Heavy sterile neutrinos from B decays and new QCD corrections to their semi-hadronic decay rates

In modern experiments on flavour physics it is possible to search for the decays of $B$ or $D$ mesons or $\tau$ leptons into final states with heavy neutrinos $N$ (a.k.a. heavy neutral leptons). I present a common study of theorists and experimentalists from Belle II on constraints on $B \rightarrow D^{*} \ell N$. Next I discuss the status of the theory predictions of the various $N$ decay rates. In scenarios in which $N$ interacts with SM particles only through sterile-active neutrino mixing, the dependence of the lifetime on the relevant mixing angles is important to determine whether $N$ decays in the detector or outside. To calculate the inclusive decay rate into semi-hadronic final states reliably one needs to include radiative QCD corrections. I present analytic results for the QCD-corrected decay rates and discuss their phenomenological impact.