Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$

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 $|\phi |\sim 25^{\circ }$ 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 $\varphi \to K^{+}{K}^{-}$ clearly.

Comments: 17 pages, 3 figures, 3 tables, references updated, final version to appear in EPJC