QCD corrections to charged-current decays with Heavy Sterile Neutrinos in initial or final state and their impact on τ decays

A bstract Searches for a Heavy Sterile Neutrino N profit from precise predictions of inclusive decay rates, which enter predictions for branching fractions and lifetime. Once the decay channels into semi-hadronic final states are open, a reliable calculation of inclusive decay rates is only possible if N is heavy enough to permit a perturbative calculation, in analogy to the well-known case of semi-hadronic τ lepton decays. We adopt the popular scenario in which N only interacts with the SM particles through N - ν ℓ mixing, where ℓ = e, μ, τ . Using literature results for W boson correlators calculated to fourth order in the strong coupling α s , we study the quality of the perturbation series for N → ℓ + hadrons to determine the mass ranges for which inclusive decay widths can be predicted in a robust way. We present novel analytic results for the decay rate of N → τ + hadrons in terms of m τ /m N . Our expressions equally apply to τ → N + hadrons, the width of which is found to be perturbatively calculable for m N ≲ 600 MeV. Applying our result to the τ lifetime, we determine the allowed parameter space for the N - ν τ mixing angle θ and m N . We find |sin θ | ≤ 0 . 2 for m N = 600 MeV and weaker bounds for a lighter N . In the mass region m N ≥ m τ we find constraints from the dependence of τ decay rates on cos θ , with |sin θ | ≤ 0.12 inferred from the τ lifetime. Combining τ → π − ντ and τ → K − ν τ data gives $$ \left|\sin \theta \right|=\left({9.1}_{-7.8}^{+3.7}\right)\cdotp {10}^{-2} $$ sin θ = 9.1 − 7.8 + 3.7 · 10 − 2 at 1 σ while N - ν τ mixing does not improve the agreement between theory and data for $$ \tau \to \ell {\overline{\nu}}_{\ell }{\nu}_{\tau } $$ τ → ℓ ν ¯ ℓ ν τ . We find current data for the decay rate Γ( τ → ℓ + nothing) about 1 σ above the SM prediction for $$ \Gamma \left(\tau \to \ell {\overline{\nu}}_{\ell }{\nu}_{\tau}\right) $$ Γ τ → ℓ ν ¯ ℓ ν τ