Bounds on fourth generation induced Lepton Flavour Violating double insertions in Supersymmetry

Abstract

We derive bounds on leptonic double mass insertions of the type $δ^{l}_{i4} δ^{l}_{4j}$ in four generational MSSM, using the present limits on $l_i \to l_j + γ$. Two main features distinguish the rates of these processes in MSSM4 from MSSM3 : (a) tan$β$ is restricted to be very small $\lesssim 3 $ and (b) the large masses for the fourth generation leptons. In spite of small $\tanβ$, there is an enhancement in amplitudes with $llrr$($δ_{i4}^{ll}δ_{4j}^{rr}$) type insertions which pick up the mass of the fourth generation lepton, $m_{τ'}$. We find these bounds to be at least two orders of magnitude more stringent than those in MSSM3.