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arXiv 1802.00155hep-phhep-ex
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再论无粲$B_q\to P P$衰变中的末态相互作用

Revisiting Final State Interaction in Charmless $B_q\to P P$ Decays

Chun-Khiang Chua

摘要:

Belle和LHCb报道了在无粲$B_{u,d,s}\to PP$模中的各种新的测量结果,其中$P$是一个低位赝标介子.这些包括$B^0\toπ^0π^0$、$ηπ^0$、$B_s\toη'η'$、$B^0\to K^+K^-$和$B^0_s\toπ^+π^-$衰变率。其中一些模式被高度抑制,是最罕见的PDMATHAMT衰变。各种模式上的直接CP不对称性不断更新。众所周知,直接CP不对称性和被抑制模的速率对末态相互作用(FSI)很敏感。随着新的测量报告和更多的数据将被收集,这是有趣的和及时的重温在$B_{u,d,s}\to PP$状态的再散射效应。我们进行$χ^2$分析与CP平均率和CP不对称性的$\overline B{}_{u,d,s}\to PP$衰变的所有可用数据。我们的数值结果进行了比较,数据和那些从因式分解的方法。在存在重散射的情况下,从因子分解结果显著提高了拟合的质量。拓扑振幅和重散射的关系进行了探讨,他们有助于提供一个更好的理解FSI的影响。根据拓扑振幅的U(3)对称性和FSI,考虑了交换再散射消失的情形。通过湮灭和全湮灭再散射,交换、湮灭、$u$ -企鹅、$u$ -企鹅湮灭和某些电弱企鹅振幅都得到显著增强.特别地,$u$ -企鹅湮灭振幅通过树振幅经由全湮灭再散射而显著增强。这些增强影响速率和CP不对称性。预测可以在不久的将来进行检查。

英文摘要:

Various new measurements in charmless $B_{u,d,s}\to PP$ modes, where $P$ is a low lying pseudoscalar meson, are reported by Belle and LHCb. These include the rates of $B^0\toπ^0π^0$, $ηπ^0$, $B_s\toη'η'$, $B^0\to K^+K^-$ and $B^0_s\toπ^+π^-$ decays. Some of these modes are highly suppressed and are among the rarest $B$ decays. Direct CP asymmetries on various modes are constantly updated. It is well known that direct CP asymmetries and rates of suppressed modes are sensitive to final state interaction (FSI). As new measurements are reported and more data will be collected, it is interesting and timely to revisit the rescattering effects in $B_{u,d,s}\to PP$ states. We perform a $χ^2$ analysis with all available data on CP-averaged rates and CP asymmetries in $\overline B{}_{u,d,s}\to PP$ decays. Our numerical results are compared to data and those from factorization approach. The quality of the fit is improved significantly from the factorization results in the presence of rescattering. The relations on topological amplitudes and rescattering are explored and they help to provide a better understanding of the effects of FSI. As suggested by U(3) symmetry on topological amplitudes and FSI, a vanishing exchange rescattering scenario is considered. The exchange, annihilation, $u$-penguin, $u$-penguin annihilation and some electroweak penguin amplitudes are enhanced significantly via annihilation and total annihilation rescatterings. In particular, the $u$-penguin annihilation amplitude is sizably enhanced by the tree amplitude via total annihilation rescattering. These enhancements affect rates and CP asymmetries. Predictions can be checked in the near future.

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