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Correlation between flavour violating decay of long-lived slepton and tau in the coannihilation scenario with Seesaw mechanism

We investigate flavour violating decays of the long-lived lightest slepton and the tau lepton in the coannihilation region of the Minimal Supersymmetric Standard Model with a Seesaw mechanism to generate neutrino masses. We consider a situation where the mass difference between the lightest neutralino, as the Lightest Supersymmetric particle (LSP), and the lightest slepton, as the Next-to-LSP, is smaller than the mass of tau lepton. In this situation, the lifetime of the lightest slepton is very long and it is determined by lepton flavour violating (LFV) couplings because the slepton mainly consists of the lighter stau and the flavour conserving 2-body decay is kinematically forbidden. We show that the lifetime can change many orders of magnitude by varying the Yukawa couplings entering the Seesaw mechanism. We also show that branching ratio of LFV tau decays are strongly correlated with the lightest slepton lifetime. Therefore the branching ratios of LFV tau decays can be determined or constrained by measuring the slepton lifetime at the LHC experiment.