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 rightarrow 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}{-}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 and B_{d,s}^0 rightarrow 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 rightarrow pi ^+ pi ^-, namely, the four-body decays of B_{d,s}^0 rightarrow (pi ^+ pi ^-)_{sigma (f_0)} (pi ^+ pi ^-)_{sigma (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_s^0 rightarrow (pi ^+ pi ^-)_{sigma (f_0)} (K^+ K^-)_{f_0}, and B_s^0 rightarrow (K^+ K^-)_{f_0} (K^+ K^-)_{f_0} could also be detected at the relevant experiments, if the f_0 rightarrow K^+ K^- could be identified from the phi rightarrow 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 and/or f_0 and to constrain both of the magnitude and the sign of varphi .