Abstract
Motivated by the observations of the decays B^0 rightarrow K_0^{*}(1430)^0 f_0(980) and B^0 rightarrow K_2^{*}(1430)^0 f_0(980) from BaBar collaboration, we study the B^{0(+)} rightarrow K_{0,2}^{*}(1430)^{0(+)} f_0(980)/sigma decays in the perturbative QCD approach for the first time. In the absence of reliable nonperturbative wave functions we only assume the scalar meson f_0(980) and sigma are two-quark ground states. In our calculations, these decays are all dominated by the hard-scattering emission and annihilation diagrams, while the factorizable emission diagrams are forbidden or suppressed heavily by the vector decay constants. Furthermore, the branching fractions are sensitive to the mixing between f_0(980) and sigma . Comparing our results with the experimental data, a large mixing angle theta is favored. Taking theta =145^circ , the orders of branching fractions of B rightarrow K_0^{*}(1430)^0 sigma , B rightarrow K_{2}^{*}(1430)^0 sigma and B rightarrow K_{0,2}^{*}(1430)^0 f_0(980) are predicted to be 10^{-4}, 10^{-5} and 10^{-6}, respectively, which can be measured in the current experiments such as LHCb and Belle-2. In addition, although these decays are penguin dominant, the mixing also leads to large direct CP asymmetries in these decays. With the precise data in future, our results could shed light on the inner structure of the scalar mesons and can be used to determine the mixing angle of the sigma -f_0(980) system.
Highlights
More and more B decays involving a light scalar meson in final states have been observed in both Belle [5
In the past few years, the decays involving a scalar meson or a tensor meson in final states have been already explored in different approaches, such as the generalized factorization approach [31], QCD factorization (QCDF)
The physics below the scale t is soft and nonperturbative, which can be parameterized into the universal hadronic wave functions of the initial and final states
Summary
B decays with scalar, axial vector and tensor particles became available. In 2002, the decay B → f0(980)K with large branching fraction was firstly observed in Belle experiment [3], and was confirmed subsequently by BaBar [4] in 2004. More and more B decays involving a light scalar meson in final states have been observed in both Belle [5–. By comparing to experimental data, we hope that our results based on two-quark picture could shed light on the inner structure and characters of the scalar mesons. [25], based on the measurements of the ratio of the coupling of f0 decaying into π π and K K the authors obtained the mixing angle to be (25.1 ± 0.5)◦ (164.3 ± 0.2)◦ with data [26,27,28], and (42.3+−85..35)◦ (158 ± 2)◦ with data [29]. In the past few years, the decays involving a scalar meson or a tensor meson in final states have been already explored in different approaches, such as the generalized factorization approach [31], QCD factorization (QCDF). The numerical results and the detailed discussions will be given in Sect. 4, and we will summarize this work in the last section
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