$B\to PP$ decays with Light-Cone Sum Rules

TL;DR

This paper employs light-cone sum rules to compute factorizable contributions to two-body nonleptonic $B$ decays into light pseudoscalars, deriving hadronic matrix elements for $B\to P_1P_2$ via a three-point correlator anchored in light-cone distribution amplitudes. The authors provide explicit LCSR expressions for the tree-level, factorizable amplitude $\langle P_2P_1|\mathcal{O}_1|B\rangle$ and evaluate branching ratios for $B^0\to\pi^+\pi^-$, $B^+\to\pi^+\pi^0$, $B^0\to K^+\pi^-$, and $B^0\to K^+K^-$, finding general agreement with experimental data within uncertainties. They also estimate ${\mathcal B}(B_s^0\to\pi^+\pi^-)$ using $f_s/f_d$ and SU(3) assumptions, obtaining $(0.781\pm0.233)\times10^{-6}$. The work highlights that including only tree-level, factorizable contributions explains much of the data but omits penguin and nonfactorizable effects, pointing to future improvements such as $\mathcal{O}(\alpha_s)$ corrections, higher-twist and three-particle LCDAs, and penguin topologies to sharpen SM tests and probe new physics.

Abstract

We study factorizable contributions to two-body nonleptonic decays of $B$ mesons using the light-cone sum rule method. By constructing three-point correlation functions and incorporating light-cone distribution amplitudes, we compute the hadronic matrix elements and branching ratios for decay channels $B^0 \to π^+π^-$, $B^+ \to π^+π^0$, $B^0 \to K^+π^-$, and $B^0 \to K^+K^-$. The results are in agreement with experimental data within uncertainties. We also estimate the branching ratio of $B_s^0 \to π^+π^-$ to be approximately $0.781\times10^{-6}$.

Figures (5)

• Figure 1: The Feynman diagrams corresponding to the operators $\mathcal{O}_i$.
• Figure 2: Dependence of the decay amplitudes on the Borel parameters $M_1^2$ and $M_2^2$ for $B^0\to\pi^+\pi^-$.
• Figure 3: Dependence of the decay amplitudes on the Borel parameters $M_1^2$ and $M_2^2$ for $B^+\to\pi^+\pi^0$.
• Figure 4: Dependence of the decay amplitudes on the Borel parameters $M_1^2$ and $M_2^2$ for $B^0\to K^+\pi^-$.
• Figure 5: Dependence of the decay amplitudes on the Borel parameters $M_1^2$ and $M_2^2$ for $B^0\to K^+K^-$.