Sterile neutrinos: direct mixing effects versus induced mass matrix of active neutrinos

TL;DR

The study analyzes how mixing between active and sterile neutrinos induces a mass-matrix correction for active neutrinos, $\mathbf{m_I} = -\frac{1}{m_S}(\mathbf{m_{aS}})(\mathbf{m_{aS}})^T$, which can be rank-1 for a single sterile and richer for multiple sterile states. By reconstructing the flavor-basis active neutrino mass matrix from oscillation data and exploring normal, inverted, and degenerate hierarchies, the authors show that the induced matrix can dominate, sub-dominant, or be negligible depending on $m_S$ and $\sin^2\theta_{aS}$, with notable implications such as possible tri-bimaximal mixing. They compile cosmological, astrophysical, and laboratory bounds across production, LSS, X-ray, CMB, BBN, SN1987A, and direct searches, identifying parameter regions where induced-mass effects remain viable (e.g., $m_S \gtrsim 300$ MeV with $\sin^2\theta_S \lesssim 10^{-9}$, or $m_S \sim 0.1$–$0.3$ eV with $\sin^2\theta_S$ around $10^{-3}$–$10^{-2}$), and discuss ways these bounds could be relaxed via low reheating temperatures, fast decays, or time-varying masses. The results highlight a complementary role for induced-mass physics in shaping lepton mixing patterns and neutrino masses, potentially guiding extensions beyond the Standard Model while remaining testable by future cosmological, astrophysical, and laboratory data.

Abstract

Mixing of active neutrinos with sterile ones generate ``induced'' contributions to the mass matrix of active neutrinos $\sim m_S \sin^2θ_{aS}$, where $m_S$ is the Majorana mass of the sterile neutrino and $θ_{aS}$ is the active-sterile mixing angle. We study possible effects of the induced matrix which can modify substantially the implications of neutrino oscillation results. We have identified the regions of $m_S$ and $\sin^2θ_{aS}$ where the induced matrix (i) provides the dominant structures, (ii) gives the sub-dominant effects and (iii) where its effects can be neglected. The induced matrix can be responsible for peculiar properties of the lepton mixing and neutrino mass spectrum, in particular, it can generate the tri-bimaximal mixing. We update and discuss bounds on the induced masses from laboratory measurements, astrophysics and cosmology. We find that substantial impact of the induced matrix is possible if $m_S \sim 0.1-1$ eV and $\sin^2θ_{aS} \sim 10^{-3} - 10^{-2}$ or $m_S \geq 200$ MeV and $\sin^2θ_{aS} \leq 10^{-9}$. The bounds can be relaxed in cosmological scenarios with low reheating temperature, if sterile neutrinos decay sufficiently fast, or their masses change with time.

Figures (3)

• Figure 1: The benchmark lines Eqs. (\ref{['small']})-(\ref{['leadA']}) and (\ref{['bench4']}) versus the current astrophysical, cosmological and laboratory bounds on $\nu_S -\nu_e$ mixing as described in the text. The colored regions are excluded in each case. The "thermalization" line and the two decay lines $\tau_S = \tau_{\rm rec}$ and $\tau_S = \tau_U$ are also shown. We show also the allowed regions for the warm dark matter and the LSND (3+1) as well as the region that could explain pulsar velocities.
• Figure 2: Same as Fig.\ref{['fig1']} but for $\nu_S -\nu_\mu$ mixing.
• Figure 3: Same as Fig.\ref{['fig1']} but for $\nu_S -\nu_\tau$ mixing.