<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi></mml:math> parameter and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msub><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mo>ℓ</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> in models with TeV sterile neutrinos
G. Hernández-Tomé, J. I. Illana, M. Masip
Abstract
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 ${H}^{0}\ensuremath{\rightarrow}{\overline{\ensuremath{\ell}}}_{i}{\ensuremath{\ell}}_{j}$ is expected to be proportional to the product of heavy-light Yukawa couplings ${y}_{i}{y}_{j}=2{s}_{{\ensuremath{\nu}}_{i}}{s}_{{\ensuremath{\nu}}_{j}}{m}_{N}^{2}/{v}^{2}$, where ${s}_{{\ensuremath{\nu}}_{i,j}}$ 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 ${y}_{i}$. 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 ${y}_{i}$ giving an acceptable contribution to the $\ensuremath{\rho}$ parameter imply $\mathcal{B}({H}^{0}\ensuremath{\rightarrow}{\overline{\ensuremath{\ell}}}_{i}{\ensuremath{\ell}}_{j})<{10}^{\ensuremath{-}8}$ for any lepton flavors, a rate that is not accessible at current colliders.