  The Proton Radius Puzzle is the inconsistency between the proton radius
determined from muonic hydrogen and the proton radius determined from atomic
hydrogen level transitions and ep elastic scattering. No generally accepted
resolution to the Puzzle has been found. Possible solutions generally fall into
one of three categories: the two radii are different due to novel
beyond-standard-model physics, the two radii are different due to novel aspects
of nucleon structure, and the two radii are the same, but there are
underestimated uncertainties or other issues in the ep experiments.
  The MUon proton Scattering Experiment (MUSE) at the Paul Scherrer Institut is
a simultaneous measurement of \mu^+ p and e^+ p elastic scattering, as well as
\mu^- p and e^- p elastic scattering, which will allow a determination of the
consistency of the \mu p and the ep interactions. The differences between + and
- charge scattering are sensitive to two-photon exchange effects, higher-order
corrections to the scattering process. The slopes of the cross sections as Q^2
-> 0 determine the proton "radius". We plan to measure relative cross sections
at a typical level of a few tenths of a percent, which should allow the proton
radius to be determined at the level of ~0.01 fm, similar to previous ep
measurements. The measurements will test several possible explanations of the
proton radius puzzle, including some models of beyond-standard-model physics,
some models of novel hadronic physics, and some issues in the radius extraction
from scattering data.
