Analysis of $B_c\to \tau {\nu }_{\tau }$ at CEPC

The precise determination of the $B_c\to \tau {\nu }_{\tau }$ branching ratio provides an advantageous opportunity for understanding the electroweak structure of the Standard Model, measuring the CKM matrix element $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ and probing new physics models. In this paper, we discuss the potential of measuring the processes of $B_c\to \tau {\nu }_{\tau }$ with $\tau$ decaying leptonically at the proposed Circular Electron Positron Collider (CEPC). We conclude that during the $Z$ pole operation, the channel signal can achieve five $\sigma$ significance with $\sim {10}^9$ $Z$ decays, and the signal strength accuracies for $B_c\to \tau {\nu }_{\tau }$ can reach around 1% level at the nominal CEPC $Z$ pole statistics of one trillion $Z$ decays assuming the total $B_c \to \tau \nu_\tau$yieldis$3.6 \times 10^6$. Our theoretical analysis indicates the accuracy could provide a strong constraint on the general effective Hamiltonian for the $b\to c\tau \nu$ transition. If the total $B_c$ yield can be determined to $\mathcal{O}(1\mathrm{\%})$ level of accuracy in the future, these results also imply $\mathrm{\mid }{V}_{cb}\mathrm{\mid }$ could be measured up to $\mathcal{O}(1\mathrm{\%})$ level of accuracy.