Radiative Corrections for Moller and Compton Asymmetries

Transcription

1 Radiative Corrections for Moller and Compton Asymmetries Andrei Afanasev Jefferson Lab Talk presented at Workshop on Precision Electron Beam Polarimetry Jefferson Lab, Newport News, June 9, 2003

2 Objectives. Review corrections from the higher-order electromagnetic effects for. Moller Scattering. Compton Scattering. Theoretical and computational approaches. Implications for Moller and Compton polarimetry

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

4 Radiative Corrections to Polarized Moller 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, (2003):. Electroweak corrections, used realistic kinematic cuts for SLAC E158

5 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

6 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

7 Results for Moller Asymmetry Fizika B8, 97 (1999) Asymmetry plotted for a) E=1 GeV; b) 5 GeV, c) 10 GeV; d) 15 GeV

8 Correction to Moller Asymmetry According to δ=a/a Born -1 Y=1-E /E Up to 2-3% correction For y=

9 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)

10 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, (1998); A. Denner, S. Dittmaier, Nucl. Phys. B540, 58 (1999)

11 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

12 Calculations Infrared divergence cancels in interference between diagrams of Fig1. and Fig.2 against Fig.3. Fortran code COMRAD, available from M. Swartz; Denner&Dittmayer used packages like FeynArts and FeynCalc

13 Numerical Results. calculated RC for the kinematics of JLab Compton polarimeter (Hall A).. For ev laser photons and E=4-6 GeV, β=

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

15 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