Search

The decays of $$B_{d,s}^0 \rightarrow \sigma \sigma , \sigma f_0, f_0 f_0$$ B d , s 0 → σ σ , σ f 0 , f 0 f 0 , with $$\sigma $$ σ and $$f_0$$ f 0 denoting the light scalar mesons $$f_0(500)$$ f 0 ( 500 ) and $$f_0(980)$$ f 0 ( 980 ) in the two-quark picture, are studied in the perturbative QCD approach based on $$k_T$$ k T factorization. With the referenced value of the mixing angle $$|\varphi | \sim 25^\circ $$ | φ | ∼ 25 ∘ for the $$\sigma -f_0$$ σ - f 0 mixing in the quark-flavor basis, it is of great interest to obtain that: (a) these neutral B-meson decays into $$\sigma \sigma , \sigma f_0$$ σ σ , σ f 0 , and $$f_0 f_0$$ f 0 f 0 have large branching ratios in the order of $$10^{-6}{-}10^{-4}$$ 10 - 6 - 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 $$B_d^0 \rightarrow \sigma \sigma , f_0 f_0$$ B d 0 → σ σ , f 0 f 0 and $$B_{d,s}^0 \rightarrow \sigma f_0$$ B d , s 0 → σ 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 $$\sigma /f_0 \rightarrow \pi ^+ \pi ^-$$ σ / f 0 → π + π - , namely, the four-body decays of $$B_{d,s}^0 \rightarrow (\pi ^+ \pi ^-)_{\sigma (f_0)} (\pi ^+ \pi ^-)_{\sigma (f_0)}$$ B d , s 0 → ( π + π - ) σ ( f 0 ) ( π + π - ) σ ( f 0 ) with still large branching ratios. On the other side, it seems that other 4 four-body decays of $$B_d^0 \rightarrow (\pi ^+ \pi ^-)_{\sigma } (K^+ K^-)_{f_0}$$ B d 0 → ( π + π - ) σ ( K + K - ) f 0 , $$B_s^0 \rightarrow (\pi ^+ \pi ^-)_{\sigma (f_0)} (K^+ K^-)_{f_0}$$ B s 0 → ( π + π - ) σ ( f 0 ) ( K + K - ) f 0 , and $$B_s^0 \rightarrow (K^+ K^-)_{f_0} (K^+ K^-)_{f_0}$$ B s 0 → ( K + K - ) f 0 ( K + K - ) f 0 could also be detected at the relevant experiments, if the $$f_0 \rightarrow K^+ K^-$$ f 0 → K + K - could be identified from the $$\phi \rightarrow K^+ K^-$$ ϕ → K + K - clearly. The (near) future experimental confirmations with good precision would help to further study the perturbative and/or nonperturbative QCD dynamics involved in these considered decay modes, as well as to explore the intrinsic characters of these scalar mesons $$\sigma $$ σ and/or $$f_0$$ f 0 and to constrain both of the magnitude and the sign of $$\varphi $$ φ .

The decays of $B_{d,s}^0 \to ����, ��f_0, f_0 f_0$, with $��$ 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 $|��| \sim 25^\circ$ for the $��-f_0$ mixing in the quark-flavor basis, it is of great interest to obtain that: (a) these neutral $B$-meson decays into $����, ��f_0$, 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 $B_d^0 \to ����, f_0 f_0$ and $B_{d,s}^0 \to ��f_0$ 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 $��/f_0 \to ��^+ ��^-$, namely, the four-body decays of $B_{d,s}^0 \to (��^+ ��^-)_{��(f_0)} (��^+ ��^-)_{��(f_0)}$. On the other side, it seems that other 4 four-body decays of $B_d^0 \to (��^+ ��^-)_�� (K^+ K^-)_{f_0}$, $B_s^0 \to (��^+ ��^-)_{��(f_0)} (K^+ K^-)_{f_0}$, 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 $��\to K^+ K^-$ clearly., 17 pages, 3 figures, 3 tables, references updated, final version to appear in EPJC