Two-photon physics in hadronic processes

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Two-photon physics in hadronic processes

• Marc Vanderhaeghen
• College of William Mary / Jefferson Lab

PPP7 workshop, Taipei, June 7 - 10, 2007
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Outline

• Elastic eN scattering beyond the one-photon
  exchange approximation
• puzzle of different results extracted for
  GE/GM
• in Rosenbluth vs polarization
  experiments
• two-photon exchange processes
• Beam (target) normal spin asymmetry in elastic eN
  scattering
• new observable
• absorptive part of double Virtual
  Compton Scattering (VCS) amplitude
• resonance region, diffractive region,
  partonic estimate (GPDs)
• in coll. with A.Afanasev, S. Brodsky, C.
  Carlson, Y.C. Chen, M. Gorchtein,
• P.A.M. Guichon, V.
  Pascalutsa, B. Pasquini

Carlson, Vdh Ann. Rev. Nucl. Part. Sci. 57
(2007) 171-204
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Early Measurements of GEp

• relied on Rosenbluth separation
• measure d?/d? at constant Q2
• GEp inversely weighted with Q2, increasing the
  systematic error above Q2 1 GeV2

Method at fixed Q2, vary angle q (or
equivalently e) and plot reduced cross section
versus e
At 6 GeV2 ?R changes by only 8 from ?0 to ?1
if GEpGMp/µp Hence, measurement of GEp with 10
accuracy requires 1.6 cross-section measurement
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Spin Transfer Reaction 1H(e,ep)

• No error contributions from
• analyzing power
• beam polarimetry

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Rosenbluth vs polarization transfer measurements
of GE/GM of proton
Puzzle two methods, two different results !
SLAC, Jlab Rosenbluth data
Jlab/Hall A Polarization data Jones et al.
(2000) Gayou et al. (2002)
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Speculation missing radiative corrections
Speculation there are radiative corrections to
Rosenbluth experiments that are
important and are not included
missing correction linear in e, not strongly Q2
dependent
Q2 6 GeV2
GE term is proportionally smaller at large Q2
if both FF scale in same way
effect more visible at large Q2
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Radiative correction diagrams
bremsstrahlung
vertex corrections
2 photon exchange box diagrams
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Status of radiative corrections
N

• Tsai (1961), Mo Tsai (1968)
• box diagram calculated using only nucleon
  intermediate state and using q1 ¼ 0 or q2 ¼ 0 in
  both numerator and denominator (calculate 3-point
  function) -gt gives correct IR divergent terms
• Maximon Tjon (2000)
• same as above, but make the above
  approximation only in numerator (calculate
  4-point function)
• use on-shell nucleon form factors in loop
  integral
• Blunden, Melnitchouk, Tjon (2003)
• further improvement by keeping the full
  numerator

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Elastic eN scattering beyond one-photon exchange
approximation
Kinematical invariants
(me 0)
equivalently, introduce
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Observables including two-photon exchange Real
parts of two-photon amplitudes
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Phenomenological analysis
Guichon, Vdh (2003)
2-photon exchange corrections can become large on
the Rosenbluth extraction,and are of different
size for both observables
relevance when extracting form factors at large
Q2
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Two-photon exchange calculation elastic
contribution
world Rosenbluth data
N
Polarization Transfer
Blunden, Tjon, Melnitchouk (2003, 2005)
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Two-photon exchange partonic calculation
hard scattering amplitude
electron helicity
quark helicity
Calculation for em -gt em can be found in
literature (e.g. van Nieuwenhuizen (1971) ),
which we verified explicitly
IR divergences of boxes must disappear or cancel
in the end, regularize through photon mass l
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Separation soft-hard parts in electron-quark box
Follow the decomposition of Grammer and Yennie
(1973) soft part calculated as 3-point function
reproduces Low Energy Theorem
kinematics partonic subprocess
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Two-photon exchange partonic calculation
hard scattering amplitude
GPD integrals
magnetic GPD
electric GPD
axial GPD
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Two-photon exchange partonic calculation
GPDs
Chen, Afanasev, Brodsky, Carlson, Vdh (2004)
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Experimental verification of TPE contributions

• Experimental verification (will be performed in
  next couple of years ! )
• non-linearity in e-dependence
• (test of model calculations)
• transverse single-spin asymmetry (imaginary part
  of two-photon amplitude)
• ratio of ep and e-p cross section (direct
  measurement of two-photon contributions)

