Intrinsic transverse momentum: Nongauge theories

Results of the parton-model type in remormalizable field theories are extended to the case that transverse momenta are held fixed rather than taken large in the scaling limit. The Drell-Yan process is treated as an example. Parton distributions P(x,kT) and f(x) defined in terms of bilocal operators are used to obtain generalized operator-product expansions in any nongauge theory. At low transverse momentum the original Drell-Yan model with the addition of intrinsic transverse momentum described by P(x,kT) is proved to be valid. The relation between these operator-product expansions and the frequently used method of infrared subtractions is explained. The ultraviolet-divergent renormalization of f(x) is proved to be identical to the infrared divergence in the infrared method. A method to extend the results to gauge theories is proposed.