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arXiv 2104.06572hep-ph
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用PQCD方法计算$B_s^0 \to a_0^+ a_0^-$和$B_d^0 \to K_0^{*+} K_0^{*-}$的纯湮没衰变

Pure annihilation decays of $B_s^0 \to a_0^+ a_0^-$ and $B_d^0 \to K_0^{*+} K_0^{*-}$ in the PQCD approach

Yutong Chen, Zewen Jiang, Xin Liu

摘要:

在双夸克结构的假设下,用微扰QCD分解方法研究了$B_s^0 \to a_0^+ a_0^-$和$B_d^0 \to K_0^{*+} K_0^{*-}$纯湮灭衰变中的{\it CP}平均分支分数和{ \it CP}破坏不对称性,其中$a_0\;[K_0^*]$表示标量$a_0(980)$和$a_0(1450)$ [ $K_0^*(800) ( {\rm or}\; κ)$和$K_0^*(1430)$ ].计算结果表明,$B_d^0 \to K_0^{*+} K_0^{*-}$模的衰变分支比为$10^{-6}$的量级,而$B_s^0 \to a_0^+ a_0^-$模的衰变速率为$10^{-5}$的量级.鉴于在赝标量扇区中具有相同夸克分量的测量模式,即$B_d^0 \to K^+ K^-$和$B_s^0 \to π^+ π^-$,预计在(不久的)将来,在大型强子对撞机美容和/或Belle-II实验中测量到的预测。同时,有趣的是发现,在情形2中,包含标量$a_0(1450)$和$K_0^*(1430)$态的Gegenbauer多项式的扭转3分布振幅$ϕ^{S}$和$ϕ^{T}$对分支比的贡献很小,而对$B_d^0 \to {K_0^*}(1430)^+ {K_0^*}(1430)^-$和$B_s^0 \to a_0(1450)^+ a_0(1450)^-$衰变中的{ \it CP}破坏有显著贡献,这表明,与渐近$ϕ^S$和$ϕ^T$相比,这些Gegenbauer多项式可以明显改变这些纯湮没衰变道中的强相位。这些预言有待于未来的实验证实,这将为进一步探索标量的内部结构和揭示湮灭衰变机制提供有用的信息。

英文摘要:

We study the {\it CP}-averaged branching fractions and the {\it 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 $a_0(980)$ and $a_0(1450)$ [$K_0^*(800) ( {\rm or}\; κ)$ and $K_0^*(1430)$], with the perturbative QCD factorization approach under the assumption of two-quark structure for the $a_0$ 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 $B_s^0 \to π^+ π^-$, 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 scenario 2 contribute slightly to the branching ratios while significantly to the {\it CP} violations in the $B_d^0 \to {K_0^*}(1430)^+ {K_0^*}(1430)^-$ and $B_s^0 \to a_0(1450)^+ a_0(1450)^-$ 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.

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