Transcript High order radiative corrections in Electron-Proton scattering Egle Tomasi-Gustafsson Saclay, France JLab, August 5, 2008 In collaboration with Yu.

High order radiative corrections
in
Electron-Proton scattering
Egle Tomasi-Gustafsson
Saclay, France
JLab, August 5, 2008
In collaboration with
Yu. Bystriskiy, V. Bytev and Prof. E.A. Kuraev
August 5, 2008
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Egle TOMASI-GUSTAFSSON
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Cross section of (quasi)elastic ep-scattering
Classify radiative corrections:
Elastic
e ( p )  p( p )  e ( p ' )  p( p' )

Inelastic

1
1
 e ( p ' )  p( p' )   ( k )

1
Higher order inelastic
double brehmstrahlung,  e ( p ' )  p( p' )   ( k )   ( k )
pair production..
 e ( p ' )  p( p' )  e ( q )  e ( q )

1

1
2

1



 ............................
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Unpolarized case
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Feynman diagrams, for the scattering amplitude
Elastic scattering
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Single bremstrahlung
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Double Bremstrahlung and Pair Production
Lowest order radiative corrections (RC): Mo and Tsai (1969)
Infrared divergences : « photon mass » , 
Logarithmic enhancement:
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Vacuum Polarization
Main contribution: vacuum polarization due to electron positron pair
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Vertex function
The contribution to F2(Q2) is suppressed by
compared to F1(Q2)
The « photon mass » , , is an auxiliary parameter,
which does not enter in the final answer for the cross section
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Collinear Emission of Photons
• Contains logarithmic enhancement
• Suffers from infrared divergences
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Scattered electron energy
final state emission
Initial state emission
Quasi-elastic scattering
3%
Not so small!
Shift to LOWER Q2
Y0
All orders of PT needed 
beyond Mo & Tsai approximation!
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Short history (I)
Schwinger: corrections to cross section for electron
scattering in external field
s=s0(1+d) (1)
Yennie, Frauchi, Suura: cross section of any pure process
(without real photon emission) is zero.
Kessler, Ericsson, Baier, Fadin, Khoze, Y. Tsai : quasi real
electron method. Emission of hard photon is described in
terms of a convolution of a radiative function with Born cross
section.
 (1) Not adequate
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Short history (II)
1977: Altarelli Parisi Gribov Lipatov, Dokshitzer: (DGLAP)
Asymptotic freedom, evolution equation, Collins factorization
theorem.
Drell-Yan picture of hard processed in QED : application of
QCD ideas to QED: radiative corrections in form of structure
functions and Drell-Yan picture
Leading terms:
and non leading terms
explicitely taken into account in DGLAP evolution
equations. In QED known as Lipatov equations (1975).
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Structure Function method
E. A. Kuraev and V.S. Fadin, Sov. J. of Nucl. Phys. 41, 466 (1985)
• SF method applied to QED processes: calculation of
radiative corrections with precision ~ 0.1%.
• Takes into account the dynamics of the process
Lipatov equations (1975)
• Formulated in terms of parton densities (leptons,
antileptons, photons)
• Many applications to different processes
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Structure Function Method (Applications)
– e+e- hadrons( J/ width)
E. A. KURAEV and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)
– ep  e’X (elastic and inelastic scattering)
E. A. KURAEV ;N.P. MERENKOV and V.S. FADIN, Sov. J. of Nucl. Phys. 47,1009 (1988)
– Decay width of mesons (FSI)
E. A. KURAEV, JETP Lett.65, 127 (1997)
– Radiative corrections for LEP beam (small angle BHABHA
scattering)
A.B.Arbuzov, E.A.Kuraev et al, Phys. Lett.B 399, 312 (1997)
– Compton and double Compton scattering
A.N.Ilyichev, E.A. Kuraev, V.Bytev and Y. P. Peresun'ko, J. Exp. Theor. Phys.100 31 (2005)
– Structure function method applied to polarized and unpolarized
electron-proton scattering: A solution of the GE(p)/GM(p)
discrepancy.
Y. Bystricky, E.A.Kuraev, E. Tomasi-Gustafsson, Phys. Rev. C75, 015207 (2007).
–
Radiative corrections to DVCS electron tensor.
V.Bytev, E.A.Kuraev, E. Tomasi-Gustafsson, Phys. Rev. C (2008)
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The Structure Function Method
E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)
Distinguish:
-leading contributions of higher order
-non leading ones
The SF method is based on:
• Renormalization group evolution equation
• Drell-Yan parton picture of the cross section in QCD
Electron SF: probability to ‘find’ electron in the
initial electron, with energy fraction x and virtuality up to Q2
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LSF: ‰ precision
E. A. K. and V.S. FADIN, Sov. J. of Nucl. Phys. 41, 466 (1985)
LLA (Leading Logarithm Approximation)

Q2
L  1, L  ln 2

me
Precision of LLA
Including K-factor
   
 
   
