$B -> πl ν$ Form Factors Calculated on the Light-Front

Abstract

A consistent treatment of $B\rightarrow πl ν$ decay is given on the light-front. The $B$ to $π$ transition form factors are calculated in the entire physical range of momentum transfer for the first time. The valence-quark contribution is obtained using relativistic light-front wave functions. Higher quark-antiquark Fock-state of the $B$-meson bound state is represented effectively by the $|B^*π\rangle$ configuration, and its effect is calculated in the chiral perturbation theory. Wave function renormalization is taken into account consistently. The $|B^*π\rangle$ contribution dominates near the zero-recoil point ($q^2\simeq 25$ GeV$^2$), and decreases rapidly as the recoil momentum increases. We find that the calculated form factor $f_+(q^2)$ follows approximately a dipole $q^2$-dependence in the entire range of momentum transfer.