Nuclear structure corrections to the Lamb shift in μHe+3 and μH3

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 7σ 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 μHe+3 and μH3, and assess solid theoretical error bars. Our predictions reduce the uncertainty in the nuclear structure corrections to the level of a few percent and will be instrumental to the on-going μHe+3 experiment. We also support the mirror μH3 system as a candidate for further probing of the nucleon polarizabilities and shedding more light on the puzzle.