B-Meson Wave Function through A Comparative Analysis of the $B\to \pi$, $K$ Transition Form Factors

The properties of the B-meson light-cone wave function up to next-to-leading order Fock state expansion have been studied through a comparative study of the $B\to \pi$, $K$ transition form factors within the $k_T$ factorization approach and the light-cone sum rule analysis. The transition form factors $F_{+,0,T}^{B\to \pi }$ and $F_{+,0,T}^{B\to K}$ are carefully re-calculated up to $\mathcal{O}(1\mathrm{/}{m}_b^2)$ within the $k_T$ factorization approach in the large recoil region, in which the main theoretical uncertainties are discussed. The QCD light-cone sum rule is applicable in the large and intermediate energy regions, and the QCD light-cone sum rule results in Ref.\cite{sumrule} are adopted for such a comparative study. It is found that when the two phenomenological parameters $\bar{\mathrm{\Lambda }}\in [0.50,0.55]$ and $\delta \in [0.25,0.30]$, the results of $F_{+,0,T}^{B\to \pi }(Q^2)$ and $F^{B\to K}_{+,0,T}(Q^2)$ from these two approaches are consistent with each other in the large recoil energy region.