ρ parameter and H0 → ℓiℓj in models with TeV sterile neutrinos

The presence of massive sterile neutrinos N mixed with the active ones induces flavor violating processes in the charged lepton sector at the loop level. In particular, the amplitude of H0 → ℓiℓj is expected to be proportional to the product of heavy-light Yukawa couplings yiyj = 2sνi sνj m2N/v2, where sνi,j express the heavy-light neutrino mixings. Here, we revisit these Higgs decays in the most generic extension of the neutrino sector, focusing on large values of yi. We show that decoupling effects and a cancellation between the two dominant contributions to these processes makes the amplitude about 100 times smaller than anticipated. We find that perturbative values of yi giving an acceptable contribution to the ρ parameter imply B(H0 → ℓiℓj) < 10−8 for any lepton flavors, a rate that is not accessible at current colliders.