This thesis examines the Z box contribution to the weak charge of
the proton. Here, by combining recent parity-violating
electron-deuteron scattering data with our current understanding of
parton distribution functions, the author shows that one can limit
this model dependence. The resulting construction is a robust model
of the and Z structure functions that can also be used to study a
variety of low-energy phenomena. Two such cases are discussed in
this work, namely, the nucleon's electromagnetic polarizabilities
and quark-hadron duality. By using phenomenological information to
constrain the input structure functions, this important but
previously poorly understood radiative correction is determined at
the kinematics of the parity-violating experiment, QWEAK, to a
degree of precision more than twice that of the previous best
estimate. A detailed investigation into available parametrizations
of the electromagnetic and interference cross-sections indicates
that earlier analyses suffered from the inability to correctly
quantify their model dependence.
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