Measuring Lepton Flavour Violation at LHC with Long-Lived Slepton in the Coannihilation Region

High precision electroweak tests, such as deviations from the Standard Model expectations of the Lepton Flavor Universality (LFU) breaking in K → lνl (with l = e or μ), represent a powerful tool to test the Standard Model and, hence, to constrain or obtain indirect hints of New Physics beyond it. We explore such a possibility within Supersymmetric theories. Interestingly enough, a process that in itself does not need lepton flavor violation to occur, i.e. the violation of μ− e non-universality in K → lνl, proves to be quite effective in constraining not only relevant regions of SUSY models where lepton flavor is conserved, but even those where specific lepton flavor violating contributions arise. Indeed, a comparison with analogous bounds coming from τ lepton flavor violating decays shows the relevance of the measurement of R e/μ K = Γ(K → eν)/Γ(K → μν) to probe Lepton Flavor Violation in SUSY. We outline the role and the interplay of the direct New Physics searches at the LHC with the indirect searches performed by LFU tests.