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

TL;DR

This paper investigates the light-front zero-mode contributions to tensor form factors in rare meson decays, showing that under certain conditions, these form factors are free from zero-mode effects, simplifying phenomenological calculations.

Contribution

It demonstrates that the tensor form factors are zero-mode free if the denominator D includes a term proportional to the light-front energy or longitudinal momentum fraction with power n>0, validating the use of LFQM.

Findings

Tensor form factors T_i are zero-mode free if D contains (1/x)^n with n>0.

In LFQM, D has n=1/2, so zero-mode contributions are negligible.

This simplifies phenomenological analysis of rare meson 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.