Beam Normal Spin Asymmetry on Nuclear Targets

1. Beam Normal Spin Asymmetryon Nuclear Targets Andrei Afanasev Jefferson Lab Hall A Collaboration Meeting, December 5, 2005 Collaborator: N. Merenkov

2. Single-Spin Asymmetries in Elastic Electron Scattering Parity-conserving • Observed spin-momentum correlation of the type: where k1,2are 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. 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. Proton Mott Asymmetry at Higher Energies BNSA for electron-muon scattering: Barut, Fronsdal, Phys.Rev.120, 1871 (1960); BNSA for electron-proton scattering: Afanasev, Akushevich, Merenkov, hep-ph/0208260 • 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

5. 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. Beam Normal Asymmetry(AA, Merenkov) Gauge invariance essential in cancellation of infra-red singularity for target asymmetry 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! 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. Phase Space Contributing to the absorptivepart of 2γ-exchange amplitude • 2-dimensional integration (Q12, Q22) for the elastic intermediate state • 3-dimensional integration (Q12, Q22,W2) 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. Special property of Mott asymmetry at high energy AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004; +Erratum (hep-ph/0407167v2) • 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); B(proton)=3.5-4 GeV-2Compare with no-structure (= Coulomb distortion) asymmetry at small θ:

9. Input parameters For small-angle (-t/s<<1) scattering of electrons with energies Ee , normal beam asymmetry is given by the energy-weighted integral σγpfrom N. Bianchi at al., Phys.Rev.C54 (1996)1688 (resonance region) and Block&Halzen, Phys.Rev. D70 (2004) 091901

10. Predictions for Mott asymmetry Use fit to experimental data on σγp and exact 3-dimensional integration over phase space of intermediate 2 photons Data from HAPPEX More to come from G0 HAPPEX

11. Mott asymmetry in the nucleon resonance region Data from MAMI: F. Maas et al., Phys.Rev.Lett.94:082001,2005

12. No suppression for Mott asymmetry with energyat fixed Q2 x10-9 x10-6 SLAC E158 kinematics Parts-per-million vs. parts-per billion scales: a consequence of non-decreasing σtotal, and hard collinear photon exchange

13. Normal Beam Asymmetry on Nuclei • Important systematic correction for parity-violation experiments (HAPPEX on 4He, 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. Summary on Mott Asymmetry in Elastic ep-Scattering • BNSA at small scattering angles evaluated using an optical theorem • Predictions for HAPPEX (p and 4He) 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 An • 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 ~Q3 for Coulomb) • If confirmed experimentally → first observation of diffractive component in elastic electron-hadron scattering