Nuclear structure corrections to the Lamb shift in $\mu^3$He$^+$ and $\mu^3$H

TL;DR

This paper provides the first ab initio calculations of nuclear structure corrections for the Lamb shift in muonic helium-3 and tritium, aiming to improve the precision of nuclear charge radius measurements and address the proton radius puzzle.

Contribution

It introduces the first ab initio calculations of nuclear structure corrections, including polarization effects, for muonic helium-3 and tritium, reducing theoretical uncertainties.

Findings

Uncertainty in nuclear corrections reduced to a few percent

Supports muonic helium-3 experiment for precise radius extraction

Proposes muonic tritium as a probe for nucleon polarizabilities

Abstract

Measuring the 2S-2P Lamb shift in a hydrogen-like muonic atom allows one to extract its nuclear charge radius with a high precision that is limited by the uncertainty in the nuclear structure corrections. The charge radius of the proton thus extracted was found to be 7-sigma away from the CODATA value, in what has become the yet unsolved "proton radius puzzle". Further experiments currently aim at the isotopes of hydrogen and helium: the precise extraction of their radii may provide a hint at the solution of the puzzle. We present the first ab initio calculation of nuclear structure corrections, including the nuclear polarization correction, to the 2S-2P transition in $\mu^3$He$^+$ and $\mu^3$H, and assess solid theoretical error bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few percents and will be instrumental to the on-going $\mu^3$He$^+$ experiment. We also support the mirror $\mu\,^3$H system as a candidate for further probing of the nucleon polarizabilities and shedding more light on the puzzle.