Probing sterile neutrino in $B$ ($D$) meson decays at Belle II (BESIII)

We present, how a systematic study of $B\to D\mathrm{\ell }N$ ($D\to K\mathrm{\ell }N$) decays with $\mathrm{\ell }=\mu ,\tau$, at Belle II (BESIII) can provide unambiguous signature of a heavy neutrino $N$ and/or constrain its mixing with active neutrinos ${\nu }_{\mathrm{\ell }}$, which is parameterized by $\mathrm{\mid }{U}_{\mathrm{\ell }N}{\mathrm{\mid }}^2$. Our constraint on $\mathrm{\mid }{U}_{\mu N}{\mathrm{\mid }}^2$ that can be achieved from the full Belle II data is comparable with what can be obtained from the much larger data set of the upgraded LHCb. Additionally, our method offers better constraint on $|U_{\mu N}|^2$formassofsterileneutrino$m_N < 2$ GeV. We can also probe the Dirac and Majorana nature of $N$ by observing the sequential decay of $N$, including suppression from observation of a displaced vertex as well as helicity flip, for Majorana $N$.