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

• Published in: arXiv.org 2022-02
• Main Authors: Hua-Dian Niu, Guo-Dong, Li, Jia-Le, Ren, Liu, Xin
• Format: Article
• Language: English
• Subjects: Flavor (particle physics); Large Hadron Collider; Mesons; Particle decay; Quantum chromodynamics; Quarks
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2110.01217

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.