Pion polarizabilities from a dispersive analysis of $\gamma\gamma \to \pi\pi$

TL;DR

This paper uses a dispersive analysis to determine charged and neutral pion polarizabilities from photon-fusion reactions, providing insights relevant for ongoing and future experiments at facilities like COMPASS, JLab, and BESIII.

Contribution

It introduces a novel dispersive method incorporating heavier left-hand cuts via conformal expansion, improving predictions of pion polarizabilities from photon-fusion data.

Findings

Determined pion polarizabilities consistent with experimental data.

Developed a conformal expansion method for left-hand cut contributions.

Extended analysis to single-virtual photon-fusion reactions.

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 single-virtual photon-fusion reactions in the space-like region, offering insight into generalized pion polarizabilities. To improve predictions within an unsubtracted 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 $\gamma\gamma \to \pi^0\pi^0$, and a fit to the cross-section data. The extension to the single-virtual case is also discussed.