We perform an analysis of the $b\to c\tau \nu$ data, including $R(D^{(⁎)})$, $R(J/\psi )$, $P_{\tau }(D^{⁎})$ and $F_L^{D^{⁎}}$, within and beyond the Standard Model (SM). We fit the $B\to D^{(⁎)}$ hadronic form factors in the HQET parametrization to the lattice and the light-cone sum rule (LCSR) results, applying the general strong unitarity bounds corresponding to $J^P=1^{-}$, $1^{+}$, $0^{-}$ and $0^{+}$. Using the obtained HQET relations between helicity amplitudes, we give the strong unitarity bounds on individual helicity amplitudes, which can be used in the BGL fits. Using the fitted form factors and taking into account the most recent Belle measurement of $R(D^{(⁎)})$ we investigate the model-independent and the leptoquark model explanations of the $b\to c\tau \nu$ anomalies. Specifically, we consider the one-operator, the two-operator new physics (NP) scenarios and the NP models with a single $R_2$, $S_1$ or $U_1$ leptoquark which is supposed to be able to address the $b\to c\tau \nu$ anomalies, and our results show that the $R_2$ leptoquark model is in tension with the limit $\mathcal{B}(B_c\to \tau \nu )<10\text{\%}$. Furthermore, we give predictions for the various observables in the SM and the NP scenarios/leptoquark models based on the present form factor study and the analysis of NP.

我们对 $b\to C\tau \nu$ 数据，包括 $\mathrm{[R}（d^{（⁎）}）$， $\mathrm{[R}（Ĵ/\psi ）$， $P_{\tau }（d^{⁎}）$ 和 $F_{\mathrm{大号}}^{d^{⁎}}$，以及超出标准模型（SM）的范围。我们适合$乙\to d^{（⁎）}$ 将HQET参数化到晶格中的强子形因子和光锥和规则（LCSR）得出，并应用与 ${Ĵ}^P={\mathrm{1个}}^{-}$， ${\mathrm{1个}}^{+}$， $0^{-}$ 和 $0^{+}$。使用获得的螺旋度振幅之间的HQET关系，我们给出了各个螺旋度振幅的强统一性边界，可以在BGL拟合中使用。使用合适的外形尺寸并考虑到最新的Belle测量$\mathrm{[R}（d^{（⁎）}）$ 我们研究了模型的独立性和瘦夸克模型的解释 $b\to C\tau \nu$异常。具体来说，我们考虑一个操作员，两个操作员的新物理（NP）方案和具有单个操作符的NP模型。${\mathrm{[R}}_{\mathrm{2个}}$， ${\mathrm{小号}}_{\mathrm{1个}}$ 或者 ${ü}_{\mathrm{1个}}$ p夸克应该能够解决 $b\to C\tau \nu$ 异常，我们的结果表明 ${\mathrm{[R}}_{\mathrm{2个}}$ p夸克模型处于极限状态 $\mathcal{乙}（{乙}_C\to \tau \nu ）<10\text{％}$。此外，基于当前的形状因子研究和NP分析，我们对SM和NP情景/钩夸克模型中的各种可观测物进行了预测。