Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

Abstract

We present a study of the two-photon-exchange (2γ-exchange) corrections to the S-levels in muonic (µD) and ordinary (D) deuterium within the pionless effective field theory (/ πEFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the / πEFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic 2γ-exchange contribution in µD larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2γ-exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2γ-exchange contributions in µD, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the / πEFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the µD Lamb shift, the 2S − 1S transition in D, and the 2S − 1S hydrogen-deuterium isotope shift, with the respective 2γ-exchange effects evaluated in a unified / πEFT approach, are in perfect agreement. CONTENTSI. Introduction II. Theoretical Framework A. 2γ Exchange in (Muonic) Deuterium B. Unpolarized Deuteron VVCS in Pionless EFT III. 2γ Exchange in Muonic Deuterium A. Elastic Contribution B. Inelastic Contribution C. Single-Nucleon Effects Beyond N3LO D. Summary of Results IV. Hydrogen-Deuterium Isotope Shift A. 2γ Exchange in Deuterium B. 2γ Exchange in Isotope Shift and Determination of Low-Energy Constant l C0 S 1

Muonic-Atom Spectroscopy and Impact on Nuclear Structure and Precision QED Theory

“…For the µD Lamb shift, recent theory predictions are in agreement, and through the H-D isotope shift are consistent with the proton radius from µH, see, e.g., Ref. [60].…”

“…For µD and µHe + , both the nucleon-and nuclear-structure effects enter. They are calculated in the data-driven dispersive framework [58,59], and in a number of theoretical approaches, such as pionless effective field theory [60], chiral effective field theory [61] or phenomenological Hamiltonians [62]. For the µD Lamb shift, recent theory predictions are in agreement, and through the H-D isotope shift are consistent with the proton radius from µH, see, e.g., Ref.…”