Generalized dipole polarizabilities of the pion

TL;DR

This paper analyzes the virtual Compton scattering amplitude of the pion, introducing generalized dipole polarizabilities as functions of virtual-photon momentum, using chiral perturbation theory to explore their properties and relations.

Contribution

It presents a theoretical study of pion's generalized dipole polarizabilities within chiral perturbation theory at one-loop order, highlighting their degeneracy and model-independent aspects.

Findings

Generalized dipole polarizabilities depend on virtual-photon momentum squared.

At one-loop level, these polarizabilities are degenerate: lpha_L(q^2)=lpha_T(q^2)=-eta(q^2).

The residual Compton amplitude can be expressed in terms of three generalized dipole polarizabilities.

Abstract

We discuss the virtual Compton scattering amplitude $\gamma^\ast+\pi\to \gamma+\pi$ which enters the reaction $\pi^-+e^-\to\pi^-+e^-+\gamma$. The low-energy scattering amplitude is divided into a model-independent part, involving only the electromagnetic form factor, and a residual part which contains structure information related specifically to (virtual) Compton scattering. In the limit of vanishing final-photon energy, the residual amplitude can be expressed in terms of three generalized dipole polarizabilities which are functions of the squared virtual-photon four-momentum. We study the VCS amplitude in the framework of chiral perturbation theory at ${\cal O}(p^4)$. At the one-loop level the generalized dipole polarizabilities are degenerate $\alpha_L(q^2)=\alpha_T(q^2)=-\beta(q^2)$.