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PQCD方法下准两体衰变$B_c \rightarrow K^{*}_0(1430,1950) D_{(s)} \rightarrow K πD_{(s)}$的分支比与CP不对称性

Branching ratios and CP asymmetries of the quasi-two-body decays $B_c \rightarrow \ K^{*}_0(1430,1950) D_{(s)} \rightarrow K πD_{(s)} $ in the PQCD approach

Zhi-Qing Zhang, Zi-Yu Zhang, Ming-Xuan Xie, Ming-Yang Li, Hong-Xia Guo

AI总结:

本研究在PQCD框架下研究B_c介子的两类准两体衰变,采用两种类时形状因子参数化方案,验证了窄宽度近似下的结果一致性,明确了LASS参数化的适用性及非共振成分的作用,并针对K_0^*(1950)的宽度差异完成了对应计算。

摘要:

本文在微扰QCD(PQCD,perterbative QCD)框架下研究了准两体衰变$B_c \to K_0^{*}(1430,1950) D_{(s)} \to K πD_{(s)}$。我们引入S波双介子分布振幅(DAs)来描述$Kπ$对的末态相互作用,该分布振幅涉及类时形状因子与盖根鲍尔多项式。计算中我们采用两种参数化方案描述类时形状因子:一种是相对论性布雷特-维格纳(RBW)公式,通常更适用于窄共振;另一种是由LASS合作组提出的LASS线型,它同时包含共振与非共振成分。我们发现,在窄宽度近似(NWA)下,由准两体衰变$B_c \to K_0^{*}(1430) D_{(s)} \to K πD_{(s)}$得到的$B_c \to K_0^{*}(1430) D_{(s)}$衰变的分支比与直接CP破坏,能与此前在两体框架下、假设$K^*_0(1430)$为最低层$\bar q s$态(即所谓的方案II(SII))计算得到的PQCD结果很好地吻合。我们得出结论:LASS参数化比RBW公式更适合描述$K_0^{*}(1430)$,且非共振成分在$B_c \to K_0^{*}(1430) D_{(s)} \to K πD_{(s)}$衰变的分支比中发挥重要作用。鉴于BaBar与LASS合作组给出的$K_0^{*}(1950)$衰变宽度测量值存在较大差异,除了对$K^*_0(1950)$共振采用两种参数化方案外,我们还使用$Γ_{K^*_0(1950)}=0.100\pm0.04$ GeV与$Γ_{K^*_0(1950)}=0.201\pm0.034$ GeV两个数值,计算了准两体衰变$B_c \to K_0^{*}(1950) D_{(s)} \to K πD_{(s)}$的分支比与CP破坏。

英文摘要:

In this paper, we investigate the quasi-two-body decays $B_c \to K_0^{*}(1430,1950) D_{(s)} \to K πD_{(s)}$ within the perterbative QCD (PQCD) framework. The S-wave two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $Kπ$ pair, which involve the time-like form factors and the Gegenbauer polynomials. In the calculations, we adopt two kinds of parameterization schemes to describe the time-like form factors: One is the relativistic Breit-Wigner (RBW) formula, which is usually more siutable for the narrow resonances, and the other is the LASS line shape proposed by the LASS Collaboration, which includes both the resonant and nonresonant components. We find that the branching ratios and the direct CP violations for the decays $B_c \to K_0^{*}(1430) D_{(s)}$ obtained from those of the quasi-two-body decays $B_c \to K_0^{*}(1430) D_{(s)} \to K πD_{(s)}$ under the narrow width approximation (NWA) can be consistent well with the previous PQCD results calculated in the two-body framework by assuming that $K^*_0(1430)$ being the lowest lying $\bar q s$ state, which is so-called scenario II (SII). We conclude that the LASS parameterization is more siutable to describe the $K_0^{*}(1430)$ than the RBW formula, and the nonresonant components play an important role in the branching ratios of the decays $B_c \to K_0^{*}(1430) D_{(s)} \to K πD_{(s)}$. In view of the large difference between the decay width measurements for the $K_0^{*}(1950)$ given by BaBar and LASS collaborations, we calculate the branching ratios and the CP violations for the quasi-two-body decays $B_c \to K_0^{*}(1950) D_{(s)} \to K πD_{(s)}$ by using two values, $Γ_{K^*_0(1950)}=0.100\pm0.04$ GeV and $Γ_{K^*_0(1950)}=0.201\pm0.034$ GeV, besides the two kinds of parameterizations for the resonance $K^*_0(1950)$.

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