Doubly virtual Compton scattering and the beam normal spin asymmetry

Abstract

We construct an invariant basis for Compton scattering with two virtual photons (VVCS). The basis tensors are chosen to be gauge invariant and orthogonal to each other. The properties of the corresponding 18 invariant amplitudes are studied in detail. We consider the special case of elastic VVCS with the virtualities of the initial and final photons equal. The invariant basis for VVCS in this orthogonal form does not exist in the literatur. We furthermore use this VVCS tensor for a calculation of the beam normal spin asymmetry in the forward kinematics. For this, we relate the invariant amplitudes to the helicity amplitudes of the VVCS reaction. The imaginary parts of these latter are related to the inclusive cross section by means of the optical theorem. We use the phenomenological value of the transverse cross section ${\sigma }_T\sim 0.1$ mbarn and the Callan-Gross relation which relates the longitudinal cross section ${\sigma }_L$ to the transverse one. The result of the calculation agrees with an existing calculation and predicts the negative values of the asymmetry $B_n$ of the order of 4-6 ppm in the energy range from 6 to 45 ppm and for very forward angles.

13 pages, 2 figures, revtex, submitted to Phys. Rev. C; new version: two figures added, typos corrected

References in corpus (8)

• Proton elastic form factor ratios to $Q^2$ = 3.5 GeV${}^2$ by polarization transfer
• Precision Rosenbluth measurement of the proton elastic form factors
• Two-photon exchange in elastic electron-nucleon scattering
• $\Delta$ resonance contribution to two-photon exchange in electron-proton scattering
• Measurement of the Transverse Beam Spin Asymmetry in Elastic Electron Proton Scattering and the Inelastic Contribution to the Imaginary Part of the Two-Photon Exchange Amplitude
• Resonance estimates for single spin asymmetries in elastic electron-nucleon scattering
• Collinear Photon Exchange in the Beam Normal Polarization Asymmetry of Elastic Electron-Proton Scattering
• Large Logarithms in the Beam Normal Spin Asymmetry of Elastic Electron--Proton Scattering

Cited by in corpus (11)

• Two-Photon Physics in Hadronic Processes
• Two-photon exchange in elastic electron-proton scattering
• Transverse target spin asymmetry in inclusive DIS with two-photon exchange
• Transverse Beam Spin Asymmetries in Forward-Angle Elastic Electron-Proton Scattering
• Analyzing power in elastic scattering of the electrons off a spin-0 target
• Dispersive contributions to $e^{+}p/e^{-}p$ cross section ratio in forward regime
• Transverse single spin asymmetries in inclusive deep-inelastic scattering
• New Measurements of the Beam-Normal Single Spin Asymmetry in Elastic Electron Scattering Over a Range of Spin-0 Nuclei
• Beam normal spin asymmetry in the quasi-RCS approximation
• Measurement of the Beam-Normal Single-Spin Asymmetry for Elastic Electron Scattering from ${}^{12}$C and ${}^{27}$Al
• The two photon exchange amplitude in $ep$ and $e\mu$ elastic scattering: a comparison