Prospects of CKM elements $|V_{cs}|$ and decay constant $f_{D_{s}^+}$ in $D_s^+\to\mu^+\nu_\mu$ decay at STCF

TL;DR

This study assesses the potential of the STCF to precisely measure the decay constant and CKM matrix element |V_{cs}| in the leptonic decay of D_s^+ mesons, enabling stringent tests of the Standard Model and new physics.

Contribution

It presents a feasibility analysis of measuring $f_{D_s^+}$ and $|V_{cs}|$ with unprecedented precision at STCF using simulated data.

Findings

Statistical sensitivity of 0.3% for the branching fraction.

Sensitivity of 0.2% for $f_{D_s^+}$ when combining current data.

Sensitivity of 0.2% for $|V_{cs}|$ when combining lattice QCD results.

Abstract

We report a feasibility study of pure leptonic decay $D_s^+\to\mu^+\nu_\mu$ by using a fast simulation software package at STCF. With an expected luminosity of $1~\mathrm{ab}^{-1}$ collected at STCF at a center-of-mass energy of 4.009 GeV, the statistical sensitivity of the branching fraction is determined to be 0.3\%. Combining this result with the $c\rightarrow s$ quark mixing matrix element $|V_{cs}|$ determined from the current global Standard Model fit, the statistical sensitivity of $D_s^+$ decay constant, $f_{D_s^+}$, is estimated to be 0.2\%. Alternatively, combining the current results of $f_{D_s^+}$ calculated by lattice QCD, the statistical sensitivity of $|V_{cs}|$ is determined to be 0.2\%, which helps probe possible new physics beyond. The unprecedented precision to be achieved at STCF will provide a precise calibration of QCD and rigorous test of Standard Model.