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 Γ^μ=γ^μ-(2k-P_V)^μ/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 (1/x)ⁿ 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 Γ^μ=γ^μ 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~(1/x)ⁿ 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.