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 _±, T _i) (i = 1, 2, 3) for the exclusive semileptonic P → Vℓν _ℓ 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 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 _-.