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 $π$ and $K$ mesons, their $ξ$-moments, the pion-to-photon transition form factor, and the pure annihilation $\bar{B}_{s}\to π^+ π^-$ and $\bar{B}_{d}\to K^+K^-$ decays. Taking $f_π$, $f_{K}$ and their ratio $f_{K}/f_π$ as constraint conditions, the $χ^2$ analyses for holographic parameters, including the mass scale parameter $\sqrtλ$ 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.

28 pages, 4 figures and 4 tables