Perturbative QCD analysis of neutral $B$-meson decays into $\sigma\sigma, \sigma f_0$ and $f_0 f_0$

TL;DR

This paper uses perturbative QCD to analyze neutral B-meson decays into light scalar mesons, predicting large branching ratios and CP violations, which can be tested in upcoming collider experiments through specific decay channels.

Contribution

It provides the first detailed perturbative QCD predictions for B-meson decays into scalar mesons, highlighting potential large CP violations and branching ratios for experimental verification.

Findings

Branching ratios estimated to be between 10^{-6} and 10^{-4}.

Large direct CP violations predicted in certain decay modes.

Decay channels involving scalar mesons can be observed via their pion decay modes.

Abstract

The decays of $B_{d,s}^0 \to \sigma\sigma, \sigma f_0, f_0 f_0$, with $\sigma$ and $f_0$ denoting the light scalar mesons $f_0(500)$ and $f_0(980)$ in the two-quark picture, are studied in the perturbative QCD approach based on $k_T$ factorization. With the referenced value of the mixing angle $|\varphi| \sim 25^\circ$ for the $\sigma-f_0$ mixing in the quark-flavor basis, it is of great interest to obtain that: (a) these neutral $B$-meson decays into $\sigma\sigma, \sigma f_0$, and $f_0 f_0$ have large branching ratios in the order of $10^{-6} \sim 10^{-4}$, which mean the possibly constructive interferences existed in the decays with different flavor states, and then are expected to be tested at the Large Hadron Collider beauty and/or Belle-II experiments in the (near) future; (b) the large direct CP violations could be easily found in the $B_d^0 \to \sigma\sigma, f_0 f_0$ and $B_{d,s}^0 \to \sigma f_0$ decays, which indicate the considerable interferences between the tree and the penguin decay amplitudes involved in these four modes, and would be confronted with the future measurements; (c) these neutral $B$-meson decays could be examined through the secondary decay chain $\sigma/f_0 \to \pi^+ \pi^-$, namely, the four-body decays of $B_{d,s}^0 \to (\pi^+ \pi^-)_{\sigma(f_0)} (\pi^+ \pi^-)_{\sigma(f_0)}$. On the other side, it seems that other 4 four-body decays of $B_d^0 \to (\pi^+ \pi^-)_{\sigma} (K^+ K^-)_{f_0}$, $B_s^0 \to (\pi^+ \pi^-)_{\sigma(f_0)} (K^+ K^-)_{f_0}$, and $B_s^0 \to (K^+ K^-)_{f_0} (K^+ K^-)_{f_0}$ could also be detected at the relevant experiments, if the $f_0 \to K^+ K^-$ could be identified from the $\phi \to K^+ K^-$ clearly.