Ultrarelativistic sneutrinos at the LHC and sneutrino-antisneutrino oscillation

Sneutrino-antisneutrino oscillation can be a very useful probe to look for signatures of lepton number violation ($\Delta L = 2$) at the LHC. Here, we discuss the effect of the boost factor $\gamma$ and the travelling distance $L$ on the probability of the oscillation. We demonstrate that these two parameters can significantly alter the probability of the oscillation when the sneutrinos are ultrarelativistic and have a very small total decay width. We propose a scenario where these requirements are fulfilled and which produces interesting signals at the LHC even for a mass splitting $\Delta m$ as small as $10^{-14}$ GeV between the sneutrino mass eigenstates.