# Presentation: 350412

## Single-Spin Beam Asymmetriesin 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-WeltonSelection 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

- Based on one-photon exchange approximation

- 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 structure**
- Model 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

- δSoft

- Q2= 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

- 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-ViolatingElectron Scattering

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

- x

- γ

- γ

- Z0

- Electromagnetic

- Neutral Weak

## 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**** ****m****e****/E****beam)**** 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 intermediate
- state

**Inelastic excitations**
**dominate**

## Beam Normal Asymmetry(AA, Merenkov)

- Gauge invariance essential in cancellation of infra-red singularity:

- 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:

- 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)**

## No suppression for beam asymmetry with energyat fixed Q2

- No suppression for beam asymmetry with energyat fixed Q2

- x10-6

- x10-9

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

- SLAC E158 kinematics

## Phase Space Contributing to the absorptivepart of 2γ-exchange amplitude

- 2-dimensional integration (Q12, Q22) for the elastic intermediate state
- 3-dimensional integration  (Q12, Q22,W2) for inelastic excitations

- Example: MAMI A4
- E= 855 MeV
- Θcm= 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,Q22,W) with      one-dimensional integral along the line (Q12≈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) quark
- Emission/reabsorption of the quark is described by GPDs

- 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

- Minor role of quark mass

## Trouble with HandbagAA, 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 assumes
- a 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/me2) ≈100% level correction to beam asymmetry
- But 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 SSAhep-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 (+h1perp), 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

## 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