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arXiv 2103.00642hep-ph
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用微扰QCD方法研究四体衰变$B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$

Four-body decays $B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$ in the perturbative QCD approach

Zhou Rui, Ya Li, Hsiang-nan Li

摘要:

我们用微扰QCD(PQCD)方法研究了$K^*(892)$对不变质量区中的四体衰变$B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$,其中$(Kπ)_{S/P}$表示一个$S$或$P$波$Kπ$组态. $P$波共振$K^*(892)$和可能的$S$波分量的贡献被包括在$Kπ$双介子分布振幅的参数化中,这是该形式主义中的非微扰输入。我们计算每个共振的分支比,并观察到相当大的$S$波贡献的$B_s$模式,以及与最近可用的LHCb数据一致。我们还推导出了$K^*\bar{K}^*$末态的极化分数,并将我们的预测与以前相应的二体$B\to K^*\bar{K}^*$衰变的PQCD分析进行了比较。与两个$U$ -自旋相关通道$B^0\rightarrow K^{*0}\bar{K}^{*0}$和$B^0_s\rightarrow K^{*0}\bar{K}^{*0}$相关的极化难题仍然存在。除了直接的$CP$不对称性,三重产品的不对称性和$S$波诱导的直接$CP$不对称性起源于各种螺旋度振幅之间的干扰,提出。结果表明,真正的三重产品的不对称性是相当小的,而直接$CP$不对称性和$S$波诱导的直接$CP$不对称性是显着的在一些衰变。我们的结果将在不久的将来接受来自$B$工厂的精确数据的严格测试。

英文摘要:

We investigate the four-body decays $B_{(s)} \rightarrow (Kπ)_{S/P} (Kπ)_{S/P}$ in the $Kπ$-pair invariant mass region around the $K^*(892)$ resonance in the perturbative QCD (PQCD) approach, where $(Kπ)_{S/P}$ denotes a $S$- or $P$-wave $Kπ$ configuration. The contributions from the $P$-wave resonance $K^*(892)$ and from possible $S$-wave components are included into the parametrization of the $Kπ$ two-meson distribution amplitudes, which are the nonperturbative inputs in this formalism. We calculate the branching ratio for each resonance and observe sizable $S$-wave contributions to the $B_s$ modes, well consistent with recently available LHCb data. We also deduce the polarization fractions for the $K^*\bar{K}^*$ final states, and compare our predictions to those in previous PQCD analyses of the corresponding two-body $B\to K^*\bar{K}^*$ decays. The polarization puzzle associated with the two $U$-spin related channels $B^0\rightarrow K^{*0}\bar{K}^{*0}$ and $B^0_s\rightarrow K^{*0}\bar{K}^{*0}$ still exists. In addition to direct $CP$ asymmetries, triple-product asymmetries and $S$-wave induced direct $CP$ asymmetries originating from the interference among various helicity amplitudes, are presented. It is shown that true triple-product asymmetries are rather small, while direct $CP$ asymmetries and $S$-wave-induced direct $CP$ asymmetries are significant in some decays. Our results will be subject to stringent tests with precise data from $B$ factories in the near future.

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