Light-front dynamic analysis of transition form factors in the process of P→Vℓνℓ

We investigate the light-front zero-mode contribution to the weak transition form factors between pseudoscalar and vector mesons using a covariant fermion field theory model in (3+1) dimensions. In particular, we discuss the form factors a−(q2) and f(q2) which have been suspected to have the zero-mode contribution in the q+=0 frame. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γμ=γμ−μ(2k−PV)/D, the form factor f(q2) is found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor n(1/x) of the struck quark with the power n>0. Although the form factor a−(q2) 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), but not with the momentum-dependent denominator (i.e. D∼n(1/x) with n>0). We identify the zero-mode contribution to a−(q2) and incorporate it as a convolution of the zero-mode operator with the initial- and final-state light-front wave functions. The covariance (i.e. frame independence) of our model has been checked by performing the light-front calculations both in the q+=0 and q+>0 frames. We present our numerical result of the B→ρ transition for an explicit demonstration of our findings.