Search for sterile neutrinos decaying into pions at the LHC

We study the possibility to observe sterile neutrinos with masses in the range between 5 GeV and 20 GeV at the LHC, using the exclusive semileptonic modes involving pions, namely W to lepton + N to n pions + lepton+lepton (n = 1, 2, 3). The two pion and three pion modes require extrapolations of form factors to large time-like $q^2$, which we do using vector dominance models as well as light front holographic QCD, with remarkable agreement. This mass region is difficult to explore with inclusive dilepton+dijet modes or trilepton modes and impossible to explore in rare meson decays. While particle identification is a real challenge in these modes, vertex displacement due to the long living neutrino in the above mass range can greatly help reduce backgrounds. Assuming a sample of $10^9$ W bosons at the end of the LHC Run 2, these modes could discover a sterile neutrino in the above mass range or improve the current bounds on the heavy-to-light lepton mixings by an order of magnitude, $U_{l N}^2 \sim 2 \times 10^{-6}$. Moreover, by studying the equal sign and opposite sign dileptons, the Majorana or Dirac character of the sterile neutrino may be revealed.