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

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.

References in corpus (7)

• Hadron structure at low Q^2
• Measurement of the Generalized Polarizabilities of the Proton in Virtual Compton Scattering at Q2= 0.92 and 1.76 GeV2
• Measurement of the Generalized Polarizabilities of the Proton in Virtual Scattering at Q2=0.92 and 1.76 GeV2: I. Low Energy Expansion Analysis
• Measurements of the Generalized Electric and Magnetic Polarizabilities of the Proton at Low Q2 Using the VCS Reaction
• A new measurement of the structure functions $P_{LL}-P_{TT}/epsilon$ and $P_{LT}$ in virtual Compton scattering at $Q^2=$ 0.33 (GeV/c)${}^2$
• New Predictions for generalized spin polarizabilities from heavy baryon chiral perturbation theory
• Low energy theorem for virtual Compton scattering and generalized sum rules of the nucleon

Cited by in corpus (8)

• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• Four-point functions and the permutation group S4
• Nucleon Compton scattering in the Dyson-Schwinger approach
• Nucleon resonances in Compton scattering
• Virtual Compton Scattering and the Generalized Polarizabilities of the Proton at Q^2=0.92 and 1.76 GeV^2
• Real and Virtual Compton Scattering: the nucleon polarisabilities
• Cottingham formula and nucleon polarizabilities
• Aligning a Majorana fermion's anapole moment with an external current through photon emission mediated by the fermion's generalized polarizabilities