Twophoton physics in elastic electronnucleon scattering

1
Two-photon physics in elastic
electron-nucleonscattering

• Marc Vanderhaeghen
• College of William Mary / JLab

JLab, May 12th 2004
2
Outline

• Introduction Rosenbluth vs polarization
  measurements of GE and GM of nucleon
• puzzle different results
  extracted for GE/GM
• Elastic electron-nucleon scattering beyond the
  one-photon exchange approximation
• Partonic calculation of two-photon exchange
  contribution
• generalized parton
  distributions of nucleon
• Results for cross section and polarization
  transfer
• SSA in elastic electron-nucleon scattering
• P.A.M. Guichon, M.Vdh PRL 91, 142303 (2003)
• Y.C. Chen, A.Afanasev, S. Brodsky, C. Carlson,
  M.Vdh hep-ph/0403058
• M. Gorchtein, P.A.M. Guichon, M. Vdh
  hep-ph/0404206
• B. Pasquini, M. Vdh in progress

3
Introduction
Rosenbluth separation method
One-photon exchange elastic electron-nucleon
cross section
Method at fixed Q2, vary angle q (or
equivalently e) and plot reduced cross
section versus e
4
One-photon theorists view
5
Polarization transfer method
Method measure ratio of sideways ( ) to
longitudinal ( ) recoil polarization of
proton (absolute normalization drops out !)
in one-photon exchange approximation
6
Rosenbluth vs polarization transfer measurements
of GE/GM of proton
SLAC Rosenbluth data
Jlab/Hall A Polarization data Jones et al.
(2000) Gayou et al. (2002)
Two methods, two different results !
7
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
8
Radiative correction diagrams
bremsstrahlung
vertex corrections
2 photon exchange box diagrams
9
Comments on radiative corrections

• Radiative corrections at electron side,
• well understood and taken care of
• Soft bremsstrahlung
• involves long-wavelength photons
• compositeness of nucleon only enters
  through
• on-shell form factors
• Box diagrams involve photons of all wavelengths
• long wavelength (soft photon) part is
  included in radiative correction (IR divergence
  is cancelled with electron proton bremsstrahlung
  interference)
• short wavelength contributions
• not done in old days

10
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

11
Elastic eN scattering beyond one-photon exchange
approximation
Kinematical invariants
(me 0)
equivalently, introduce
12
Observables including two-photon exchange Real
parts of two-photon amplitudes
13
Phenomenological analysis
2-photon exchange is a candidate to explain the
discrepancy between both experimental methods
Guichon, Vdh (2003)
14
Partonic calculation of two-photon exchange
contribution
handbag
cats ears

• main contribution at large Q2
• handbag diagrams (one active quark)
• to reproduce the IR divergent contribution at
  nucleon correctly (i.e. to satisfy the Low Energy
  Theorem)
• need cats ears diagrams (two active quarks)

15
Calculation of hard scattering amplitude
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
16
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
17
Calculation of soft part at nucleon level
LET sum of soft contributions from the partonic
calculation has to match the soft contributions
at nucleonic level
To satisfy the LET, one has to include the
soft-photon contributions from the cats ears
diagrams
Pictorially
soft
soft
soft
soft
18
Calculation of bremsstrahlung
IR finite
soft part of electron-nucleon box
bremsstrahlung contribution Maximon, Tjon
(2000)
Experimentalists do corrections according to
Mo-Tsai relative to Mo-Tsai, the above formula
gives a correction factor (1 p a) terms of
size 0.001
19
Convolution with GPDs
result for handbag amplitude (large Q2 )
work in frame q 0, nm is a Sudakov vector (
n2 0, n . P 1 )
handbag amplitude depends on GPD(x, x 0,
Q2), which also appear in other wide angle
scattering processes (e.g. WACS)
20
Hard part to invariant amplitudes for elastic eN
scattering
GPD integrals
magnetic GPD
electric GPD
axial GPD
21
Observables including two-photon exchange in
terms of A, B, C (real parts)
22
Model for GPDs at large Q2
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)
23
Test of GPDs models form factors
gaussian valence model
non-linear Regge model
24
Form factors used as input in calculation
magnetic proton form factor Brash et al. (2002)
electric proton form factor GE / GM of proton
fixed from polarization data Gayou et al. (2002)
25
with
Cross section
1g 2g (hardsoft)
1 g
1g 2g (hard)
26
with
Cross section
1 g
1g 2g (non-linear Regge model )
1g 2g (gaussian valence model )
27
e / e- Ratio
Direct test of real part of 2g amplitude
data figure from Arrington (2003)
28
Polarization transfer observables
1g 2g
1g
2 g correction on is small
2 g correction on can be tested at
small e !
29
SSA in elastic eN scattering
spin of beam OR target NORMAL to scattering plane

on-shell intermediate state (MX W)
lepton
hadron
30
Integrand beam normal spin asymmetry
Ee 0.855 GeV
MAID
31
Beam normal spin asymmetry
(elastic)
MAMI data (prelim.)
32
Target normal spin asymmetry
general formula, of order e2
involves the imaginary part of two-photon
exchange amplitudes
33
Target normal spin asymmetry partonic
calculation
two-photon electron-quark amplitude
magnetic GPD
electric GPD
34
Target normal spin asymmetry PROTON results

GM term
GPD prediction
elastic
GE term
JLab proposals could reach 0.1 precision
35
Target normal spin asymmetry NEUTRON results
GE term

elastic
GPD prediction
GM term
sizeable asymmetry on neutron no cancellation
effect as on proton
36
Elastic electron-nucleon amplitudes with
electron helicity flip
In Born approximation
37
Elastic electron-quark amplitudes with electron
helicity flip
lepton mass
new amplitude
38
Beam normal spin asymmetry partonic calculation
magnetic GPD
electric GPD
magnetic GPD
electric GPD
39
Beam normal spin asymmetry results
Results of GPD calculation
Note elastic contribution to Bn is negligibly
small
Present PV experimental set-ups (0.1 ppm
precision) opportunity to measure this
asymmetry
40
Conclusions

• Developed the formalism to describe elastic
  electron-nucleon scattering beyond the one-photon
  exchange approximation
• Performed a partonic calculation of two-photon
  exchange contribution in terms of generalized
  parton distributions of nucleon (handbag
  calculation)
• Able to resolve existing discrepancy between
  Rosenbluth and polarization transfer observables
  quantitatively
• SSA in elastic electron-nucleon scattering
• promising observables to access doubly
  (spacelike) virtual Compton scattering