Beam Normal Spin Asymmetry on Nuclear Targets

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Beam Normal Spin Asymmetryon Nuclear Targets

• Andrei Afanasev
• Jefferson Lab
• Hall A Collaboration Meeting, December 5, 2005

Collaborator N. Merenkov
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Single-Spin Asymmetries in Elastic Electron
Scattering

• Parity-conserving
• Observed spin-momentum correlation of the type
• where k1,2 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
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

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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
Transverse beam SSA, units are parts per million
Figures from AA et al, 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., PRC63064001,2001) for 200 MeV
  electrons
• Calculations of Diaconescu, Ramsey-Musolf (2004)
  low-energy expansion version of hep-ph/0208260

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MAMI data on Mott Asymmetry

• F. Maas et al., MAMI A4 Collab.
• Phys.Rev.Lett.94082001, 2005
• Pasquini, Vanderhaeghen
• Phys.Rev.C70045206,2004
• Surprising result Dominance of inelastic
  intermediate excitations

Elastic intermediate state
Inelastic excitations dominate
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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
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Phase Space Contributing to the absorptivepart
of 2?-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 Tcm 57 deg SAMPLE,
E200 MeV Tcm 145 deg
Soft intermediate electron Both photons are
hard collinear
One photon is Hard collinear
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Special property of Mott asymmetry at high energy
AA, Merenkov, Phys.Lett.B59948,2004,
Phys.Rev.D70073002,2004 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 sgtgt-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-2 Compare with
no-structure ( Coulomb distortion) asymmetry at
small ?
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Input parameters
For small-angle (-t/sltlt1) scattering of electrons
with energies Ee , normal beam asymmetry is
given by the energy-weighted integral

• s?p from N. Bianchi at al., Phys.Rev.C54
  (1996)1688 (resonance region) and BlockHalzen,
• Phys.Rev. D70 (2004) 091901

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Predictions for Mott asymmetry

• Use fit to experimental data on s?p and exact
  3-dimensional integration over phase space of
  intermediate 2 photons

Data from HAPPEX More to come from G0
HAPPEX
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Mott asymmetry in the nucleon resonance region
Data from MAMI F. Maas et al.,
Phys.Rev.Lett.94082001, 2005
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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 stotal, and hard
collinear photon exchange
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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
  (CooperHorowitz, Phys.Rev.C72034602,2005)

Five orders of magnitude enhancement in HAPPEX
kinematics due to excitation of inelastic
intermediate states in 2?-exchange (Normal
Asymmetry -5/-1ppm for PREX)
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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 -51ppm
• 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