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

Understand

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.