标题： 通过常见衰变模式到$B_s$和$\bar{B}_s$的求和确定 CP 违反相位$γ$ 显示英文标题

标题： Determination of the CP Violating Phase $γ$ by a Sum Over Common Decay Modes to $B_s$ and $\bar{B}_s$

摘要： 为了帮助确定单位三角形的角$\gamma$的困难，Aleksan、Dunietz 和 Kayser 提出了类型的模式$K^-D^+_s$，这些模式同时属于$B_s$和$\bar{B}_s$。 我们指出，通过所有最终态包含基态介子的模式求和，可以提高统计量，即 $K^-D^+_s$, $K^{*-}D_+^s$, $K^-D^{*+}_s$, $K^{*-}D^{*+}_s$. 关键点是这些不同贡献相对于时间依赖性不对称性的稀释因子$D$的相位。 每个对$D$的贡献与一个乘积$F^{cb}$ $F^{ub}$ $f_{D_s}$ $f_K$ 成正比，其中$F$表示形式因子，$f$为衰变常数。 在一定的相位约定下，格点计算在将形式因子和衰变常数外推到轻夸克时没有显示出符号的变化。 然后，我们可以证明所有模态都建设性地贡献于稀释因子，除了$P$波$K^{*-}D^{*+}_s$，它是小的。 基于波函数重叠的夸克模型论证也确认了这种符号的稳定性。 通过对所有这些模态求和，我们发现相对于$K^-D^+_s$的统计量增加了六倍。 对于总和$D_{tot}$的稀释因子，在与数据上$B \to \psi K(K^*)$不冲突或从半轻子奇夸克形式因子外推的理论方案中，其值非常稳定，给出$D_{tot} \geq 0.6$，始终接近$D(K^- D^+_s)$。 显示英文摘要

摘要： To help the difficult determination of the angle $\gamma$ of the unitarity triangle, Aleksan, Dunietz and Kayser have proposed the modes of the type $K^-D^+_s$, common to $B_s$ and $\bar{B}_s$. We point out that it is possible to gain in statistics by a sum over all modes with ground state mesons in the final state, i.e. $K^-D^+_s$, $K^{*-}D_+^s$, $K^-D^{*+}_s$, $K^{*-}D^{*+}_s$. The delicate point is the relative phase of these different contributions to the dilution factor $D$ of the time-dependent asymmetry. Each contribution to $D$ is proportional to a product $F^{cb}$ $F^{ub}$ $f_{D_s}$ $f_K$ where $F$ denotes form factors and $f$ decay constants. Within a definite phase convention, lattice calculations do not show any change in sign when extrapolating to light quarks the form factors and decay constants. Then, we can show that all modes contribute constructively to the dilution factor, except the $P$-wave $K^{*-}D^{*+}_s$, which is small. Quark model arguments based on wave function overlaps also confirm this stability in sign. By summing over all these modes we find a gain of a factor 6 in statistics relatively to $K^-D^+_s$. The dilution factor for the sum $D_{tot}$ is remarkably stable for theoretical schemes that are not in very strong conflict with data on $B \to \psi K(K^*)$ or extrapolated from semileptonic charm form factors, giving $D_{tot} \geq 0.6$, always close to $D(K^- D^+_s)$.