Doubly virtual Compton scattering and the beam normal spin asymmetry

Details Doubly virtual Compton scattering and the beam normal spin asymmetry Doubly virtual Compton scattering and the beam normal spin asymmetry

2005-12-08

arxiv.org/abs/hep-ph/0512106v3

Phys.Rev.C73:035213,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1103/PhysRevC.73.035213

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 $\sigma_T\sim0.1$ 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.

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