Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering $\pi e\to \pi e\gamma$

Abstract

We present a calculation of the cross section and the event generator of the reaction $\pi e\to \pi e\gamma$. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric ${\alpha }_L(q^2)$, the transverse electric ${\alpha }_T(q^2)$, and the magnetic $\beta (q^2)$ which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilities $\bar{\alpha }$ and $\bar{\beta }$, respectively. The calculation of the cross section is done in the framework of chiral perturbation theory at $\mathcal{O}(p^4)$. A pion VCS event generator has been written which is ready for implementation in GEANT simulation codes or for independent use.

Comments: 33 pages, Revtex, 15 figures