Abstract

A bstract We present a measurement of the ratio $$ {R}_{\mu }=\mathcal{B}\left({\tau}^{-}\to {\mu}^{-}{\overline{\nu}}_{\mu }{\nu}_{\tau}\right)/\mathcal{B}\left({\tau}^{-}\to {e}^{-}{\overline{\nu}}_e{\nu}_{\tau}\right) $$ R μ = B τ − → μ − ν ¯ μ ν τ / B τ − → e − ν ¯ e ν τ of branching fractions $$ \mathcal{B} $$ B of the τ 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 ± 2 fb − 1 at a centre-of-mass energy of 10.58 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 μ = 0.9675 ± 0.0007 ± 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 τ decays of 0.9974 ± 0.0019, in agreement with the standard model expectation of unity.