1. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Two-Photon Exchange for Elastic Electron-Nucleon Scattering Andrei Afanasev Jefferson Lab JLab Users Workshop June 22, 2005

2. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Plan of talk Two-photon exchange effects in the process e+p→e+p. Models for two-photon exchange. Cross sections. Polarization transfer. Single-spin asymmetries. Parity-violating asymmetry. Refined bremsstrahlung calculations

3. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Elastic Nucleon Form Factors Based on one-photon exchange approximation Two techniques to measure Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross

4. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Do the techniques agree?. Both early SLAC and Recent JLab experiments on (super)Rosenbluth separations followed Ge/Gm~const. JLab measurements using polarization transfer technique give different results (Jones’00, Gayou’02) Radiative corrections, in particular, a short-range part of 2-photon exchange is a likely origin of the discrepancy SLAC/Rosenbluth JLab/Polarization ~5% difference in cross-section

5. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Electron Scattering: LO and NLO in α em Radiative Corrections: Electron vertex correction (a) Vacuum polarization (b) Electron bremsstrahlung (c,d) Two-photon exchange (e,f) Proton vertex and VCS (g,h) Corrections (e-h) depend on the nucleon structure Guichon&Vanderhaeghen’03: Can (e-f) account for the Rosenbluth vs. polarization experimental discrepancy? Look for ~3%... Main issue: Corrections dependent on nucleon structure Model calculations: Blunden, Melnitchuk,Tjon, Phys.Rev.Lett.91:142304,2003 Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004

6. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Separating soft photon exchange. Tsai; Maximon & Tjon. We used Grammer &Yennie prescription PRD 8, 4332 (1973) (also applied in QCD calculations). Shown is the resulting (soft) QED correction to cross section. NB: Corresponding effect to polarization transfer and/or asymmetry is zero ε δ Soft Q 2 = 6 GeV 2

7. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Lorentz Structure of 2-γ amplitude Generalized form factors are functions of two Mandelstam invariants; Specific dependence is determined by nucleon structure

8. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy New Expressions for Observables We can formally define ep-scattering observables in terms of the new form factors: For the target asymmetries: A x =P x, A y =P y, A z =-P z

9. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Calculations using Generalized Parton Distributions Hard interaction with a quark Model schematics: Hard eq-interaction GPDs describe quark emission/absorption Soft/hard separation Use Grammer-Yennie prescription AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013

10. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Short-range effects; on-mass-shell quark (AA, Brodsky, Carlson, Chen,Vanderhaeghen) Two-photon probe directly interacts with a (massless) quark Emission/reabsorption of the quark is described by GPDs Note the additional effective (axial-vector) 2 interaction; absence of mass terms

11. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy `Hard’ contributions to generalized form factors GPD integrals Two-photon-exchange form factors from GPDs

12. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Two-Photon Effect for Rosenbluth Cross Sections. Data shown are from Andivahis et al, PRD 50, 5491 (1994). Included GPD calculation of two- photon-exchange effect. Qualitative agreement with data:. Discrepancy likely reconciled

13. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Two-Photon Effect for Rosenbluth Cross Sections. Blunden, Melnitchouk, Tjon, Phys.Rev.Lett.91:142304,2003; nucl- th/0506039

14. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Updated Ge/Gm plot AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013

15. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Polarization transfer. Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio

16. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Charge asymmetry. Cross sections of electron-proton scattering and positron-proton scattering are equal in one-photon exchange approximation. Different for two- or more photon exchange To be measured in JLab Experiment 04-116, Spokepersons W. Brooks et al.

17. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Quark+Nucleon Contributions to A n. Single-spin asymmetry or polarization normal to the scattering plane. Handbag mechanism prediction for single-spin asymmetry/polarization of elastic ep-scattering on a polarized proton target Only minor role of quark mass

18. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Parity Violating elastic e-N scattering Longitudinally polarized electrons, unpolarized target Neutral weak form factors contain explicit contributions from strange sea G Z A (0) = 1.2673 ± 0.0035 (from  decay)  = Q 2 /4M 2  = [1+2(1+  )tan 2 (  /2)] -1  ’= [  (  +1)(1-  2 )] 1/2

19. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy 2γ-exchange Correction to Parity-Violating Electron Scattering. New parity violating terms due to (2gamma)x(Z 0 ) interference should be added: x γγ Z0Z0 Electromagnetic Neutral Weak

20. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy GPD Calculation of 2γ×Z-interference. Can be used at higher Q 2, but points at a problem of additional systematic corrections for parity-violating electron scattering. The effect evaluated in GPD formalism is the largest for backward angles: AA & Carlson, hep-ph/0502128, Phys. Rev. Lett. 94, 212301 (2005): measurements of strange-quark content of the nucleon are affected, Δs may shift by ~10% Important note: (nonsoft) 2γ-exchange amplitude has no 1/Q 2 singularity; 1γ-exchange is 1/Q 2 singular => At low Q2, 2γ-corrections is suppressed as Q 2 P. Blunden used this formalism and evaluated correction of 0.16% for Q weak

21. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Proton Mott Asymmetry at Higher Energies. Due to absorptive part of two-photon exchange amplitude (elastic contribution: dotted, elastic+inelastic: solid curve for target case). Nonzero effect observed by SAMPLE Collab for beam asymmetry (S.Wells et al., PRC63:064001,2001) for 200 MeV electrons Transverse beam SSA, note (α m e /E beam) suppression, units are parts per million calculation by AA et al, hep-ph/0208260 Spin-orbit interaction of electron moving in a Coulomb field N.F. Mott, Proc. Roy. Soc. London, Set. A 135, 429 (1932).

22. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy MAMI data on Mott Asymmetry. F. Maas et al., Phys.Rev.Lett.94:082001, 2005. Pasquini, Vanderhaeghen: Surprising result: Dominance of inelastic intermediate excitations Elastic intermediate state Inelastic excitations dominate

23. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Beam Normal Asymmetry (AA, Merenkov) Gauge invariance essential in cancellation of infra-red singularity: Feature of the normal beam asymmetry: After m e is factored out, the remaining expression is singular when virtuality of the photons reach zero in the loop integral! But why are the expressions regular for the target SSA?! Also available calculations by Gorshtein, Guichon, Vanderhaeghen, Pasquini; Confirm quasi-real photon exchange enhancement in the nucleon resonance region

24. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Phase Space Contributing to the absorptive part of 2γ-exchange amplitude. 2-dimensional integration (Q 1 2, Q 2 2 ) for the elastic intermediate state. 3-dimensional integration (Q 1 2, Q 2 2,W 2 ) for inelastic excitations Example: MAMI A4 E= 855 MeV Θcm= 57 deg `Soft’ intermediate electron; Both photons are hard collinear One photon is Hard collinear

25. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Peaking Approximation. Dominance of collinear-photon exchange =>. Can replace 3-dimensional integral over (Q 1 2,Q 2 2,W) with one- dimensional integral along the line (Q 1 2 ≈0; Q 2 2 =Q 2 (s-W 2 )/(s-M 2 )). Save computing time. Avoid uncertainties associated with (unknown) double-virtual Compton amplitude. Provides more direct connection to VCS and RCS observables

26. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Special property of normal beam asymmetry. Reason for the unexpected behavior: hard collinear quasi-real photons. Intermediate photon is collinear to the parent electron. It generates a dynamical pole and logarithmic enhancement of inelastic excitations of the intermediate hadronic state. For s>>-t and above the resonance region, the asymmetry is given by: Also suppressed by a standard diffractive factor exp(-BQ 2 ), where B=3.5-4 GeV -2 Compare with no-structure asymmetry at small θ: AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004; +Erratum (2005)

27. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Input parameters. Used σ γp from parameterization by N. Bianchi at al., Phys.Rev.C54 (1996)1688 (resonance region) and Block&Halzen, Phys.Rev. D70 (2004) 091901

28. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Predictions for normal beam asymmetry Use fit to experimental data on σ γp and exact 3-dimensional integration over phase space of intermediate 2 photons HAPPEX Data expected from HAPPEX, G0

29. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy No suppression for beam asymmetry with energy at fixed Q 2 x10 -6 x10 -9 Parts-per-million vs. parts-per billion scales: a consequence of soft Pomeron exchange, and hard collinear photon exchange SLAC E158 kinematics

30. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Beam SSA in the resonance region

31. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Trouble with `Handbag’ for beam normal asymmetry Model schematics: Hard eq-interaction GPDs describe quark emission/absorption Soft/hard photon separation Use Grammer-Yennie prescription Hard interaction with a quark Applied for BSSA by Gorshtein, Guichon, Vanderhaeghen, NP A741, 234 (2004) Exchange of hard collinear photons is kinematically forbidden if one assumes a handbag approximation (placing quarks on mass shell), BUT… Collinear-photon-exchange enhancement (up to two orders of magnitude) is allowed for off-mass-shell quarks (higher twists) and Regge-like contributions => If the handbag approximation is violated at ≈ 0.5% level, It would result in (0.5%)log 2 (Q 2 /m e 2 ) ≈100% level correction to beam asymmetry  But target asymmetry, TPE corrections to Rosenbluth and polarization transfer predictions will be violated at the same 0.5% level

32. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Lessons from SSA in Elastic ep-Scattering. Collinear photon exchange present in (light particle) beam SSA. (Electromagnetic) gauge invariance of is essential for cancellation of collinear-photon exchange contribution for a (heavy) target SSA. Unitarity is very helpful in reducing model dependence of calculations at small scattering angles, in particular for beam asymmetry

33. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Mott Asymmetry Promoted to High Energies. Excitation of inelastic hadronic intermediate states by the consecutive exchange of two photons leads to logarithmic and double-logarithmic enhancement due to contributions of hard collinear quasi-real photons for the beam normal asymmetry. The strongest enhancement has a form: log 2 (Q 2 /m e 2 ) => two orders of magnitude+unsuppressed angular dependence. Can be generalized to transverse asymmetries in light spin-1/2 particle scattering via massless gauge boson exchange. Beam asymmetry at high energies is strongly affected by effects beyond pure Coulomb distortion. Supports Qiu-Sterman twist-3 picture of SSA in QCD. What else can we learn from elastic beam SSA?. Check implications of elastic hadron scattering in QCD (Can large A n,t in pp elastic be due to onset of collinear multi-gluon exchange + inelastic excitations?). Large SSA in deep-inelastic collisions due to hard collinear gluon exchange; in pQCD need NNLO to obtain unsupressed collinear gluons

34. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Full Calculation of Bethe-Heitler Contribution Radiative leptonic tensor in full form AA et al, PLB 514, 269 (2001) Additional effect of full soft+hard brem → +1.2% correction to ε-slope Resolves additional ~25% of Rosenbluth/polarization discrepancy! Additional work by AA at al., using MASCARAD (Phys.Rev.D64:113009,2001) Full calculation including soft and hard bremsstrahlung

35. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Bethe-Heitler corrections to polarization transfer and cross sections AA, Akushevich, Merenkov Phys.Rev.D64:113009,2001; AA, Akushevich, Ilychev, Merenkov, PL B514, 269 (2001) Pion threshold: u m =m π 2 In kinematic of elastic ep-scattering measurements, cross sections are more sensitive to RC

36. Andrei Afanasev, JLab Users Workshop, 6/22/05 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy. Quark-level short-range contributions are substantial (3-4%) ; correspond to J=0 fixed pole (Brodsky-Close-Gunion, PRD 5, 1384 (1972)).. Structure-dependent radiative corrections calculated using GPDs bring into agreement the results of polarization transfer and Rosenbluth techniques for Gep measurements. Full treatment of brem corrections removed ~25% of R/P discrepancy in addition to 2γ. Collinear photon exchange + inelastic excitations dominance for beam asymmetry. Experimental tests of multi-photon exchange. Comparison between electron and positron elastic scattering (JLab E04-116). Measurement of nonlinearity of Rosenbluth plot (JLab E05-017). Search for deviation of angular dependence of polarization and/or asymmetries from Born behavior at fixed Q 2 (JLab E04-019). Elastic single-spin asymmetry or induced polarization (JLab E05-015). 2γ add-ons for parity-violating measurements (HAPPEX, G0) Through active theoretical support emerged JLab research program of Testing precision of the electromagnetic probe Double-virtual VCS studies with two spacelike photons Two-photon exchange for electron-proton scattering