Slepton mass-splittings as a signal of LFV at the LHC

Precise measurements of slepton mass-splittings might represent a powerful tool to probe supersymmetric (SUSY) lepton flavour violation (LFV) at the LHC. We point out that mass-splittings of the first two generations of sleptons are especially sensitive to LFV effects involving $\tau-\mu$ transitions. If these mass-splittings are LFV induced, high-energy LFV processes like the neutralino decay ${\nt}_2\to\nt_1\tau^{\pm}\mu^{\mp}$ as well as low-energy LFV processes like $\tau\to\mu\gamma$ are unavoidable. We show that precise slepton mass-splitting measurements and LFV processes both at the high- and low-energy scales are highly complementary in the attempt to (partially) reconstruct the flavour sector of the SUSY model at work. The present study represents another proof of the synergy and interplay existing between the LHC, i.e. the {\em high-energy frontier}, and high-precision low-energy experiments, i.e. the {\em high-intensity frontier}