Single-Spin Beam Asymmetries in QED and QCD

Andrei Afanasev, Single-Spin Beam Asymmetries in QCD and QED, SSA Workshop, BNL, 6/3/05Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Single-Spin Beam Asymmetriesin QED and QCD

Andrei Afanasev

Jefferson Lab

RIKEN BNL Workshop on Single-Spin Asymmetries

June 3, 2005, BNL


Plan of talk

I. Two-photon exchange effects in the process e+p→e+p

. Normal beam spin asymmetry (parity-conserving)

. (Non)cancellation of hard collinear photon exchange

. Enhancement of inelastic excitations

. (Non)suppression of the asymmetry with energy

. Trouble with handbag

II. Beam asymmetry in SIDIS

. Model results and implications


Parity-Conserving Single-Spin Asymmetries in Scattering Processes(early history). George C. Stokes, Trans. Cambr. Phil. Soc. 9, 399 (1852), introduced

parameters describing polarization states of light.

. 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


Wolfeinstein-Simon-WeltonSelection Rules

Quoted from PR D90, 1036 (1953)

. If only S-waves are effective in the reaction, there can be no polarization

. If only levels of the compound nucleus having J=1/2 and a single parity (or J=0 with any parity) are effective, there will be no polarization

. If only spin 0 is effective for the final channel, the polarization vanishes

. Polarization results from the interference of the different subchannels contributing to the reaction. Hence, if there is only a single nonzero element of the scattering matrix, the polarization will vanish

. If there is no spin-orbit coupling, the polarization will vanish


Elastic ep-scattering

. Need more than 1 photon exchange to generate SSA

. Did not attract much attention until the `Rosenbluth vs. polarization’ puzzle


Elastic Nucleon Form Factors

pm

q

peefi

fifi

utFtFuuueM

MM

))()(( 22121

1

•Based on one-photon exchange approximation

)0(

,

:1

)1(2

:)(

2121

2

220

y

ME

M

E

z

x

z

x

EM

P

FFGFFG

techniqueonPolarizatiG

G

A

A

P

P

techniqueRosenbluthGG

•Two techniques to measure

Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross


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

JLab/Polarization

~5% difference in cross-section


Electron Scattering: LO and NLO in αem

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

•Guichon&Vanderhaeghen’03:Can (e-f) account for the Rosenbluth vs. polarization experimental discrepancy? Look for ~3% ...

Main issue: Corrections dependent on nucleon structureModel calculations: •Blunden, Melnitchuk,Tjon, Phys.Rev.Lett.91:142304,2003•Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004


Updated Ge/Gm plot

AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013


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 and/or asymmetry is zero

ε

δSoftQ2= 6 GeV2


Polarization transfer (ibid.)

. Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio


Parity Violating elastic e-N scattering

Longitudinally polarized electrons,

unpolarized target

2

e e pp

unpol

AMEF

LR

LR AAAQGA

224

2

sRFGQG

GGRGRQGe

AZA

eA

sME

nME

nA

pME

pAW

ZME

)()(

)1()1)(sin41()(2

,,,22

,

45.3

sin41

282

W

MeAWA

MZMM

EZEE

GGA

GGA

GGA

)sin41(

)(

2

Neutral weak form factors contain explicit contributions from strange sea

GZA(0) = 1.2673 ± 0.0035 (from decay)

= Q2/4M2

= [1+2(1+)tan2(/2)]-1

’= [(+1)(1-2)]1/2


2γ-exchange Correction to Parity-ViolatingElectron Scattering

. New parity violating terms due to (2gamma)x(Z0) interference should be added:

xγ γ Z0

Electromagnetic Neutral Weak

eZAAW

ZVAAA

eZMA

ZAVAA

GGAA

GGAA

)Re()1)(sin41(Re

)Re()1)(1()(Re2

21

221


GPD Calculation of 2γ×Z-interference. Can be used at higher Q2, but points at a

problem of additional systematic corrections for parity-violating electron scattering. The effect evaluated in GPD formalism is the largest for backward angles:

