  We propose a theoretical scenario to solve the proton radius puzzle which
recently arises from the muonic hydrogen experiment. In this framework, 4 + n
dimensional theory is incorporated with modified gravity. The extra
gravitational interaction between the proton and muon at very short range
provides an energy shift which accounts for the discrepancy between
spectroscopic results from muonic and electronic hydrogen experiments. Assuming
the modified gravity is a small perturbation to the existing electromagnetic
interaction, we find the puzzle can be solved with stringent constraint on the
range of the new force. Our result not only provides a possible solution to the
proton radius puzzle but also suggest a direction to test new physics at very
small length scale.
