Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Beam Normal Spin Asymmetryon Nuclear Targets

Andrei Afanasev

Jefferson Lab

Hall A Collaboration Meeting, December 5, 2005

Collaborator: N. Merenkov

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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 k1,2 are initial and final electron momenta, s is a polarization vectorof 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)

21 kks

1ks

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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 intermediatestate

Inelastic excitationsdominate

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Beam Normal Asymmetry(AA, Merenkov)

0

ˆ

)ˆ1)(ˆ()ˆ(4

1

)ˆ()ˆ1)(ˆ()ˆ(4

1

2Im

),(

1212

512

512

22

210

3

22

2,

qHqHqHqLqLqL

aa

TMpMpTrH

mkmkmkTrL

QQ

HL

k

kd

QsD

QA

p

eeee

Pen

Gauge invariance essential in cancellation of infra-red singularity for target asymmetry0/0 2

22

1 QorandQifHL

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

2

2

2

222

22

1 log,log~0/e

e

e

eem

Qm

m

QmAQorandQifconstmHL

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Phase Space Contributing to the absorptivepart of 2γ-exchange amplitude

. 2-dimensional integration (Q12, Q2

2) for the elastic intermediate state

. 3-dimensional integration (Q12, Q2

2,W2) for inelastic excitations Examples: MAMI A4

E= 855 MeVΘcm= 57 deg;

SAMPLE, E=200 MeV;Θcm= 145 deg

`Soft’ intermediate electron;Both photons are hard collinear

One photon is Hard collinear

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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:

2

)2)(log(8

)(2

2

22

21

212

2BQ

e

ep

en e

m

Q

FF

FFQmA

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 θ:

AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004;+Erratum (hep-ph/0407167v2)

3s

mA ee

n

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Input parameters

σγp from N. Bianchi at al.,

Phys.Rev.C54 (1996)1688 (resonance region) and Block&Halzen,

Phys.Rev. D70 (2004) 091901

e

th

Etotp

en qd

EA

)0;(

1 22,12

For small-angle (-t/s<<1) scattering of electrons with energies Ee , normal beam asymmetry is given by the energy-weighted integral

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Predictions for Mott asymmetry

Use fit to experimental data on σγp and exact 3-dimensional integration over phase space of intermediate 2 photons

HAPPEX

Data from HAPPEX More to come from G0

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

No suppression for Mott asymmetry with energyat fixed Q2

x10-6 x10-9

Parts-per-million vs. parts-per billion scales: a consequence ofnon-decreasing σtotal, and hard collinear photon exchange

SLAC E158 kinematics

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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 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)

Andrei Afanasev, Hall A Collab. Meeting, 12/5/2005Operated 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 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