Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Radiative Corrections for Moller and Compton Asymmetries

Andrei AfanasevJefferson Lab

Talk presented at Workshop

on Precision Electron Beam PolarimetryJefferson Lab, Newport News, June 9, 2003

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Objectives

. Review corrections from the higher-order electromagnetic effects for . Moller Scattering. Compton Scattering

. Theoretical and computational approaches

. Implications for Moller and Compton polarimetry

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Moller Scattering

. C. Moller, Annalen Phys., Lpz, 14, 531 (1932): . Electron-electron scattering cross section calculated using one-

photon exchange (Born) approximation. M. Redhead, Proc. R. Soc. (1953); R. Polovin, Sov.Phys.-JETP, 4, 385

(1957); Y. Tsai, Phys. Rev. D 20, 269 (1960):. Calculated radiative corrections to unpolarized Moller scatering

cross section. A.A. Kresnin, L.N. Rosentweig, Sov.Phys.-JETP, 288 (1957):

. Polarization asymmetry of Moller scattering calculated

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Radiative Corrections to PolarizedMoller Scattering

. L. DeRaad, Y. Ng, Phys. Rev. D 11, 1586 (1975); L. DeRaad, Phys.Rev. D 11, 3328 (1975):. Radiative corrections to polarized Moller scattering using the

formalism from L. Mo, Y. Tsai, Rev. Mod. Phys. 41, 205 (1969) and R. Gastmans, Y. Van Ham, Phys. Rev. D 10, 385 (1974).

. A. Denner, S. Pozzorini, Eur. Phys. J. C 7, 185 (1999):. Electroweak corrections for the polarized case, soft photons

. N.M. Shumeiko, J. Suarez, Fizika B 8, 97 (1999); J. Phys. G 26, 113 (2000): Electromagnetic corrections, hard bremsstrahlung included

. F.J. Petriello, Phys. Rev. D 67, 033006 (2003):. Electroweak corrections, used realistic kinematic cuts for SLAC

E158

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Contributions to RC: Moller Case

Born approximation. Both t channel (a) and u-channel (b) diagrams are required

Vacuum polarization and vertex corrections

Two-photon exchange

Bremsstrahlung

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Details of calculations

. The contributions with virtual photons contain infra-red (IR) divergence

. IR divergence is cancelled in the final result from interference between the Born term and the diagrams with real photon emission

. Different approaches to cancel IR divergence may or may not lead to artificial dependence on the parameter ∆E (usually chosen to be the spectrometer resolution)

. Bremsstrahlung is either resticted to either photons or includes both hard and soft contributions . The approach to treat IR divergence parameter-free was proposed

by D. Bardin, N. Shumeiko, Nucl.Phys. B127, 242 (1977) and applied for the polarized Moller scattering by Shumeiko and Suarez, who also included hard brem effects

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Results for Moller Asymmetry

Shumeiko@Suarez, Fizika B8, 97 (1999)

Asymmetry plotted for a) E=1 GeV;b) 5 GeV, c) 10 GeV; d) 15 GeV

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Correction to Moller AsymmetryAccording to Shumeiko@Suarez

δ=A/ABorn-1

Y=1-E’/E

Up to 2-3% correctionFor y=0.4-0.6

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Comments and outlook for Moller Polarimetry

. According to Shumeiko&Suarez, RC to Moller asymmetry may reach several per cent in kinematics of JLab

. The correction is larger for larger acceptances

. Note that in designing Moller polarimeters, the acceptances were made large in order to reduce target electron motion (`Levchuk’) effect. Need to include radiative corrections into data analysis for

precision measurements. Example of SLAC E158: When realistic kinematic cuts were

considered, the calculated correction appeared to be smaller (Petriello)

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Radiative Corrections to Compton Scattering

. L.M. Brown, R. Feynman, Phys.Rev. 85, 231 (1952). First calculated virtual and real-soft-photon RC to the Klein-

Nishina formula. W.-Y. Tsai, L.L. DeRaad, K.A. Milton, Phys. Rev. D 6, 1428 (1972);

K.A.Milton, W.-Y. Tsai, L.L. DeRaad, ibid., 6, 1411 (1972).. Same for the polarized case

. A. Gongora-T, R.G. Stuart, Z.Phys. C 42, 617 (1989). Derived helicity amplitudes for hard-photon radiation

. H. Veltman, Phys. Rev. D40, 2810 (1989); E: D42, 1856 (1990).. RC correction for polarized case, including hard radiation

. M. Swartz, Phys. Rev. D 58, 014010 (1998); A. Denner, S. Dittmaier, Nucl. Phys. B540, 58 (1999)

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Thirring’s Theorem

. In the low-energy limit, QED corrections to the Compton scattering cross section vanish to all orders of perturbation theory (W. Thirring, Phil. Mag. 41, 1193 (1950) ). . Reasons: a) Definition of electromagnetic charge in the Thomson

limit and b) electromagnetic gauge invariance. The relative corrections are suppressed by a factor of electron

velocity β for small β (see also S. Dittmaier, Phys. Lett. B409, 509 (1997) )

. RC for Klein-Nishina cross section are negligible in the kinematics of Compton polarimetry at JLab. But RC to asymmetries are not suppressed…

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Calculations

Infrared divergence cancels ininterference between diagrams ofFig1. and Fig.2 against Fig.3.

Fortran code COMRAD, available fromM. Swartz;Denner&Dittmayer used packages likeFeynArts and FeynCalc

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Numerical Results

. Denner@Dittmaier calculated RC for the kinematics of JLab Compton polarimeter (Hall A).. For 1.165 eV laser photons and E=4-6 GeV, β=0.034-0.066

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Summary for Compton

. RC for JLab Compton polarimetry are expected at 1/3 per cent level

Andrei Afanasev, Workshop on Precision Electron Beam Polarimetry, JLab, 6/9/03Operated by the Southeastern Universities Research Association for the U.S. Dept. of Energy

Conclusions

. Calculations of radiative corrections to Moller asymmetry demonstrate that 2-3% effects are possible for JLab Moller polarimeters. Simulations using experimental acceptances are needed to evaluate

resulting systematic corrections to beam asymmetry measurements. For Compton polarimetry, the correction does not exceed 0.4% for

JLab kinematics