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

We study the light-front zero-mode contribution to the transition form factors (g, f, a±, Ti) (i = 1, 2, 3) for the exclusive semileptonic P → Vℓνℓ and rare P → Vℓ+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 Γμ = γμ − (2k − PV)μ/D, the six form factors (g, f, a+, T1, T2, T3) 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 Γμ = γμ 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−.