SU_f(3)-Symmetry Breaking Effects of the B\to K Transition Form Factor in the QCD Light-Cone Sum Rules

TL;DR

This paper improves the calculation of the B→K transition form factor using QCD light-cone sum rules, focusing on SU(3) symmetry breaking effects and eliminating uncertain twist-3 contributions for more accurate results.

Contribution

It introduces an improved LCSR approach that removes the uncertain twist-3 contribution and incorporates radiative corrections, providing a more precise analysis of SU(3) breaking effects in B→K transitions.

Findings

The SU_f(3)-breaking effect ratio is 1.16±0.03.

Elimination of twist-3 contribution reduces uncertainties.

Consistent analysis with perturbative QCD results across energy regions.

Abstract

We present an improved calculation of the $B\to K$ transition form factor with chiral current in the QCD light-cone sum rule (LCSR) approach. Under the present approach, the most uncertain twist-3 contribution is eliminated. And the contributions from the twist-2 and the twist-4 structures of the kaon wave function are discussed, including the $SU_f(3)$-breaking effects. One-loop radiative corrections to the kaonic twist-2 contribution together with the leading-order twist-4 corrections are studied. The $SU_f(3)$ breaking effect is obtained, $ \frac{F^{B\to K}_{+}(0)}{F^{B\to\pi}_{+}(0)}=1.16\pm 0.03$. By combining the LCSR results with the newly obtained perturbative QCD results that have been calculated up to ${\cal O}(1/m^2_b)$ in Ref.\cite{hwf0}, we present a consistent analysis of the $B\to K$ transition form factor in the large and intermediate energy regions.