Outline

1. 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

2. 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:

3. at a fix Q2, vary ε ( 1/ε= 1 +2(1+τ)tan2(θlab/2) ) Rosenbluth separationmethod (LT) reduced cross section: Polarization transfer method Polarized electron beam → sideways and longitudinal polarization for recoil proton

4. Two independent measurement of R(GE/GM) SLAC Rosenbluth data Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002) Twomethods, twodifferentresults !

5. 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:

6. where In one-photon-exchange approximation, thephases and all the F3-6 terms vanished, they must originate from process involving at least the change of two-photon. Similarly, define

7. Observables including two-photon exchange effect is more visible at large Q2(τ) effect is small as Y2γis small where Y2γis proportional to the real part of form factor F3. P. Guichon and M.Vanderhaeghen,(2003)

8. Partonic calculation of two-photon exchange contribution at large Q2 To estimateδGM,δF2 ,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. • “Cat’s ears” diagrams is important for getting over all IR divergence correct.

9. hard scattering amplitude l(k’) l(k) l(k) + q(pq) → l(k’) + q(p’q) H pq p’q + SDirect and SCross N(p2) N(p1) electron helicity quark helicity kinematics for partonic subprocess :

10. λ is infinitesimal photon mass soft soft soft soft soft soft soft

11. 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.

12. Soft part in nucleon level bremsstrahlung contribution : Maximon, Tjon (2000) where IR finite The maximun energy of the soft emission photon (ΔE) dependence on the sensitivity of the detector. ΔE ≈ 1% E’e , so the above formula gives correction factor (1 + p a) + terms of size 0.001

13. result for e-q scattering amplitude work in frame q+ = 0, nm is a Sudakov vector ( n2 = 0, n . P = 1 ) handbag amplitude depends onGPD(x, x = 0, Q2), x=Pq+/P+ Hard part in nucleon level (GPDs)

14. A,B & C can be defined by GPD integrals “magnetic” GPD “electric” GPD “axial” GPD

15. 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)

16. Fianl inputs for form factor GM & R(GE/GM) R(GE/GM) : GE / GM of proton fixed from polarization dataGayou et al. (2002) Magnetic proton form factor: Brash et al. (2002) Electirc proton form factor: GM x R(GE/GM)

17. Result: polarization transfer observables s, -u, Q2 > M2

18. Result: cross section with s, -u, Q2 > M2 Y.C. Chen et al. PRL(2004)

20. 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.