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

TL;DR

This paper compares the B-meson light-cone wave function properties by analyzing $B o \pi$, $K$ transition form factors using $k_T$ factorization and light-cone sum rule methods, finding consistent results in the large recoil region.

Contribution

It provides a detailed comparative analysis of B-meson transition form factors using two different theoretical approaches, refining the understanding of the wave function properties.

Findings

Form factors from both approaches agree in the large recoil region.

Main uncertainties are discussed within the $k_T$ factorization approach.

Phenomenological parameters are constrained for consistency.

Abstract

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 $F^{B\to\pi}_{+,0,T}$ and $F^{B\to K}_{+,0,T}$ are carefully re-calculated up to ${\cal O}(1/m_b^2)$ 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 $\bar\Lambda\in [0.50,0.55]$ and $\delta\in[0.25,0.30]$, the results of $F^{B\to\pi}_{+,0,T}(Q^2)$ and $F^{B\to K}_{+,0,T}(Q^2)$ from these two approaches are consistent with each other in the large recoil energy region.