The $B_s\to K$ Form Factor in The Whole Kinematically Accessible Range

Abstract

A systematic analysis is presented of the $B_s\to K$ form factor $f(q^2)$ in the whole range of momentum transfer $q^2$, which would be useful to analyzing the future data on $B_s\to K$ decays and extracting $|V_{ub}|$. With a modified QCD light cone sum rule (LCSR) approach, in which the contributions cancel out from the twist 3 wavefunctions of $K$ meson, we investigate in detail the behavior of $f(q^2)$ at small and intermediate $q^2$ and the nonperturbative quantity $f_{B^{\ast }}{g}_{B^{\ast }{B}_{s}K}$ $(f_{B^{\ast }}$ is the decay constant of $B^{\ast }$ meson and $g_{B^{\ast }{B}_{s}K}$ the $B^{\ast }{B}_{s}K$ strong coupling), whose numerical result is used to study $q^2$ dependence of $f(q^2)$ at large $q^2$ in the single pole approximation. Based on these findings, a form factor model from the best fit is formulated, which applies to the calculation on $f(q^2)$ in the whole kinematically accessible range. Also, a comparison is made with the standard LCSR predictions.

Comments: 11 pages, Latex, 1 eps figure, Final version to appear in Phys.Rev.D