Lepton universality, rare decays, and split fermions

We investigate the constraint on the split fermions in extra dimensions by considering the universality of W leptonic decays →Wlᵢνᵢ, the charged lepton decays lᵢ→lⱼνᵢνⱼ, and the lepton flavor violating process lᵢ→lⱼlₖlₕ where lᵢ=e,μ or τ. For the standard model (SM) background of →Wlᵢνᵢ, we extended the one loop quantum correction to include effects of order mₗ²/MW² and the Higgs boson mass dependence. We find that in general the split fermion scenarios giving rise to 4D effective Yukawa matrices of the Kaluza-Klein Higgs bosons which are misaligned with respect to the fermion mass matrix. This holds true also for gauge bosons as well. This leads to decays of lᵢ→lⱼlₖlₕ at the tree level and muonium antimuonium conversion. Interestingly the leptonic universality of W boson decays are not affected at this level.