AA & Carlson, hep-ph/0502128, Phys. Rev. Lett. 94, 212301 (2005): measurements of strange-quark content of the nucleon are affected, Δs may shift by ~10%

Important note: (nonsoft) 2γ-exchange amplitude has no 1/Q2 singularity;1γ-exchange is 1/Q2 singular => At low Q2, 2γ-corrections is suppressed as Q2


Proton Mott Asymmetry at Higher Energies

. 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 (α me/Ebeam) suppression, units are

parts per million calculation by AA et al, hep-ph/0208260

Spin-orbit interaction of electron moving in a Coulomb field N.F. Mott, Proc. Roy. Soc. London, Set. A 135, 429 (1932).


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 intermediatestate

Inelastic excitationsdominate


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

en

Gauge invariance essential in cancellation of infra-red singularity:

0/0 22

21 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 available calculations by Gorshtein, Guichon, Vanderhaeghen, Pasquini;Confirm quasi-real photon exchange enhancement in the nucleon resonance region


Special property of normal beam asymmetry

. 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(log8

)(2

2

22

21

212

2

e

ep

en m

Q

FF

FFQmA

Also suppressed by a standard diffractive factor exp(-BQ2), where B=3.5-4 GeV-2 Compare with no-structure asymmetry at small θ:

AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004;

+Erratum (2005)

3s

mA ee

n


No suppression for beam asymmetry with energyat fixed Q2

x10-6 x10-9

Parts-per-million vs. parts-per billion scales: a consequence ofsoft Pomeron exchange, and hard collinear photon exchange

SLAC E158 kinematics


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

Example: MAMI A4E= 855 MeVΘcm= 57 deg

`Soft’ intermediate electron;Both photons are hard collinear

One photon is Hard collinear


Peaking Approximation

. Dominance of collinear-photon exchange =>

. Can replace 3-dimensional integral over (Q12,Q2

2,W) with one-dimensional integral along the line (Q1

2≈0; Q22=Q2(s-W2)/(s-M2))

. Save computing time

. Avoid uncertainties associated with (unknown) double-virtual Compton amplitude

. Provides more direct connection to VCS and RCS observables


Lessons from SSA in Elastic ep-Scattering

. Collinear photon exchange present in (light particle) beam SSA

. (Electromagnetic) gauge invariance of is essential for cancellation of collinear-photon exchange contribution for a (heavy) target SSA


Short-range effects; on-mass-shell quark(AA, Brodsky, Carlson, Chen,Vanderhaeghen)

Two-photon probe directly interacts with a (massless) quarkEmission/reabsorption of the quark is described by GPDs

su

tii

t

s

t

s

ut

u

s

su

t

s

ui

t

u

s

tf

su

suii

t

s

t

s

ut

u

s

su

t

s

ui

t

u

s

tti

s

uf

uuAuuV

fAAfVVt

eA

A

V

qeqeqe

qeqeqe

Aqe

Vqeemq

eqeq

2)]2))(log(log(

1))((log

1[

4

)(

)]log(1

))(log(1

[2

2)]2))(log(log(

1))((log

1[

4

)(

)]log(1

))(log(1

[2

)log(])[log(2

,

),(2

2

222

2

22

22

222

2

22

2

,5,,

,,,

22

Note the additional effective (axial-vector)2 interaction; absence of mass terms


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

HGPDondependenceNo

BGAGA MER

n

~

)Im(2

1)Im(

1)1(2

Minor role of quark mass


Trouble with HandbagAA, Brodsky, Carlson, Chen, Vanderhaeghen Model schematics:

• Hard eq-interaction•GPDs describe quark emission/absorption •Soft/hard photon separation

•Use Grammer-Yennie prescription

•Hard interaction with a quark•Applied for BSSA by Gorshtein, Guichon, Vanderhaeghen, NP A741, 234 (2004)

