Feasibility Study of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ Decay and Test of Lepton Flavor Universality with Leptonic $D_s^{+}$ Decays at STCF

Abstract

We report a sensitive study of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ decay via ${\tau }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\tau }$ with an integrated luminosity of 1 ab${}^{-1}$ at the center-of-mass energy of $4.009$ GeV at a future Super Tau Charm Facility (STCF). Under the help of the fast simulation software package, the statistical sensitivity for the absolute branching fraction of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ is determined to be $2\times 10^{-4}$. Combining with our previous prospect of $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$, the ratio of the branching fractions for $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ over $D_s^{+}\to {\mu }^{+}{\nu }_{\mu }$ can achieve a relative statistical precision of 0.5%, which will provide the most stringent test of the $\tau$-$\mu$ lepton flavor universality in heavy quark decays. Taking the decay constant $f_{D_s^{+}}$ from lattice QCD calculations or the CKM matrix element $|V_{cs}|$ from the CKMfitter group as an input, the relative statistical uncertainties for $|V_{cs}|$ and $f_{D_s^{+}}$ are estimated to be 0.3% and 0.2%, respectively.

9 pages, 3 figures

References in corpus (1)

• Measurement of the Absolute Branching Fraction of $D_s^{+}\to {\tau }^{+}{\nu }_{\tau }$ via ${\tau }^{+}\to e^{+}{\nu }_e{\bar{\nu }}_{\tau }$