Prospect for measurement of $CP$-violating observables in $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays at a future $Z$ factory

Abstract

A precise determination of the CKM angle $\gamma$ from $B_s^0$ oscillations in $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays offers a critical test of the Standard Model and probes for new physics. We present a comprehensive study on the prospects of measuring $\gamma$ at a future Tera-$Z$ factory, utilizing the baseline detector concept of the Circular Electron Positron Collider (CEPC). A two-dimensional simultaneous fit framework, incorporating flavor tagging, decay time resolution modeling, and acceptance corrections, is developed using full Monte Carlo simulations of $B_s^0\to D_s^{\mp }\left(\to K^{\mp }{K}^{\pm }{\pi }^{\mp }\right)K^{\pm }$ decays and inclusive background processes. The effective flavor tagging power reaches $23.6\%$, while the decay time resolution is determined to be $26\mathrm{fs}$. Projecting to full statistics of signal events across three dominant $D_s^{-}$ decay channels, we estimate a statistical precision of $\sigma (\gamma )=0.69^{\circ }$, which corresponds to $4.1$ Tera-$Z$ boson equivalent data. This study establishes the feasibility of sub-degree level $\gamma$ measurements at a $Z$-factory, highlighting its unique advantages in time-dependent $CP$ violation studies through ultra-precise vertexing and background suppression capabilities.

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