Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions

TL;DR

This paper presents a next-to-leading-order chiral perturbation theory calculation of unpolarized doubly-virtual Compton scattering off the nucleon, revealing discrepancies with dispersive evaluations at low momentum transfer and comparing Lorentz-invariant and heavy-baryon frameworks.

Contribution

The work provides a complete NLO chiral perturbation theory analysis of VVCS amplitudes and structure functions, highlighting differences with dispersive data and between theoretical frameworks.

Findings

Significant disagreements with dispersive evaluations at low Q

Reproduction of heavy-baryon expressions from Lorentz-invariant results

Demonstration of differences between B$ ext{chi}$PT and HB$ ext{chi}$PT

Abstract

The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of low-energy VVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarized VVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the corresponding structure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted, where possible, with "data-driven" dispersive evaluations of low-energy structure quantities, such as nucleon polarizabilities. We find significant disagreements with dispersive evaluations at very low momentum-transfer $Q$; for example, in the slope of polarizabilities at zero momentum-transfer. By expanding the results in powers of the inverse nucleon mass, we reproduce the known "heavy-baryon" expressions. This serves as a check of our calculation, as well as demonstrates the differences between the manifestly Lorentz-invariant (B$\chi$PT) and heavy-baryon (HB$\chi$PT) frameworks.