Pion Generalized Dipole Polarizabilities by Virtual Compton Scattering $\ddot{I}€e\to \ddot{I}€e{\hat{I}}^3$

Abstract

We present a calculation of the cross section and the event generator of the reaction $\ddot{I}€e\to \ddot{I}€e{\hat{I}}^3$. This reaction is sensitive to the pion generalized dipole polarizabilities, namely, the longitudinal electric $\hat{I}{\pm }_L(q^2)$, the transverse electric $\hat{I}{\pm }_T(q^2)$, and the magnetic ${\hat{I}}^2(q^2)$ which, in the real-photon limit, reduce to the ordinary electric and magnetic polarizabilities $\bar{\hat{I}}\pm$ and ${\bar{\hat{I}}}^2$, 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.

33 pages, Revtex, 15 figures