# Studies on the $B \to \kappa \bar \kappa$ decays in the perturbative QCD approach

## TL;DR

This paper investigates $B o ext{kappa} ar{ ext{kappa}}$ decays using perturbative QCD, predicting decay rates and CP asymmetries, and highlighting potential for future experimental tests and new physics searches.

## Contribution

First analysis of $B o ext{kappa} ar{ ext{kappa}}$ decays in perturbative QCD with $k_T$ factorization, providing predictions for decay rates and CP asymmetries.

## Key findings

- Large decay rates for $B_s^0 o ext{kappa}^+ ext{kappa}$ decays (~$10^{-5}$).
- Pure annihilation $B_d^0 o ext{kappa}^+ ext{kappa}$ decay rate around $3 imes 10^{-6}$.
- Pure penguin modes have zero direct and mixing-induced CP violations in the Standard Model.

## Abstract

The $B \to \kappa \bar \kappa$ decays are investigated for the first time in the perturbative QCD formalism based on the $k_T$ factorization theorem, where the light scalar $\kappa$ is assumed as a two-quark state. Our numerical results and phenomenological analyses on the CP-averaged branching ratios and CP-violating asymmetries show that: (a) the $B_s^0 \to \kappa^+ \kappa^-$ and $B_s^0 \to \kappa^0 \bar \kappa^0$ decays have large decay rates around ${\cal O}(10^{-5})$, which could be examined by the upgraded Large Hadron Collider beauty and/or Belle-II experiments in the near future; (b) a large decay rate about $3 \times 10^{-6}$ appears in the pure annihilation $B_d^0 \to \kappa^+ \kappa^-$ channel, which could provide more evidences to help distinguish different QCD-inspired factorization approaches, even understand the annihilation decay mechanism; (c) the pure penguin modes $B_d^0 \to \kappa^0 \bar \kappa^0$ and $B_s^0 \to \kappa^0 \bar \kappa^0$ would provide a promising ground to search for the possible new physics because of their zero direct and mixing-induced CP violations in the standard model. The examinations with good precision from the future experiments will help to further study the perturbative and/or nonperturbative QCD dynamics involved in these considered decay modes.