We address the physics implications of a precision determination of the weak
charge of the proton, QWP, from a parity violating elastic electron proton
scattering experiment to be performed at the Jefferson Laboratory. We present
the Standard Model (SM) expression for QWP including one-loop radiative
corrections, and discuss in detail the theoretical uncertainties and missing
higher order QCD corrections. Owing to a fortuitous cancellation, the value of
QWP is suppressed in the SM, making it a unique place to look for physics
beyond the SM. Examples include extra neutral gauge bosons, supersymmetry, and
leptoquarks. We argue that a QWP measurement will provide an important
complement to both high energy collider experiments and other low energy
electroweak measurements. The anticipated experimental precision requires the
knowledge of the order alpha_s corrections to the pure electroweak box
contributions. We compute these contributions for QWP, as well as for the weak
charges of heavy elements as determined from atomic parity violation.Comment: 22 pages of LaTeX, 5 figure
