Light-front zero-mode contribution to the tensor form factors for the exclusive rare $P\to V{\ell }^{+}{\ell }^{-}$ decays

Abstract

We study the light-front zero-mode contribution to the tensor form factors $T_i(i=1,2,3)$ for the exclusive rare $P\to V{\ell }^{+}{\ell }^{-}$ 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 ${\Gamma }^{\mu }={\gamma }^{\mu }-(2k-P_V{)}^{\mu }/D$, the three tensor form factors $T_i(i=1,2,3)$ 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 $T_i(i=1,2,3)$ can be computed in LFQM safely without involving any complicate zero-mode contribution. The lack of zero-mode contribution benefits the phenomenology with LFQM.

Comments: 13 pages, 2 figures, to appear in Phys. Lett. B