A proof of factorization for deep inelastic neutrino scattering

It is proven in this paper that the structure functions for the hadron quantity describing deep inelastic neutrino scattering factor into the product of a short-distance coefficient function, the non-perturbative parton distribution function which encompasses the underlying structure of the target, and the function for soft radiation which does not emerge in the case of electron scattering for which weak radiative corrections are usually practically ignored. This is shown to all orders of perturbative quantum chromodynamics and electroweak theory, and to leading order in the power expansion of the effective field theory used as a tool. It is based on the observation that there is no necessity to go into the partonic level of the physical process, for a generalized version of the operator product expansion affords a framework for the study of inclusive processes, where the momentum carried in by one current operator and out by the other is allowed to go to infinity. It is discovered following this line of argument that the objects entering the factorization theorem need not be SU(2) x U(1) gauge singlets, whether or not we perform the factorization in the symmetric phase. The factorization analysis provides initial conditions for evolution to arbitrary energies that allows for re-summation of large logarithms for loop calculations to the extent of accuracy requested.