It was previously shown that unlike the ratios $R_K^{\mu e}\equiv R_K\equiv \mathrm{\Gamma }(B\to K{\mu }^{+}{\mu }^{-})/\mathrm{\Gamma }(B\to K{e}^{+}{e}^{-})$ and $R_{K^{*}}^{\mu e}\equiv R_{K^{*}}\equiv \mathrm{\Gamma }(B\to K^{*}{\mu }^{+}{\mu }^{-})/\mathrm{\Gamma }(B\to K^{*}{e}^{+}{e}^{-})$, the ratios $R_K^{\tau \mu }$ and $R_{K^{*}}^{\tau \mu }$ can deviate from their Standard Model (SM) predictions even with universal new physics couplings. This observation highlights the critical need to identify and establish genuine lepton flavor universality violating (LFUV) observables in the $\tau -\mu$ sector. This work embarks on establishing genuine LFUV ratio observables in $B\to K\ell \ell$ and $B\to K^{*}\ell \ell$ decays through comprehensive analysis of their angular distributions. We find that like $R_{K^{*}}^{\tau \mu }$, the ratios $R_{A_{FB}}^{\tau \mu }$ and $R_{f_L}^{\tau \mu }$ do not qualify as genuine LFUV observables, whereas the ratios of all optimized observables in $B\to K^{*}\ell \ell$ decays within the $\tau -\mu$ sector definitively do. In the case of $B\to K\ell \ell$ decays, similar to $R_K^{\tau \mu }$, the ratio $R_{F_H}$ is influenced by mass effects and therefore cannot be considered a genuine LFUV observable in the $\tau -\mu$ sector. However, the ratio ${\mathrm{\Gamma }}_{\tau }(1-F_H^{\tau })/{\mathrm{\Gamma }}_{\mu }(1-F_H^{\mu })$ stands as the sole genuine LFUV observable in $B\to K\ell \ell$ decays. Furthermore, by making use of new physics Lorentz structures which provide a better fit to the current $b\to s\ell \ell$ data as compared to the SM, we demonstrate how the nongenuine LFUV ratios $R_{A_{FB}}^{\tau \mu }$ and $R_{f_L}^{\tau \mu }$ can be employed to distinguish between framework with solely universal lepton couplings and those with both universal and nonuniversal couplings.

中文翻译：

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B→(K,K*)ℓℓ 的 τ−μ 扇区中真正的轻子味普遍性破坏可观测值衰变


之前已经表明，与比率不同 $R_K^{\mu e}\equiv R_K\equiv \mathrm{\Gamma }(B\to K{\mu }^{+}{\mu }^{-})/\mathrm{\Gamma }(B\to K{e}^{+}{e}^{-})$ 和 $R_{K^{*}}^{\mu e}\equiv R_{K^{*}}\equiv \mathrm{\Gamma }(B\to K^{*}{\mu }^{+}{\mu }^{-})/\mathrm{\Gamma }(B\to K^{*}{e}^{+}{e}^{-})$ ，比率 $R_K^{\tau \mu }$ 和 $R_{K^{*}}^{\tau \mu }$ 即使使用通用的新物理耦合，也可能会偏离标准模型（SM）的预测。这一观察结果强调了识别和建立真正的轻子风味普遍性破坏（LFUV）可观测值的迫切需要 $\tau -\mu$ 部门。这项工作着手建立真正的 LFUV 比率可观测值 $B\to K\ell \ell$ 和 $B\to K^{*}\ell \ell$ 通过综合分析它们的角度分布来衰减。我们发现就像 $R_{K^{*}}^{\tau \mu }$ ，比率 $R_{A_{FB}}^{\tau \mu }$ 和 $R_{f_L}^{\tau \mu }$ 不符合真正的 LFUV 可观测量量，而所有优化可观测量量的比率 $B\to K^{*}\ell \ell$ 内衰变 $\tau -\mu$ 部门肯定会这样做。如果是 $B\to K\ell \ell$ 衰变，类似于 $R_K^{\tau \mu }$ ，比率 $R_{F_H}$ 受质量效应的影响，因此不能被视为真正的 LFUV 可观测到的 $\tau -\mu$ 部门。然而，该比例 ${\mathrm{\Gamma }}_{\tau }(1-F_H^{\tau })/{\mathrm{\Gamma }}_{\mu }(1-F_H^{\mu })$ 是唯一可观测到的真正的 LFUV $B\to K\ell \ell$ 腐烂。此外，通过利用新的物理洛伦兹结构，可以更好地适应当前的情况 $b\to s\ell \ell$ 与 SM 数据相比，我们展示了非正品 LFUV 比率如何 $R_{A_{FB}}^{\tau \mu }$ 和 $R_{f_L}^{\tau \mu }$ 可用于区分仅具有通用轻子耦合的框架和具有通用和非通用耦合的框架。