Minimal active-sterile neutrino mixing in seesaw type I mechanism with sterile neutrinos at GeV scale

Abstract

Renewed interest in GeV-scale sterile neutrinos capable of explaining active neutrino oscillations via see-saw type I mechanism has been expressed in several proposals of direct searches. Given this activity we estimate the minimal values of sterile-active mixing angles provided one, two, or three sterile neutrinos are lighter than D-meson.1. Neutrino oscillations definitely ask for some extension of the Standard Model of particle physics (SM), and may be the simplest, yet complete and renormalizable, version is introducing three new Majorana massive fermions, N I , I = 1, 2, 3, sterile with respect to all SM gauge interactions. One can write down the most general renormalizable Lagrangianwhere M I are the Majorana masses and Y αI stand for Yukawa couplings with lepton doublets L α , α = e, µ, τ and SM Higgs doublet H (H a = ab H * b , a = 1, 2). When the Higgs field gains vacuum expectation value v = 246 GeV, Yukawa couplings in (1) yield mixing between sterile N I and active ν α neutrino states. Diagonalization of the neutral fermion mass matrix provides active neutrinos with masses m i and mixing which are responsible for neutrino oscillation phenomena.With some hierarchy between model parameters Y αI and M I /v, when the Dirac mass scale Y v is well below the Majorana mass scale M , active-sterile neutrino mixing angles are small, U ∼ Y v/M 1, and active neutrino masses are double suppressed, m ∼ U 2 M . This is a type I seesaw mechanism (for a review see e.g., Ref.[1]) which explains naturally why active neutrino mass scale is much lower than masses of other SM particles. However, the Dirac mass scale and hence the size of Yukawa couplings are not fixed from this reasoning: the seesaw mechanism determines not Y and M but ratio Y 2 /M . 1

Low-scale leptogenesis with three heavy neutrinos

“…Finally, a similar problem arises in the determination of the lower bound on the mixings. While the light neutrino oscillation data and the requirement for the N i to decay before BBN both impose lower bounds on the U 2 i that depend on m lightest [84,133], neither of them can impose a lower bound on the individual U 2 ai for n = 3. The BBN constraint can always be avoided if the N i decays into a SM final state of different flavour, while the neutrino oscillation data can always be explained if another heavy neutrino provides the required mixing with the flavour a.…”

NA62 sensitivity to heavy neutral leptons in the low scale seesaw model

“…For n = 3 the flavour mixing patterns are far less restricted. There is no lower bound on the individual U 2 ai from neutrino oscillation data [65,81]. It is, for instance, possible to set F e1 = F µ1 = 0 by fixing the entirely unconstrained Majorana phases α 1 and α 2 for arbitrary choices of all other parameters, including m lightest .…”

“…The smaller mass difference ("solar mass difference") is given by ∆m authors, see e.g. [16,19,20,31,37,38,[63][64][65]. The constraints depend on the number n of heavy neutrinos.…”

Perspectives for tests of neutrino mass generation at the GeV scale: Experimental reach versus theoretical predictions

“…10 The tau mixing element jU τI j 2 is not shown since the main source of sterile neutrinos for the SHiP and DUNE experiments are from charmed hadrons which have a similar mass of the tau-lepton-meaning jU τI j 2 may only contribute to production (via decays of tau-leptons from D s -mesons) because of the mass difference between the charm meson and the tau-lepton. Therefore, it is considered irrelevant for subsequent sterile neutrino decays [140,141].…”