1

L 
 0.2%
 400
2
   
   L   0.01 %
   
Even when corrections in first order PT are d~100%,
the accuracy of higher order RC (LSF) is / d1% !
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The LSF cross section (for ep )
• If the electron is detected in a calorimeter: the cross section
is integrated over the scattered electron energy fraction:
1
 dzD( z ,  )  1
0
• The K-factor includes all non leading contributions:
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Results
Q2=1 GeV2
Q2=3 GeV2
SF Born
RC Born
………
Polarization
Q2=5 GeV2
Both calculations assume
dipole FFs
The slope changes
(due to different RC)
E.T-G, Phys. Part. Nucl. Lett. 4, 281-288 (2007).
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Unpolarized Cross section
Q2=1 GeV2
Q2=3 GeV2
Born +dipole FFs
(=unpolarized experiment+Mo&Tsai)
SF (with dipole FFs)
SF+2 exchange
Q2=5 GeV2
SF: change the slope!
2 exchange very small!
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Polarization ratio
q =80°
Yu. Bystricky, E.A.Kuraev, E. T.-G, Phys. Rev. C 75, 015207 (2007)
Born
SF
SF+2 exchange
q =60°
q =20°
2 exchange very small!
2 destroys linearity!
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Radiative Corrections (SF method)
Yu. Bystricky, E.A.Kuraev, E. Tomasi-Gustafsson, Phys. Rev. C75, 015207 (2007)
SLAC data
SF corrected
JLab data
SF corrected
Polarization data
Rosenbluth parameters
highly correlated!
E.T-G, Phys. Part. Nucl. Lett. 4, 281 (2007)
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Bethe-Heitler
DVCS
Interference
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Charge Asymmetry
RC (LSF)
RC(1st order)
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HELICITY Asymmetry
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Conclusions
•High precision experiments need highly precise
Radiative Corrections
•Higher order corrections become
more and more important at large Q2
•The lepton structure function method can
be applied to different electromagnetic
processes with permille precision
•Higher order corrections depend on the relevant
kinematical variables
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Radiative Corrections (first order)
The cross section:
The correction ( in powers of Z):
Z0: electron emission and vacuum polarization
Z1: interference 1-2 exchange
Z2: target emission
L.C. Maximon and J.A Tjon, PRC 62, 054320(2000)
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LSF Corrections (High orders included)
The cross section:
The correction ( Leading Logarithm Approximation):
The vacuum polarization:
The K-factor:
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Radiative Corrections
ds ( Q , )  ds
RC
2
Born
( Q , )( 1   )
2
Q2=1 GeV2
Yu. Bystricky, E.A.Kuraev, E. T-G,
Phys. Rev. C75, 015207 (2007)
L.C. Maximon and J.A Tjon,
PRC 62, 054320(2000)
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Radiative Corrections
MT (Z2) proton LSF proton
LSF electron (not LLA)
MT (Z) two photon
LSF LLA
LSF total
MT (Z0) electron
MT total
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MT proton
LSF proton
LSF electron (not LLA)
MT (Z0) two photon
LSF LLA
LSF total
MT (Z0) electron
MT (Z0) total
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LSF correction (SLAC data) point by point
Q2=5 GeV2
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The Pauli and Dirac Form Factors


The electromagnetic current in terms of the Pauli and Dirac FFs:
Related to the Sachs FFs :
Normalization
F1p(0)=1, F2p(0)= κp
GEp(0)=1, GMp(0)=μp=2.79
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Analytical properties of Compton amplitude
• Elastic form factors and inelastic channels
are not independent  SUM RULES
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Analytical properties of Compton amplitude
Neglect left contribution and close contour on the right side
(10% accuracy):
Cancellation of strong interaction effects
in FFs and inelastic channels!
Cancellation proved exactly in QED: the L2 * contribution to FFs is cancelled by soft photon emission
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resonance (example of inelastic channels)
• Small contribution ~0.5%
• Opposite sign with respect to
proton intermediate state
Cancellation of contributions in
elastic and inelastic channels
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Interference of 1 2 exchange
– Enhancement due to the fast decreasing of form factors
(transferred momentum equally shared between the two
photons).
– Dipole approximation of FFs: Q02=0.71GeV2
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Interference of 1 2 exchange
• Explicit calculation for structureless proton
– The contribution is small, for unpolarized and
polarized ep scattering
– Does not contain the enhancement factor L
– The relevant contribution to K is ~ 1
E.A.Kuraev, V. Bytev, Yu. Bystricky, E.T-G, Phys. Rev. D74, 013003 (1076)
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Two Photon Exchange
No exact calculation for ep scattering
( inelastic intermediate states..)
but
electron-muon scattering
constitutes an upper limit!
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QED versus QCD
Imaginary part of the 2 amplitude
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QED versus QCD
Q2=0.05 GeV2
Q2=1.2 GeV2
Q2=2 GeV2
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