• CLAS experiment E04-116 aims at a measurement of
  the ?-dependence of the e/e- ratio for Q2-values
  up to 2.0 GeV2
• At the VEPP-3 ring that ratio will be measured at
  two ?- and Q2-values

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e - dependence of TPE contributions (I)
Chen, Kao, Yang (2007)
Polynomial fit
log fit
1? only Rosenbluth
1? 2? log fit
1? 2? polynomial fit
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e - dependence of TPE contributions (II)
polynomial fit
log fit
Chen, Kao, Yang (2007)
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Polarization transfer observables
1g 2g
1g
2 g correction on is small
2 g correction on can be tested at
small e !
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proton Dirac Pauli FFs
GPD framework
PQCD
modified Regge GPD model
data SLAC
data JLab/HallA
data JLab/HallA
Belitsky, Ji, Yuan (2003)
Guidal, Polyakov, Radyushkin, Vdh (2005)
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Normal spin asymmetries in elastic eN scattering
directly proportional to the imaginary part of
2-photon exchange amplitudes
spin of beam OR target NORMAL to scattering plane

OR
on-shell intermediate state
order of magnitude estimates
target
beam
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SSA in elastic eN scattering
time reversed states
momenta and spins reversed
rotation over 180o around axis ? to plane
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Unitarity
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Perturbation theory in ?em
1 ? exchange gives no contribution to spin
asymmetries
spin asymmetries arise from interference between
1? exchange and absorptive part of 2? exchange
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to
De Rujula et al. (1971)
1? exchange
function of elastic nucleon form factors
2? exchange
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• elastic contribution

on-shell nucleon intermediate nucleon

• inelastic contribution

X ? N
resonant and non-resonant ? N intermediate states
calculated with MAID2003 unitary isobar model
all 13 resonances below 2 GeV included
Drechsel, Hanstein, Kamalov, Tiator (1999)
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Beam normal spin asymmetry
Pasquini Vdh (2004)
for Ee 0.570 GeV Bn -8.590.89 ppm
measurement of resonance form factors over range
in Q2
New measurements at MAMI at backward angles
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x10-6
Bn
Bn in diffractive region
Q2 0.05 GeV2
E158 Bn -3.5 -gt -2.5 ppm (K. Kumar,
prelim.)
no suppression of Bn with energy at fixed Q2
ps (GeV)
Afanasev Merenkov
s?p
Note on SLAC E158 30 inelastic events included
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Beam normal spin asymmetry experiments
Expt. E(GeV) ?e Q2 GeV2 Bn(ppm)
SAMPLE 0.192 146 0.10 -16.45.9
A4 0.570 35 0.11 -8.590.89
A4 0.855 35 0.23 -8.522.31
HAPPEX 3.0 16 0.11 -6.7 1.5
G0 3.0 19 0.15 -4.06 1.62
G0 3.0 37 0.25 -4.82 2.85
E-158(ep) 46.0 3.0 0.06 -3.5 -gt -2.5
E-158(ee) 46.0 100 0.03
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Elastic electron-nucleon amplitudes with electron
helicity flip
In Born approximation
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Elastic electron-quark amplitudes with electron
helicity flip
lepton mass
new amplitude
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Beam normal spin asymmetry partonic calculation
magnetic GPD
electric GPD
magnetic GPD
electric GPD
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Beam normal spin asymmetry proton results
Results of GPD calculation
Note elastic contribution to Bn is negligibly
small
Future PV experimental set-ups (0.1 ppm
precision) challenge to measure this asymmetry
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Summary
difference Rosenbluth vs polarization data -gt GEp
/GMp now mainly understood as due to two-photon
exchange effects -gt quantitative theoretical
calculations needed -gt precision test several
new expt. planned
Normal spin asymmetries (NSA) in elastic
electron-nucleon scattering unique new tool to
access the imaginary part of 2? exchange
amplitudes -gt Imaginary part of 2? amplitude
absorptive part of non-forward doubly
VCS tensor -gt Unitarity to relate the absorptive
part of doubly VCS tensor to
pion-electroproduction amplitudes
beam NSA in the resonance region as a new tool to
extract resonance transition form
factors -gt In hard scattering region use
handbag approach to relate beam and target NSA to
moments of GPDs