•Exchange of hard collinear photons is kinematically forbidden if one assumesa handbag approximation (placing quarks on mass shell) , BUT…•Collinear-photon-exchange enhancement (up to two orders of magnitude) is allowed for off-mass-shell quarks (higher twists) and Regge-like contributions=> If the handbag approximation is violated at ≈ 0.5% level, It would result in (0.5%)log2(Q2/me

2) ≈100% level correction to beam asymmetryBut target asymmetry, TPE corrections to Rosenbluth and polarization transfer predictions will be violated at the same 0.5% level


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

. Can be generalized to transverse asymmetries in light spin-1/2 particle scattering via massless gauge boson exchange

. Beam asymmetry at high energies is strongly affected by effects beyond pure Coulomb distortion

. Supports Qiu-Sterman twist-3 picture of SSA

. What else can we learn from elastic beam SSA?

. Check implications of elastic hadron scattering in QCD

(Can large An,t in pp elastic be due to onset of collinear multi-gluon exchange + inelastic excitations?)

. Large SSA in deep-inelastic collisions due to hard collinear gluon exchange; in pQCD need NNLO to obtain unsupressed collinear gluons


Nucleon Structure Case

. Single-spin asymmetries in the scattering processes would vanish without contributions from both spin and orbital angular momentum

. Brodsky, Hwang & Schmidt, Phys. Lett. B530, 99 (2002) demonstrated how final state interactions at the parton level result in leading-twist contributions to the single-spin target asymmetry. Essential ingredients of the BHS model are:

. Orbital angular momentum in the initial nucleon state, so that the struck parton may have helicities both parallel and antiparallel to the initial nucleon

. Gluon exchange takes place in the final state, generating both phase differences and transverse-momentum dependence


AA+C. Carlson on Beam SSAhep-ph/0308163

. Assume BHS mechanism for generating single-spin asymmetries, viz.

. Gluon exchange takes place in the final state, generating both phase differences and transverse-momentum dependence

. Asymmetry is due to interference between (a) and absorptive part of (b)

. No assumptions are required on the details of nucleon spin structure

•Concluded: this mechanism is not ~e(x)*Collins fragmentation•Followed by Yuan (+h1

perp), Gamberg et al., Metz-Schlegel, Bachetta-Mulders-Pijlman (+gperp)->jet case


Details of calculation

. Assume that NLO contribution is small, neglecting terms O(NLO2)

. The asymmetry is proportional to the imaginary part of LT-interference

. The calculation is free of infrared and ultraviolet divergence

. Contributions from soft gluons cancel at the observable asymmetry level

. Assume for this calculation that s is frozen (=0.3)

. Assume kT is small


Electromagnetic gauge invariance

. 3 different methods to ensure (electromagnetic) gauge invariance

(1 method proposed by Metz, Schlegel, Eur.Phys.J.A22:489-494, 2004 )


Calculations vs CLAS’02 Data


Summary on beam SSA in SIDIS

. BSSA is due to the correlation,

. Target SSA is due to

. Since no `artificially T-odd’ fragmentatrion, named `photon Sivers effect’ in AA, Carlson, hep-ph/0308163

. Beam SSA is suppressed by an extra power of 1/Q compared to target SSA, since it is due to LT (photon) interference

. Predictions for beam SSA do not depend on the assumptions of orbital angular momentum contribution to the nucleon light-cone wave function, while the remaining assumption (gluon exchange in the final state) is the same

. Result very sensitive to the method of restoring electromagnetic gauge invariance through adding non-partonic contributions

hpqS

hp pqS


Conclusions

. Reaction mechanism similar to the one proposed earlier by Brodsky et al. for target SSA gives the magnitude for beam SSA compatible with experiment

. High sensitivity to non-partonic contributions, especially at small xBj

. Beam SSA is due to the orbital angular momentum at the photon-parton level (`photon Sivers effect’) - no T-odd fragmentation is involved

. Measurement of BSSA is important for interpretation of target SSA data

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Single-Spin Beam Asymmetries in QED and QCD