Reconsideration of the $B \to K^*$ Transition Form Factors within the QCD Light-Cone Sum Rules

Abstract

In this paper, we study the $B \to K^*$ transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e. the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the $B \to K^*$ TFFs are arranged according to the twist structure of the $K^*$-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3 and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs $A_{1/2}$, $V$ and $T_1$, thus the twist-4 terms should be kept for a sound prediction. We also observe that even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point $q^2=0$ but also for their ascending trends in whole $q^2$-region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semi-leptonic decay $B \to K^* \mu^+ \mu^-$. Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs, i.e. the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs, and hence their related observables, to those LCDAs.