Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

Abstract

We study the light-front zero-mode contribution to the transition form factors (g, f, a ±, T i ) (i = 1, 2, 3) for the exclusive semileptonic P → V lν l and rare P → V l +l− decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ μ = γ μ − (2k − P V ) μ /D, the six form factors (g, f, a +, T 1, T 2, T 3) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) n of the struck quark with the power n > 0. Although the form factor a − is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ μ = γ μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a −.