Pion polarizabilities from a dispersive analysis of γγ → ππ

Abstract

We present results for the charged and neutral pion polarizabilities, obtained through a dispersive analysis of photon-fusion reactions with two pions in the final state. This analysis is motivated by current and future measurements at COMPASS, JLab (Hall D), and the BESIII measurement of singlevirtual photon-fusion reactions in the space-like region, offering insight into generalized pion polarizabilities. To improve upon predictions within an un-subtracted dispersion formalism with only the pion left-hand cut, one needs to consider the influence of heavier left-hand cuts. We parametrize the latter using an expansion in a suitably constructed conformal variable, capturing the analytical structure of the left-hand cuts. The coefficients in this expansion are determined from the matching with the Lagrangian-based approach, the Adler zero constraint for γγ → π0π0, and a fit to the cross-section data. The extension to the single-virtual case is also discussed.