Light-front holographic distribution amplitudes of pseudoscalar mesons and their application to $B$-meson decays

Abstract

In this paper the dynamical spin effects of the light-front holographic wavefunctions for light pseudoscalar mesons are studied using two different assumptions. These improved wavefunctions are then confronted with a number of sensitive hadronic observables: the decay constants of $\pi$ and $K$ mesons, their $\xi$-moments, the pion-to-photon transition form factor, and the pure annihilation ${\bar{B}}_s\to {\pi }^{+}{\pi }^{-}$ and ${\bar{B}}_d\to K^{+}{K}^{-}$ decays. Taking $f_{\pi }$, $f_K$ and their ratio $f_K/f_{\pi }$ as constraint conditions, the ${\chi }^2$ analyses for holographic parameters, including the mass scale parameter $\sqrt{\lambda }$ and effective quark masses, are all consistent with the mass scale which controls the slopes of the light-quark hadronic Regge trajectories. In addition, we also show how the improved light-front holographic distribution amplitudes regulate the end-point divergences which appear in the annihilation amplitudes of $B\to PP$ decays.

Comments: 28 pages, 4 figures and 4 tables