Measurement of the branching fraction of leptonic decay $D_s^+\to\tau^+\nu_\tau$ via $\tau^+\to\pi^+\pi^0\bar \nu_\tau$

TL;DR

This paper measures the branching fraction of the leptonic decay $D_s^+ o au^+ u_ au$ using BESIII data, providing precise values for the decay constant and CKM matrix element, which test the Standard Model.

Contribution

First measurement of the $D_s^+ o au^+ u_ au$ branching fraction via $ au^+ o ho^+ ar{ u}_ au$ with improved precision, and extraction of decay constant and CKM matrix element.

Findings

Branching fraction $ imes$ $|V_{cs}|$ measured as 244.8 MeV.

Decay constant $f_{D_s^+}$ determined as 251.6 MeV.

CKM matrix element $|V_{cs}|$ found to be 0.980.

Abstract

By analyzing $6.32~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at the center-of-mass energies between 4.178 and 4.226\,GeV with the BESIII detector, we determine the branching fraction of the leptonic decay $D_s^+\to\tau^+\nu_\tau$ with $\tau^+\to\pi^+\pi^0\bar \nu_\tau$, to be $\mathcal{B}_{D_s^+\to\tau^+\nu_\tau}=(5.29\pm0.25_{\rm stat}\pm0.20_{\rm syst})\%$. We estimate the product of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^+$ decay constant $f_{D^+_s}$ to be $f_{D_s^+}|V_{cs}|=(244.8\pm5.8_{\rm stat}\pm4.8_{\rm syst})~\mathrm{MeV}$ using the known values of the $\tau^+$ and $D_s^+$ masses as well as the $D_s^+$ lifetime, together with our branching fraction measurement. Combining with the value of $|V_{cs}|$ obtained from a global fit in the standard model and $f_{D_s^+}$ from lattice quantum chromodynamics, we obtain $f_{D_s^+}=(251.6\pm5.9_{\rm stat}\pm4.9_{\rm syst})$\,MeV and $|V_{cs}| = 0.980\pm0.023_{\rm stat}\pm0.019_{\rm syst}$.