New approach to low energy Virtual Compton Scattering and generalized polarizabilities of the nucleon

TL;DR

This paper introduces a unified, Lorentz-covariant framework for low energy virtual Compton scattering that clarifies previous inconsistencies and defines six new generalized polarizabilities of the nucleon, continuous in photon virtuality.

Contribution

It provides a consistent low energy theorem for VCS by defining a new operator basis, resolving previous issues with the low energy limit, and introduces six generalized polarizabilities.

Findings

Unified description of low energy VCS with real and virtual photons.

Introduction of six new generalized polarizabilities.

Polarizabilities are continuous functions of photon virtuality.

Abstract

Virtual Compton scattering off the nucleon (VCS) is studied in the regime of low energy of the outgoing real photon. This regime allows one to directly access the generalized polarizabilities of the nucleon in a VCS experiment. In the derivation of the low energy theorem for VCS that exists in the literature, the low energy limit taken for virtual initial photons does not match on that for real photons, when one approaches the initial photon's mass shell. While this problem has for a long time been attributed to the non-analyticity of the Compton amplitude with respect to the photon virtuality, I demonstrate that it is merely due to an ill-defined low energy limit for VCS, on one hand, and to a particular way of constructing the VCS amplitude, use in the literature, on the other. I provide a uniform description of low energy Compton scattering with real and virtual photons by defining a Lorentz-covariant operator sub-basis for Compton scattering in that regime, that has six independent structures. Correspondingly, six new generalized polarizabilities are introduced in the Breit frame. These polarizabilities are defined as continuous functions of the photon virtuality and at the real photon point match onto the nucleon polarizabilities known from real Compton scattering.