Outline

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Outline
Two-photon exchange contribution to the elastic
e-p scattering at large momentum transfer
Motivation General scattering amplitude in
elastic e-N scattering Partonic calculation at
large Q2 Result Summary
Yu-Chun Chen National Taiwan University
October 24th 2005
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Motivation
Why we interested in two-photon physics
Starting from the electric and magnetic
form factors (GE GM) which are defined by the
electromagnetic current Jµ then the
differential cross section for e-N scattering is
given by
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Rosenbluth separation method (LT)
reduced cross section
Polarization transfer method
Polarized electron beam ? sideways and
longitudinal polarization for recoil proton
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Two independent measurement of R(GE/GM)
SLAC Rosenbluth data
Jlab/Hall A Polarization data Jones et al.
(2000) Gayou et al. (2002)
Two methods, two different results !
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General scattering amplitude in elastic e-N
scattering
k
k
l(k) N(p) ? l(k) N(p),
p
p
For a theory respects Lorentz, parity and
charge conjugation invariance, the elastic
electron-nucleon scattering amplitude can be
expanded in terms of six independent Lorentz
structure, and one can separate the elastic
electron-nucleon scattering amplitude into
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where
In one-photon-exchange approximation, the
phases and all the F3-6 terms vanished, they
must originate from process involving at least
the change of two-photon. Similarly, define
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Observables including two-photon exchange
effect is more visible at large Q2(t)
effect is small as Y2? is small
where Y2? is proportional to the real part of
form factor F3.
P. Guichon and M.Vanderhaeghen,(2003)
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Partonic calculation of two-photon exchange
contribution at large Q2
To estimatedGM,dF2 ,and F3 at large Q2, we
start from calculating the elastic e-q
scattering with massless quarks.
Main contributions comes from handbag
diagrams when both photons are hard at large Q2.
Cats ears diagrams is important for getting
over all IR divergence correct.
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hard scattering amplitude
l(k)
l(k)
l(k) q(pq) ? l(k) q(pq)
H
pq
pq

SDirect and SCross
N(p2)
N(p1)
electron helicity
quark helicity
kinematics for partonic subprocess
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soft part of electron-proton box
where L(z) is the spence function defined by
The sum of the soft part of handbag and cat-ears
diagrams in quark level give the whole soft
contribution of box diagram in nucleon level.
Now, we can separate the soft part from handbag
calculation result.
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Soft part in nucleon level
bremsstrahlung contribution Maximon, Tjon
(2000)
where
IR finite
The maximun energy of the soft emission photon
(?E) dependence on the sensitivity of the
detector. ?E 1 Ee , so the above formula
gives correction factor (1 p a) terms of
size 0.001
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Hard part in nucleon level (GPDs)
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A,B C can be defined by GPD integrals
magnetic GPD
electric GPD
axial GPD
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Final inputs for GPDs
use gaussian-valence model Radyushkin (1998),
Diehl et al. (1999)
s 0.8 GeV2
Forward parton distributions at m2 1 GeV2
MRST2002 NNLO
Leader, Sidorov, Stamenov (2002)
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Fianl inputs for form factor GM R(GE/GM)
R(GE/GM) GE / GM of proton fixed from
polarization data Gayou et al. (2002)
Magnetic proton form factor Brash et al. (2002)
Electirc proton form factor GM x R(GE/GM)
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Result polarization transfer observables
s, -u, Q2 gt M2
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with
Result cross section
s, -u, Q2 gt M2
Y.C. Chen et al. PRL(2004)
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Summary

• Develop the formalism to describe the elastic e-N
  scattering beyond one-photon exchange
  approximation, and performed a partonic
  calculation of two-photon exchange contribtuon in
  GPDs.
• When taking the polarization transfer
  determinations of the form factors input, adding
  in the 2 photon correction, does reproduce the
  cross section data.