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准二体衰变$B_{(s)} \to D (ρ(1450),ρ(1700)) \to D ππ$的微扰QCD分解方法

Quasi-two-body decays $B_{(s)} \to D (ρ(1450),ρ(1700)) \to D ππ$ in the perturbative QCD factorization approach

Ai-Jun Ma, Ya Li, Wen-Fei Wang, Zhen-Jun Xiao

备注：
8 pages, 1 figure and 3 tables. Some modifications, matching the published version
发表信息：
Phys. Rev. D 96, 093011 (2017)
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摘要：

利用微扰QCD（PQCD）分解方法中的准二体衰变框架，用$D=(D_{(s)}, \bar{D}_{(s)})$计算了衰变$B_{(s)} \to D (ρ(1450),ρ(1700))\to D ππ$的分支比.从{ \it BABAR}协作组对$e^+ e^- \to π^+ π^-(γ)$数据的分析中获得的π介子矢量形状因子$F_π$与双π介子分布振幅$Φ^{I=1}_{ππ}$有关。所考虑的准二体衰变的分支比的PQCD预测是在$10^{-10} \sim 10^{-4}$的范围内。如果考虑到较大的理论误差，则对${\cal B}(B^0\to \bar{D}^0 (ρ^0(1450),ρ^0(1700)) \to \bar{D}^0 π^+π^-)$的PQCD预言与LHCb报告的测量值吻合得很好。与传统的PQCD方法不同，我们可以从相应的准二体衰变的结果中提取出二体衰变$B_{(s)} \to D (ρ(1450),ρ(1700))$的衰变率。PQCD对${\cal B}(B_{(s)} \to D ρ(1450))$和${\cal B}(B_{(s)} \to D ρ(770))$的预测在量级上是相似的：这是一个有趣的关系，有待于将来的实验测量来检验。

英文摘要：

By employing a framework for the quasi-two-body decays in the perturbative QCD (PQCD) factorization approach, we calculate the branching ratios of the decays $B_{(s)} \to D (ρ(1450),ρ(1700))\to D ππ$ with $D=(D_{(s)}, \bar{D}_{(s)})$. The pion vector form factor $F_π$, acquired from a {\it BABAR} Collaboration analysis of $e^+ e^- \to π^+ π^-(γ)$ data, is involved in the two-pion distribution amplitudes $Φ^{I=1}_{ππ}$. The PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the range of $10^{-10} \sim 10^{-4}$. The PQCD predictions for ${\cal B}(B^0\to \bar{D}^0 (ρ^0(1450),ρ^0(1700)) \to \bar{D}^0 π^+π^-)$ agree well with the measured values as reported by LHCb if one takes still large theoretical errors into account. Unlike the traditional way of the PQCD approach, one can extract the decay rates for the two-body decays $B_{(s)} \to D (ρ(1450),ρ(1700))$ from the results of the corresponding quasi-two-body decays. The PQCD predictions for ${\cal B}(B_{(s)} \to D ρ(1450))$ and ${\cal B}(B_{(s)} \to D ρ(770))$ are similar in magnitude: an interesting relation to be tested by future experimental measurements.

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