Nonperturbative method for radiative corrections applied to lepton-proton scattering

We present a new, nonperturbative method to effect radiative corrections in lepton- (electron or muon) nucleon scattering, useful for existing or planned experiments. This method relies on a spectral function derived in a previous paper, which takes into account both real soft photons and virtual ones and hence is free from infrared divergence. Hard effects are computed perturbatively and then included in the form of "hard factors" in the nonperturbative soft formulas. Practical computations are effected using the Gauss-Jacobi integration method which reduces the relevant integrals to a rapidly converging sequence. For the simple problem of the radiative quasielasitc peak, we get an exponentiated form conjectured by Schwinger and found by Yennie, Frautschi, and Suura. We compare also our results with the peaking approximation and with the exact one-photon-emission formula of Mo and Tsai. Applications of our method to the continuous spectrum include the radiative tail of the ${\Delta }_{33}$ resonance in $e+p$ scattering and radiative corrections to the Feynman scale-invariant $F_2$ structure function for the kinematics of two recent high-energy muon experiments.