Lepton Flavour Violation in Supersymmetry

Abstract

Supersymmetry is one of the most popular and highly motivated theories beyond the Standard Model. Apart from providing a solution to the hierarchy problem, it also leads to unification of couplings at high energies and has a candidate particle for dark mat- ter. The Large Hadron Collider (LHC) has looked for supersymmetric particles in their searches with no success till date. The collider is set to restart colliding particles again in 2015 at an upgraded energy scale of 13 TeV. The entire particle physics fraternity is hopeful of observing first signs of supersymmetric particle in the coming years. Once the particles are detected, the next step for the experimentalists would be to obtain the properties of these particles, for instance their masses and mixing. One of the features of interest is Lepton Flavour Violation (LFV). Lepton flavour is inherently conserved in the Standard Model owing to the massless nature of neutrinos. Supersymmetry in its general form does not require generational lepton number conser- vation. However, the null results in various experiments looking for LFV decays has put strong constraints on the possibility of flavour violation in supersymmetric models. Notwithstanding these constraints, the possibility of flavour violation in the decay of supersymmetric particles is not completely ruled out. In fact under certain conditions, significant LFV could be possible. In this study, we have calculated the constraints on slepton (supersymmetric lepton) mass matrix coming from rare decays of electron, muon and tau. Based on these re- sults, we obtain the condition for substantial flavour violation. Next we study a signal for lepton flavour violating decay of a supersymmetric particle neutralino, which can be investigated at the LHC.