Contributions from the color-octet matrix elements to the $\overline{B}$ ${\to}$ ${\pi}{\pi}$ decays with QCD factorization approach

TL;DR

This paper revisits $ar{B} o \pi\pi$ decays using QCD factorization, highlighting the significance of color-octet matrix elements in explaining experimental branching ratios.

Contribution

It introduces the consideration of color-octet current matrix elements (COCME) in $ar{B} o \pi\pi$ decays, which were previously neglected, and demonstrates their impact on branching ratio predictions.

Findings

Form factor $F_0^{B o \pi}$ $ oughly$ 0.22 fits latest data.

COCME contributions help explain experimental branching ratios.

They are less influential on $CP$ asymmetries.

Abstract

Motivated by the ${\pi}{\pi}$ puzzle in nonleptonic $B$ decays in the time of high-precision and huge-data for particle physics, we restudy the $\overline{B}$ ${\to}$ ${\pi}{\pi}$ decays with QCD factorization approach. An additional contributions from the color-octet current matrix elements (COCME) which are unnoticed in almost all the previous calculation, are taken into consideration and parameterized by $X$. It is found that (1) form factor $F_{0}^{B{\pi}}$ ${\approx}$ $0.22$ is favored by the available latest measurements. (2) The COCME contributions are helpful to interpret the experimental data on branching ratios rather than $CP$ asymmetries for the $\overline{B}$ ${\to}$ ${\pi}{\pi}$ decays.