Probing inelastic states with elastic ep scattering via QED loops

1. Probing inelastic states with elastic ep scattering via QED loops Andrei Afanasev Jefferson Lab DIS 2005 Madison, WI 4/29/05

2. Plan of talk • Proton form factor measuments • Two-photon exchange problem • New things learned: VCS with two space-like photons • GPD-framework calculation • Anomalous behavior of Mott asymmetry at high energies

3. Elastic electron scattering and nucleon structure • Study Form Factors at high Q2: • QCD, GPDs; Helicity Flip; OAM; Ji’s sum rule • Status of nucleon form factor measurements : • See review C.Hyde-Wright, K. de Jager, Annu.Rev.Nucl.Part.Sci. 54, 217 (2004)

4. Elastic Nucleon Form Factors • Based on one-photon exchange approximation • Two techniques to measure

5. 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 ~5% difference in cross-section ~500% difference in polarization JLab/Polarization

6. Radiative Corrections for Elastic (eP) Scattering • 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 Main issue: Corrections dependent on nucleon structure; Model calculations by Blunden, Melnitchuk,Tjon, Phys.Rev.Lett.91:142304,2003 Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004

7. Lorentz Structure of 2-γ amplitude

8. New Expressions for Observables We can formally define ep-scattering observables in terms of the new form factors: For the target asymmetries: Ax=Px, Ay=Py, Az=-Pz

9. Calculations using Generalized Parton Distributions • Model schematics: • Hard eq-interaction • GPDs describe quark emission/absorption • Soft/hard separation • Use Grammer-Yennie prescription Hard interaction with a quark

10. 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 is zero ε δSoft Q2= 6 GeV2

11. Short-range effects(AA, Brodsky, Carlson, Chen,Vanderhaeghen) Two-photon probe directly interacts with a (massless) quark Emission/reabsorption of the quark is described by GPDs

12. `Hard’ contributions to generalizedform factors GPD integrals Two-photon-exchange form factors from GPDs

13. 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

14. Updated Ge/Gm plot

15. Polarization transfer (ibid.) • Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio

16. 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 • Parity-violating measurements of strange-quark content of the nucleon are also affected: AA, Carlson, Δs may shift by ~10%, to appear PRL(2005)

17. Loop integration limits • Infinite limits for the real (dispersive) amplitude, both intermediate photons are space-like, 4-dimensional integration => enters cross section, double-spin asymmetries, charge asymmetry • One (two) constraints are set for the inelastic (elastic) absorptive amplitude through Cutkosky cuts: example E=5 GeV, inelastic at Q2=4 GeV2, (left), elastic at varied Q2 (right) => enters beam and target single-spin asymmetries

18. Phase Space Contributing to An (or Pn) • 2-dimensional integration (Q12, Q22) for the elastic intermediate state • 3-dimensional integration (Q12, Q22,W2) for inelastic excitations W2 Q22 Q12

19. Quark+Nucleon Contributions to An • 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

20. Proton Mott Asymmetry at Higher Energies Spin-orbit interaction of electron moving in a Coulomb field N.F. Mott, Proc. Roy. Soc. London, Set. A 135, 429 (1932). • 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 (αme/Ebeam) suppression, units are parts per million calculation by AA et al, hep-ph/0208260

21. 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

22. Beam Normal Asymmetry(AA, Merenkov) Cancellation of infra-red singularity: Feature of the normal beam asymmetry: After me is factored out, the remaining expression is singular when virtuality of the photons reach zero in the loop integral! Also available calculations by Gorshtein, Guichon, Vanderhaeghen, Pasquini; Confirm quasi-real photon exchange enhancement in the nucleon resonance region

23. Special property of normal beam asymmetry AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004 • 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(-BQ2), where B=3.5-4 GeV-2Compare with no-structure asymmetry at small θ:

24. No suppression for beam asymmetry with energyat fixed Q2 x10-9 x10-6 SLAC E158 kinematics Parts-per-milllion vs. parts-per billion scales: a consequence of Nucleon structure and soft Pomeron exchange

25. 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: log2(Q2/me2) => two orders of magnitude+unsuppressed angular dependence. • Beam asymmetry at high energies is strongly affected by effects beyond pure Coulomb distortion • What else can we learn from elastic beam SSA? • Two-Photon Pomeron coupling non-diagonal in photon helicity • Check implications of elastic hadron scattering in QCD (Can large AN in pp elastic be due to onset of collinear multi-gluon exchange + inelastic excitations?)

26. Two-photon exchange for electron-proton scattering • 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 Generalized Parton Distributions bring into agreement the results of polarization transfer and Rosenbluth techniques for Gep measurements • Collinear photon exchange dominance for beam asymmetry • Experimental tests of multi-photon exchange • Comparison between electron and positron elastic scattering • Measurement of nonlinearity of Rosenbluth plot • Search for deviation of angular dependence of polarization and/or asymmetries from Born behavior at fixed Q2 • Elastic single-spin asymmetry or induced polarization • All above tests are now approved JLab experiments => a program of double-virtual VCS studies with two spacelike photons