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We investigate flavour violating decays of the long-lived lightest sleptonand the tau lepton in the coannihilation region of the Minimal SupersymmetricStandard Model with a Seesaw mechanism to generate neutrino masses. We considera situation where the mass difference between the lightest neutralino, as theLightest Supersymmetric particle (LSP), and the lightest slepton, as theNext-to-LSP, is smaller than the mass of tau lepton. In this situation, thelifetime of the lightest slepton is very long and it is determined by leptonflavour violating (LFV) couplings because the slepton mainly consists of thelighter stau and the flavour conserving 2-body decay is kinematicallyforbidden. We show that the lifetime can change many orders of magnitude byvarying the Yukawa couplings entering the Seesaw mechanism. We also show thatbranching ratio of LFV tau decays are strongly correlated with the lightestslepton lifetime. Therefore the branching ratios of LFV tau decays can bedetermined or constrained by measuring the slepton lifetime at the LHCexperiment.

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