论文标题
$γ（k \toμ^+μ^ - ）（t）$和$ {\ cal b}（k_l \toμ^+μ^ - ）/{\ cal b}（k_l \toγγ）$之间的精确关系
A Precision Relation between $Γ(K\toμ^+μ^-)(t)$ and ${\cal B}(K_L\toμ^+μ^-)/{\cal B}(K_L\toγγ)$
论文作者
论文摘要
我们发现，$ \ Mathcal {b}（k_l \rightArrowμ^+μ^ - ）$和$ \ MATHCAL {B}（k_l \rightArrowγγ）$之间的阶段出现在单位性关系中。对未来KAON设施的这种关系的调查构成了标准模型测试，理论精度约为$ 2 \％$。该阶段对于敏感性研究具有进一步的重要性，以测量时间相关的$ k \rightarrowμ^+μ^ - $衰减率以提取CKM矩阵元素组合$ \ vert v_ {ts} v_ {td} v_ {td} \ sin（β+β_S）\ vert \ vert \ vert \ vert v_ {ts} v_ {td}我们找到一个独立于模型的理论清洁预测，$ \ cos^2φ_0= 0.96 \ pm 0.03 $。引用的错误是理论和实验错误的组合，并且两者都预计将来会收缩。使用手性扰动理论中的大$ n_c $限制的输入，我们找到了对具有负$ \cosφ_0$的解决方案的理论偏好，将角度$φ_0$的四倍歧义降低到了两个方面。
We find that the phase appearing in the unitarity relation between $\mathcal{B}(K_L\rightarrow μ^+μ^-)$ and $\mathcal{B}(K_L\rightarrow γγ)$ is equal to the phase shift in the interference term of the time-dependent $K\rightarrow μ^+μ^-$ decay. A probe of this relation at future kaon facilities constitutes a Standard Model test with a theory precision of about $2\%$. The phase has further importance for sensitivity studies regarding the measurement of the time-dependent $K\rightarrow μ^+μ^-$ decay rate to extract the CKM matrix element combination $\vert V_{ts} V_{td} \sin(β+β_s)\vert\approx A^2λ^5\barη$. We find a model-independent theoretically clean prediction, $\cos^2φ_0 = 0.96 \pm 0.03$. The quoted error is a combination of the theoretical and experimental errors, and both of them are expected to shrink in the future. Using input from the large-$N_C$ limit within chiral perturbation theory, we find a theory preference towards solutions with negative $\cosφ_0$, reducing a four-fold ambiguity in the angle $φ_0$ to a two-fold one.
