Test of light-lepton universality in $\tau$ decays with the Belle II experiment

We present a measurement of the ratio $R_{\mu }=\mathcal{B}({\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau })\mathrm{/}\mathcal{B}({\tau }^{-}\to e^{-}{\bar{\nu }}_e{\nu }_{\tau })$ of branching fractions $\mathcal{B}$ of the $\tau$ lepton decaying to muons or electrons using data collected with the Belle II detector at the SuperKEKB $e^{+}{e}^{-}$ collider. The sample has an integrated luminosity of $362\text{\hspace{0.17em}⁣}\pm \text{\hspace{0.17em}⁣}2{\text{fb}}^{-1}$ at a centre-of-mass energy of $10.58\text{GeV}$. Using an optimised event selection, a binned maximum likelihood fit is performed using the momentum spectra of the electron and muon candidates. The result, $R_{\mu }=0.9675\pm 0.0007\pm 0.0036$, where the first uncertainty is statistical and the second is systematic, is the most precise to date. It provides a stringent test of the light-lepton universality, translating to a ratio of the couplings of the muon and electron to the $W$ boson in $\tau$ decays of $0.9974\pm 0.0019$, in agreement with the standard model expectation of unity.