Pionless Effective Field Theory Evaluation of Nuclear Polarizability in Muonic Deuterium

TL;DR

This paper uses pionless effective field theory to calculate the nuclear polarizability contribution to the Lamb shift in muonic deuterium, aiding in precise determination of the deuteron charge radius.

Contribution

It provides a systematic EFT-based calculation of the deuteron polarizability effects up to NNLO, including analytical expressions and numerical results.

Findings

Agreement with previous calculations

Analytical expressions for transition matrix elements

Numerical estimates of Lamb shift contributions

Abstract

We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relativistic and other higher-order effects. We find agreement with previous calculations and explain the accuracy of our calculation.