1. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Beam Normal Spin Asymmetry on Nuclear Targets Andrei Afanasev Jefferson Lab Hall A Collaboration Meeting, December 5, 2005 Collaborator: N. Merenkov

2. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Single-Spin Asymmetries in Elastic Electron Scattering Parity-conserving. Observed spin-momentum correlation of the type: where k 1,2 are initial and final electron momenta, s is a polarization vector of a target OR beam. For elastic scattering asymmetries are due to absorptive part of 2-photon exchange amplitude. Parity-Violating (nonzero for one-boson exchange)

3. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Parity-Conserving Single-Spin Asymmetries in Scattering Processes (early history). N. F. Mott, Proc. R. Soc. (London), A124, 425 (1929), noticed that polarization and/or asymmetry is due to spin-orbit coupling in the Coulomb scattering of electrons (Extended to high energy ep- scattering by AA et al., 2002).. Julian Schwinger, Phys. Rev. 69, 681 (1946); ibid., 73, 407 (1948), suggested a method to polarize fast neutrons via spin-orbit interaction in the scattering off nuclei. Lincoln Wolfeinstein, Phys. Rev. 75, 1664 (1949); A. Simon, T.A.Welton, Phys. Rev. 90, 1036 (1953), formalism of polarization effects in nuclear reactions

4. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 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; shown is elastic contribution. Nonzero effect observed by SAMPLE Collaboration (S.Wells et al., PRC63:064001,2001) for 200 MeV electrons. Calculations of Diaconescu, Ramsey-Musolf (2004): low-energy expansion version of hep- ph/0208260 Transverse beam SSA, units are parts per million Figures from AA et al, hep-ph/0208260 BNSA for electron-muon scattering: Barut, Fronsdal, Phys.Rev.120, 1871 (1960); BNSA for electron-proton scattering: Afanasev, Akushevich, Merenkov, hep-ph/0208260

5. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy MAMI data on Mott Asymmetry. F. Maas et al., [MAMI A4 Collab.] Phys.Rev.Lett.94:082001, 2005. Pasquini, Vanderhaeghen: Phys.Rev.C70:045206,2004 Surprising result: Dominance of inelastic intermediate excitations Elastic intermediate state Inelastic excitations dominate

6. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 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 for target asymmetry 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 calculations by Vanderhaeghen, Pasquini (2004); Gorchtein, hep-ph/0505022; Kobushkin, nucl-th/0508053 confirm quasi-real photon exchange enhancement

7. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 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 Examples: MAMI A4 E= 855 MeV Θcm= 57 deg; SAMPLE, E=200 MeV; Θcm= 145 deg `Soft intermediate electron; Both photons are hard collinear One photon is Hard collinear

8. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Special property of Mott asymmetry at high energy. 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 ); B(proton)=3.5-4 GeV -2 Compare with no-structure (= Coulomb distortion) asymmetry at small θ: AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004; +Erratum (hep-ph/0407167v2)

9. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Input parameters σ γp from N. Bianchi at al., Phys.Rev.C54 (1996)1688 (resonance region) and Block&Halzen, Phys.Rev. D70 (2004) 091901 For small-angle (-t/s<<1) scattering of electrons with energies Ee, normal beam asymmetry is given by the energy-weighted integral

10. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Predictions for Mott asymmetry Use fit to experimental data on σ γp and exact 3-dimensional integration over phase space of intermediate 2 photons HAPPEX Data from HAPPEX More to come from G0

11. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Mott asymmetry in the nucleon resonance region Data from MAMI: F. Maas et al., Phys.Rev.Lett.94:082001, 2005

12. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy No suppression for Mott asymmetry with energy at fixed Q 2 x10 -6 x10 -9 Parts-per-million vs. parts-per billion scales: a consequence of non-decreasing σ total, and hard collinear photon exchange SLAC E158 kinematics

13. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Normal Beam Asymmetry on Nuclei. Important systematic correction for parity-violation experiments (HAPPEX on 4 He, PREX on Pb). Measures (integrated) absorptive part of Compton scattering amplitude. Coulomb distortion: only10 -10 effect (Cooper&Horowitz, Phys.Rev.C72:034602,2005) Five orders of magnitude enhancement in HAPPEX kinematics due to excitation of inelastic intermediate states in 2γ-exchange (Normal Asymmetry -5+/-1ppm for PREX)

14. Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005 Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy Summary on Mott Asymmetry in Elastic ep-Scattering. BNSA at small scattering angles evaluated using an optical theorem. Predictions for HAPPEX (p and 4 He) consistent with experiment. Prediction for PREX is -5±1ppm. Strong-interaction dynamics for BNSA small-angle ep-scattering above the resonance region is soft diffraction. For the diffractive mechanism A n. a) Is not suppressed with beam energy (vs 1/E for Coulomb). b) Scales as ~A/Z up to shadowing corrections (vs ~Z for Coulomb distortion). c) Proportional ~Q for small angles (vs ~Q 3 for Coulomb). If confirmed experimentally first observation of diffractive component in elastic electron-hadron scattering