Deuteron VVCS and nuclear structure effects in muonic deuterium at N3LO in pionless EFT
Abstract
We present our studies of the forward unpolarised doublyvirtual Compton scattering (VVCS) off the deuteron and the closely related twophotonexchange ($2\gamma$exchange) corrections to the Lamb shift of muonic deuterium. The deuteron VVCS amplitude is calculated in the framework of pionless effective field theory, up to nexttonexttonexttoleading order (N3LO) for the longitudinal and nexttoleading 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 twonucleon onephoton contact coupling that enters the longitudinal amplitude at N3LO. The obtained deuteron VVCS amplitude serves as a highprecision modelindependent input to examine the $2\gamma$exchange corrections. Substantial differences with the recent dispersive evaluations are identified, namely, the elastic contribution appears to be larger by several standard deviations, thus ameliorating the current discrepancy between theory and experiment on the size of $2\gamma$exchange effects. A correlation between the values of the deuteron charge and Friar radii is found that can be used to judge on the quality of a parametrisation of the deuteron charge elastic form factor. The discrepancy between the theory and the empirical result for the $2\gamma$exchange correction in muonic deuterium appears to be completely eliminated. To further confirm this, we revisit the hydrogendeuterium isotope shift in the same framework. Our work provides an alternative selfconsistent and highprecision evaluation of the $2\gamma$exchange correction in (muonic) deuterium.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 arXiv:
 arXiv:2203.13030
 Bibcode:
 2022arXiv220313030L
 Keywords:

 Nuclear Theory;
 High Energy Physics  Phenomenology;
 Nuclear Experiment
 EPrint:
 11 pages, 6 figures, to appear in the proceedings of the 10th International Workshop on Chiral Dynamics  CD2021, 1519 November 2021, Beijing, China (Online)