1 / 33

Single-Spin Beam Asymmetries in QED and QCD

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)

aldis
Download Presentation

Single-Spin Beam Asymmetries in QED and QCD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Single-Spin Beam Asymmetriesin QED and QCD Andrei Afanasev Jefferson Lab RIKEN BNL Workshop on Single-Spin Asymmetries June 3, 2005, BNL

  2. 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

  3. 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

  4. 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

  5. Elastic ep-scattering • Need more than 1 photon exchange to generate SSA • Did not attract much attention until the `Rosenbluth vs. polarization’ puzzle

  6. Elastic Nucleon Form Factors • Based on one-photon exchange approximation • Two techniques to measure Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross

  7. 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 ~5% difference in cross-section JLab/Polarization

  8. 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

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

  10. 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

  11. Polarization transfer (ibid.) • Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio

  12. Parity Violating elastic e-N scattering Longitudinally polarized electrons, unpolarized target t = Q2/4M2 e = [1+2(1+t)tan2(q /2)]-1 e’= [t(t+1)(1-e2)]1/2 Neutral weak form factors contain explicit contributions from strange sea GZA(0) = 1.2673 ± 0.0035 (from b decay)

  13. 2γ-exchange Correction to Parity-ViolatingElectron Scattering • New parity violating terms due to (2gamma)x(Z0) interference should be added: x Z0 γ γ Electromagnetic Neutral Weak

  14. 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

  15. Proton Mott Asymmetry at Higher Energies Spin-orbit interaction of electron moving in a Coulomb field N.F. Mott, Proc. Roy. Soc. London, Set. A 135, 429 (1932). • 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 (αme/Ebeam) suppression, units are parts per million calculation by AA et al, hep-ph/0208260

  16. 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

  17. 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

  18. Special property of normal beam asymmetry AA, Merenkov, Phys.Lett.B599:48,2004, Phys.Rev.D70:073002,2004; +Erratum (2005) • 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-2Compare with no-structure asymmetry at small θ:

  19. No suppression for beam asymmetry with energyat fixed Q2 x10-9 x10-6 SLAC E158 kinematics Parts-per-million vs. parts-per billion scales: a consequence of soft Pomeron exchange, and hard collinear photon exchange

  20. 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 `Soft’ intermediate electron; Both photons are hard collinear Example: MAMI A4 E= 855 MeV Θcm= 57 deg One photon is Hard collinear

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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 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

  26. 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

  27. 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

  28. 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 (+h1perp), Gamberg et al., Metz-Schlegel, • Bachetta-Mulders-Pijlman (+gperp)->jet case

  29. 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

  30. Electromagnetic gauge invariance • 3 different methods to ensure (electromagnetic) gauge invariance (1 method proposed by Metz, Schlegel, Eur.Phys.J.A22:489-494, 2004 )

  31. Calculations vs CLAS’02 Data

  32. 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

  33. 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

More Related