Pure annihilation decays of B_s~0→a_0~+a_0~- and B_d~0→K_0~(*+)K_0~(*-) in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays ofB _s~0→a_0~+a _0~-andB _d~0→K_0~(*+)K_0~(*-),where a_0K_0~*]denotes the scalar a_0(980) and a_0(1450)K_0~*(800)(ork)and K_0~*(1430)],with the perturbative QCD factorization approach under the assumption of two-quark structure for the a_0and K_0~*states.The numerical results show that the branching ratios of theB _d~0→K_0~(*+)K_0~(*-)decays are in the order of 10~(-6),while the decay rates of theB_s~0→a_0~+a _0~-modes are in the order of 10~(-5).In light of the measured modes with the same quark components in the pseudoscalar sector,namely,B _d~0→K~+K~-and B_s~0→p p~(+-),the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-Ⅱ experiments in the (near) future.Meanwhile,it is of great interest to find that the twist-3 distribution amplitudes φ~S and φ~T with inclusion of the Gegenbauer polynomials for the scalar a_0(1450) and K_0~*(1430)states in scenario2 contribute slightly to the branching ratios while significantly to the CP violations in the B_d~0→K_0~*(14 30)~+K_0*(14 30)~-and B_s~0→a_0(1450)~+a_0(1450)~-decays,which indicates that,compared to the asymptotic φ~Sand φ~T,these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels.These predictions await for the future confirmation experimentally,which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.

Pure annihilation decays of Bs0 → a0+ a0− and Bd0 → ${K}_{0}^{* +}$ ${K}_{0}^{* -}$ in the PQCD approach

We study the CP-averaged branching fractions and the CP-violating asymmetries in the pure annihilation decays of ${B}_{s}^{0}\to {a}_{0}^{+}{a}_{0}^{-}$ and ${B}_{d}^{0}\to {K}_{0}^{* +}{K}_{0}^{* -}$, where ${a}_{0}\ {K}_{0}^{* }]$ denotes the scalar a₀(980) and a₀(1450) ${K}_{0}^{* }(800)(\mathrm{or}\ \kappa )$ and ${K}_{0}^{* }(1430)$], with the perturbative QCD factorization approach under the assumption of two-quark structure for the a₀ and ${K}_{0}^{* }$ states. The numerical results show that the branching ratios of the ${B}_{d}^{0}\to {K}_{0}^{* +}{K}_{0}^{* -}$ decays are in the order of 10⁻⁶, while the decay rates of the ${B}_{s}^{0}\to {a}_{0}^{+}{a}_{0}^{-}$ modes are in the order of 10⁻⁵. In light of the measured modes with the same quark components in the pseudoscalar sector, namely, ${B}_{d}^{0}\to {K}^{+}{K}^{-}$ and ${B}_{s}^{0}\to {\pi }^{+}{\pi }^{-}$, the predictions for the considered decay modes in this work are expected to be measured at the Large Hadron Collider beauty and/or Belle-II experiments in the (near) future. Meanwhile, it is of great interest to find that the twist-3 distribution amplitudes φ^S and φ^T with inclusion of the Gegenbauer polynomials for the scalar a₀(1450) and ${K}_{0}^{* }(1430)$ states in scenario 2 contribute slightly to the branching ratios while significantly to the CP violations in the ${B}_{d}^{0}\to {K}_{0}^{* }{\left(1430\right)}^{+}{K}_{0}^{* }{\left(1430\right)}^{-}$ and ${B}_{s}^{0}\to {a}_{0}{\left(1450\right)}^{+}{a}_{0}{\left(1450\right)}^{-}$ decays, which indicates that, compared to the asymptotic φ^S and φ^T, these Gegenbauer polynomials could change the strong phases evidently in these pure annihilation decay channels. These predictions await for the future confirmation experimentally, which could further provide useful information to help explore the inner structure of the scalars and shed light on the annihilation decay mechanism.