Regularization of the fermion self-energy and the electromagnetic vertex in the Yukawa model within light-front dynamics

Abstract

In light-front dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a nonrotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the light-front plane. Explicitly covariant formulation of light-front dynamics allows us to parametrize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of independent invariant amplitudes, extra (nonphysical) terms should appear, with spin structures which explicitly depend on the orientation of the light-front plane. The number of form factors, i.e., the coefficients of this decomposition, therefore also increases. The spin-$1/2$ fermion self-energy is determined by three scalar functions, instead of the two standard ones, while for the elastic electromagnetic vertex the number of form factors increases from two to five. In the present paper we calculate perturbatively all these form factors in the Yukawa model. Then we compare the results obtained in the two following ways: (i) by using the light-front dynamics graph technique rules directly; (ii) by integrating the corresponding Feynman amplitudes in terms of the light-front variables. For each of these methods, we use two types of regularization: the transverse and longitudinal cutoffs, and the Pauli-Villars regularization. In the latter case, the dependence of amplitudes on the light-front plane orientation vanishes completely provided enough Pauli-Villars subtractions are made.