Light-front zero-mode contribution to the tensor form factors for the exclusive rare P→Vℓ+ℓ− decays

We study the light-front zero-mode contribution to the tensor form factors Ti (i=1,2,3) for the exclusive 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 three tensor form factors Ti(i=1,2,3) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front energy or the longitudinal momentum fraction factor (1/x)n of the struck quark with the power n>0. Since the denominator D used in the light-front quark model (LFQM) has the power n=1/2, the three tensor form factors Ti (i=1,2,3) can be computed in LFQM safely without involving any complicate zero-mode contribution. The lack of zero-mode contribution benefits the phenomenology with LFQM.