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The measurements of $R_{K^{(*)}}=\mathcal B(B\toK^{(*)}\mu^{+}\mu^{-})/\mathcal B(B\to K^{(*)}e^{+}e^{-})$ in recent years havehinted lepton flavor non-universality and thus drawn widespread attentions. Ifthese anomalies are induced by new physics (NP), deviations from the SMpredictions may also be found in other channels via the same process at thequark 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. Byassuming that NP only affects the $b\to s\mu^+\mu^-$ transition, we find thatthe 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 andinsensitive to the mixing angle $\theta_{K_1}$, while the$R_{K_1^{(L,T)}(1400)}$ are sensitive to both NP and $\theta_{K_1}$. Anotherratio $R_\mu(K_1)=\mathcal B(B\to K_1(1400)\mu^+\mu^-)/\mathcal B(B\toK_1(1270)\mu^+\mu^-)$ is shown to depend weekly on the effects from the NPmodels (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.

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