Explaining the Proton Radius Puzzle with Disformal Scalars
  We analyse the consequences of a disformal interaction between a massless
scalar and matter particles in the context of atomic physics. We focus on the
displacement of the atomic energy levels that it induces, and in particular the
change in the Lamb shift between the 2s and 2p states. We find that the
correction to the Lamb shift depends on the mass of the fermion orbiting around
the nucleus, implying a larger effect for muonic atoms. Taking the cut-off
scale describing the effective scalar field theory close to the QCD scale, we
find that the disformal interaction can account for the observed difference in
the proton radius of muonic versus electronic Hydrogen. Explaining the proton
radius puzzle is only possible when the scalar field is embedded in non-linear
theories which alleviate constraints from collider and stellar physics. Short
distance properties of the Galileon where non-perturbative effects in vacuum
are present ensure that unitarity is preserved in high energy particle
collisions. In matter, the chameleon mechanism alleviates the constraints on
disformal interactions coming from the burning rates for stellar objects. We
show how to combine these two properties in a single model which renders the
proposed explanation of the proton radius puzzle viable.
