Mixing of active and sterile neutrinos

We investigate mixing of neutrinos in the vMSM (neutrino Minimal Standard Model), which is the MSM extended by three right-handed neutrinos. Especially, we study elements of the mixing matrix Theta(alpha I) between three left-handed neutrinos v(L alpha) (alpha = e, mu, tau) and two sterile neutrinos N-I (I = 2, 3) which are responsible to the seesaw mechanism generating the suppressed masses of active neutrinos as well as the generation of the baryon asymmetry of the universe. It is shown that Theta(eI) can be suppressed by many orders of magnitude compared with Theta(mu I) and Theta(tau I), when the Chooz angle theta(13) is large in the normal hierarchy of active neutrino masses. We then discuss the neutrinoless double beta decay in this framework by taking into account the contributions not only from active neutrinos but also from all the three sterile neutrinos. It is shown that N-2 and N-3 give substantial, destructive contributions when their masses are smaller than a few 100 MeV, and as a results Theta(eI) receive no stringent constraint from the bounds on such decays. Finally, we discuss the impacts of the obtained results on the direct searches of N-2,N-3 in meson decays for the case when N-2,N-3 are lighter than pion mass. We show that there exists the allowed region for N-2,N-3 with such small masses in the normal hierarchy case even if the current bound on the lifetimes of N-2,N-3 from the big bang nucleosynthesis is imposed. It is also pointed out that the direct search by using pi(+) -> e(+) + N-2,N-3 and K+ -> e(+) + N-2,N-3 might miss such N-2,N-3 since the branching ratios can be extremely small due to the cancellation in Theta(eI), but the search by K+ -> mu(+) + N-2,N-3 can cover the whole allowed region by improving the measurement of the branching ratio by a factor of 5.