Testing Leptoquark and $Z^{\prime}$ Models via $B\to K_{1}(1270,1400)\mu^{+}\mu^{-}$ Decays

The measurements of $R_{K^{(*)}}=\mathcal B(B\to K^{(*)}\mu^{+}\mu^{-})/\mathcal B(B\to K^{(*)}e^{+}e^{-})$ in recent years have hinted lepton flavor non-universality and thus drawn widespread attentions. If these anomalies are induced by new physics (NP), deviations from the SM predictions may also be found in other channels via the same process at the quark level. In this work, we study in $B\to K_{1}(1270,1400)\mu^{+}\mu^{-}$ decays the effects of two popular classes of NP models which can address the $b\to s$ anomalies, i.e. the leptoquark models and the $Z^{\prime}$ models. By assuming that NP only affects the $b\to s\mu^+\mu^-$ transition, we find that the unpolarized and polarized lepton flavor universality (LFU) ratios $R_{K_1^{(L,T)}(1270)}$ are useful to distinguish among the NP models (scenarios) and the SM because they are sensitive to the NP effects and insensitive to the mixing angle $\theta_{K_1}$, while the $R_{K_1^{(L,T)}(1400)}$ are sensitive to both NP and $\theta_{K_1}$. Another ratio $R_\mu(K_1)=\mathcal B(B\to K_1(1400)\mu^+\mu^-)/\mathcal B(B\to K_1(1270)\mu^+\mu^-)$ is shown to depend weekly on the effects from the NP models (scenarios) under consideration, and thus can be used to determine the $\theta_{K_1}$ and complement the $R_{K_1^{(L,T)}}$ in the probe for NP.