Unified dispersive approach to real and virtual photon-photon scattering at low energy

TL;DR

This paper develops a unified dispersive framework for analyzing real and virtual photon-photon scattering at low energies, incorporating pion form factors, phase shifts, and polarizabilities, with applications to muon g-2 calculations.

Contribution

It generalizes existing real photon scattering models to include virtual photons, explicitly accounting for dependencies on phase shifts, form factors, and polarizabilities, while ensuring analyticity and consistency.

Findings

Explicit dependence on $\u0013$ phase-shifts and pion form factors.

Application to muon g-2 hadronic vacuum polarization.

Less model-dependent estimate of $\u0013$ contributions.

Abstract

Previous representations of pion pair production amplitudes by two real photons at low energy, which combine dispersion theoretical constraints with elastic unitariy, chiral symmetry and soft photon constraints are generalized to the case where one photon is virtual. The constructed amplitudes display explicitly the dependence on the $\pi\pi$ phase-shifts, on pion form factors and on pion polarizabilities. They apply both for space-like and time-like virtualities despite the apparent overlap of the left and right-hand cuts, by implementing a definition of resonance exchange amplitudes complying with analyticity and consistent limiting prescriptions for the energy variables. Applications are made to the pion generalized polarizabilies, to vector meson radiative decays, and to the $\sigma\gamma$ electromagnetic form factor. Finally, and evaluation of the contribution of $\gamma\pi\pi$ states in the hadronic vacuum polarization to the muon $g-2$ is given, which should be less model dependent than previous estimates.