfolded data
Extract F2(x,Q2 )/ using analytical calculations (GALUGA)
Study x and Q2 dependence of F2(x,Q2)/
Compare results with theoretical predictions and previous
experimental results
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Monte Carlo Programs
PHOJET(1.05c): hadron-hadron,photon-hadron,photon-photon collisions
Dual Parton Model (soft and hard processes) with QCD
improved parton model.
Two-photon luminosity calculated from the flux of transversely
polarized photons. Δσ ee   N γ ΓTσ γ γ dQ2dP2dW  σ γ γ  L TTdQ2dP2dW  σ γ γ ΔL
(*)
* (*)
* (*)
* (*)
PYTHIA(6.203): general purpose MC, (LO) hard-scattering processes,
elastic, diffractive and low pt events.
Classification according to photon interactions: direct, resolved, VDM
and hard scales: photon virtualities and parton pt.
TWOGAM(1.71):
direct, resolved, VDM processes separately generated
3 cross sections adjusted to fit x distribution of the data.
Photon flux: exact (LO) formula
Background: PYTHIA (ee  Zγ  qqγ)and DIAG (ee  ee- τ τ- )
Detector simulation: GEANT and GEISHA
stat. MC >5 x stat. data; MC’s reconstructed the
same way as data
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How
do we and
see itselection
in the detector?
Triggers
Triggers:
LUMI-tag condition
“Single-tag”

>> 0  electron observed inside the detector
Single-tag trigger
Highest
energy cluster; shape e.m. shower

 0  other electron
undetected
process
70% Ebeam deposited in ECAL or LUMI, in
E /E
>0.7
tag
antitag
tag
coincidence with 1 track in the central tracking
chambers
beam
LUMI polar angle
0.0325(rad)  θtag  0.0637(rad)
TEC trigger
Outer TEC trigger: 2 tracks back-to-back in the
transverse plane within 60O, pt>150 MeV
Anti-tag condition
To ensure low virtuality of the target photon
Inner TEC trigger: complementary; at least two
tracks in the internal chambers with any
configuration of tracks.
Emax/Ebeam<0.2
e- tagged
in LUMI
e
-  97%
trig
e+ not
detected
e+
*(*) interaction
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Selection
Hadronic channel (e+e- e+e- hadrons):
Hadrons in the final state contain several: π , π0
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
Background rejection for e+e- Zqq
  events: low energy in the central detectors
EECAL+HCAL<0.4
s
 misidentified as the tagged electron.
Exclude low Wvis
Exclude resonances and low efficiency region
Wvis>4 GeV
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Selected events
Qvis2
well measured
Q2
x 2
Q  Wγγ2
Qgen2
Unfolding
Energy of the target photon is not known (second electron undetected)
Reconstruct events using information from etag and final state hadrons
Boost of  system  hadrons partially detected
Observed xvis distribution is distorted compared to the xtrue distribution
Multidimensional method based on Bayes Theorem
Correction with MC’s: Pythia,Twogam (compare x-shapes)
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Unfolding
Probabilities that the effects measured in bin “i” are originating from the causes in bins “j”.
After
Comparison
unfolding,
of the
the events
reconstructed
are corrected
xxvis
Causes: xgen,j
for
and
detector
generated
acceptance
value xgen
and efficiency:
Effects: xvis,i
Number of unfolded events assignable to each of the
causes:
Unfolded events
N(xunf | xgen, j ) 
Experimentaly observed events
N(xvis | xgen, j )
1 nE
MC
P(x
|
x
)N(x
)


gen,
j
vis,
i
vis,
i
ε'j i1
ε'j
Correlation between generated and measured MC events
Correlation, i.e. “Smearing matrix”:
S  P(xgen, j | x
0
ji
MC
vis, i
)
0
P(xMC
vis, i | x gen, j )P (xgen, j )
nc
MC
0
 P(xvis, i | x gen, l )P (xgen, l )
l 1
For Sji=1 each observed event xvis must come
from one of the causes xgen.
MC
ε  NMC
vis /Ngen
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Extraction of F2
To obtain F2
Δσmeas (ee   e e hadrons)
[F (x,Q ) α]meas 
ΔσGaluga (ee   e e hadrons)
γ
2
2
Radiative corrections:
Nunfolded  Nbackground
Δσmeas 
L  acce
re fficie
ncy
RADCOR
[Nucl.ptance
Phys.Btrigge
253 (1985)
421;
Comp. Phys. Comm. 40 (1986) 271 ]
Calculates initial and final state radiation for ee2  eeμμ
GALUGA cross section calculated in the given Q and x range ΔσGaluga  Δσee  
Corrections mainly due to initial state radiation from the electron scattered at large angle.
2
dNγ(*) output
dσeγuse ddσ
(x,
Qnce
) , 2π α2
F2γ dσ
 1ee GALUGA
as
fe
re
eγre
eX




(1“tagged
 (1  y)2 )electron”
 F2γ (x,Q2 )  y 2FLγ (x,Q2 )
Final2 state 2radiation
together
with
the
2  detected
2
2
4
dxdQ
dP dxdQ
dxdQdue to small
xQ y value
FLγ sedz
ttodP
Q PM,dz
contributi
on small(1%)
Radiation from other “electron”  negligible
dσ eγ  ΓTarget
dP2dWflux
T σ γ * γ (*) photon
Δσnon rad
γ
2
γ
2
2 [F (x,Q ) α]

R

[F
(x,
Q
) uncertaint
α]meas y on ΔσGaluga 2%
PR~0.07
GeV
calculated
using
GVMD
and
ρ
pole
form
factors,
2
rad

corr
2
Δσtot
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Comparison: PYTHIA & TWOGAM
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Evolution of F2 with x
GRV*
γ
γ
f γ  fPL
 fhad
fPL perturbatively calculable. For
fhad use approximate similarity of
the vector meson and the pion is
used.
Starting distribution hadron-like
(based on VDM)
γ
f γ  qγ  q  gγ  κ
4π α
fπ (x,Q02 )
2
fρ
fπ (x,Q02 ) ~ xa (1  x)b
Galuga calculation: GVDM to a  form factor comparison: 2%.
Estimation of the radiative corrections 2%
*GRV[M. Glück, E. Reya, and A. Vogt, Photonic Parton Distributions, Phys. Rev. D 46, (1992) 1973.]
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Q2 evolution of F2
fit:
44% CL
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71% CL
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Comparison with other LEP experiments and GRV-set1
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.]
Comparison has its limits ! Each experiment uses different methods.
Other experiments: expectations of a MC generated with a well defined PDF
Present L3 measurements: analytical calculations (GALUGA)
Radiative corrections: present L3 measurements and OPAL
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Kinematical range:LEP2
LUMI Q2 range
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
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Summary and conclusions
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.
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Thank you! 
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