Search for light sterile neutrinos from $W^\pm$ decays at the LHC

We study the feasibility to observe sterile neutrinos with masses in the range 5 GeV $< m_N < 20$ GeV at the LHC, using exclusive semileptonic modes involving pions, $W\to \ell N \to \pi \ell\ell, 2\pi \ell\ell$ and $3\pi \ell\ell$. We thus cover a mass window that is between what can be studied in meson factories and high energy colliders. We run simulations for these exclusive events, where pions should be distinguished from the background provided the neutrino decay exhibits a vertex displacement from its production point. In a previous work we have estimated the theoretical rates and here we analyze the observability of the processes at the LHC, given the fact that exclusive hadronic states may be difficult to identify. We study the sensitivity bounds for the observation and discovery of sterile neutrinos in the above mass range. By the end of Run-3, current bounds on heavy-to-light lepton mixings in the lower mass end ($\sim 5$ GeV) could be improved by about an order of magnitude to $|U_{\ell N}|^2\sim 5\times 10^{-6}$, and the High-Luminosity LHC could reach $|U_{\ell N}|^2 \lesssim 3\times 10^{-7}$ in the mass range below 11 GeV. Studying in addition equal sign and opposite sign dileptons, the Majorana or Dirac character of the sterile neutrino could be revealed.