Proton radius puzzle and quantum gravity at the Fermi scale

Abstract

We show how the "proton radius puzzle" emerging from the measurement of the Lamb shift in muonic hydrogen may be solved by means of a binding energy contribution due to an effective Yukawian gravitational potential related to charged weak interactions. The residual discrepancy from the experimental result should be mainly attributable to the need for the experimental determination of the gravitational radius of the proton. The absence of an analogous contribution in the Lamb shift of electronic hydrogen should imply the existence of generation-dependent interactions, corroborating previous proposals. Muonic hydrogen plays a crucial role to test possible scenarios for a gravitoweak unification, with weak interactions seen as manifestations of quantum gravity effects at the Fermi scale.