Forward doubly-virtual Compton scattering off an unpolarised deuteron in pionless effective field theory

TL;DR

This paper calculates the forward unpolarised doubly-virtual Compton scattering off the deuteron using pionless effective field theory, providing precise, model-independent inputs for future muonic deuterium Lamb shift studies.

Contribution

It presents a high-order pionless EFT calculation of deuteron VVCS, extracting unknown couplings and studying polarisabilities, advancing theoretical understanding of deuteron structure.

Findings

Determined the deuteron charge form factor from VVCS amplitude.

Extracted the two-nucleon one-photon contact coupling at N3LO.

Provided high-precision inputs for muonic deuterium Lamb shift calculations.

Abstract

We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilities of the deuteron. The calculated unpolarised VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.