Measurement of the $\tau$-lepton mass with the Belle~II experiment

We present a measurement of the $\tau$-lepton mass using a sample of about 175 million $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events collected with the Belle II detector at the SuperKEKB $e^{+}{e}^{-}$ collider at a center-of-mass energy of $10.579\mathrm{G}\mathrm{e}\mathrm{V}$. This sample corresponds to an integrated luminosity of $190\mathrm{f}{\mathrm{b}}^{-1}$. We use the kinematic edge of the $\tau$ pseudomass distribution in the decay ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ and measure the $\tau$ mass to be $1777.09\pm 0.08\pm 0.11\mathrm{M}\mathrm{e}\mathrm{V}\text{\hspace{0.17em}⁣}\mathrm{/}{\mathrm{c}}^2$, where the first uncertainty is statistical and the second systematic. This result is the most precise to date.