Light-front dynamic analysis of transition form factors in the process of image

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 image dimensions. In particular, we discuss the form factors image and image which have been suspected to have the zero-mode contribution in the image frame. While the zero-mode contribution in principle depends on the form of the vector meson vertex image, the form factor image 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 image of the struck quark with the power image. Although the form factor image is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex image term or from the other term just with a constant D (i.e. image), but not with the momentum-dependent denominator (i.e. image with image). We identify the zero-mode contribution to image 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 image and image frames. We present our numerical result of the image transition for an explicit demonstration of our findings.