MiniBooNE Results and Neutrino Schemes with 2 sterile Neutrinos: Possible Mass Orderings and Observables related to Neutrino Masses

TL;DR

This work analyzes neutrino mass schemes with two additional sterile species, outlining eight possible mass orderings and classifying them into 2+3, 3+2, and 1+3+1 patterns. It focuses on non-oscillation probes—the sum of neutrino masses $\Sigma$, the beta-decay mass $m_\beta$, and the neutrinoless double beta decay effective mass $\langle m \rangle$—to determine whether these observables can distinguish between the orderings, using representative sterile-squared differences and mixings from LSND/MiniBooNE fits. The study finds that six of the eight orderings predict observable signals in KATRIN and future $0\nu\beta\beta$ experiments, while cosmological bounds on $\Sigma$ pose serious but potentially evadable constraints, underscoring the need for complementary probes. Additionally, it discusses the role of decays of high-energy astrophysical neutrinos as a possible discriminator among mass patterns and notes the broad phenomenology and challenges of two-sterile scenarios, including their tension with standard cosmology.

Abstract

The MiniBooNE and LSND experiments are compatible with each other when two sterile neutrinos are added to the three active ones. In this case there are eight possible mass orderings. In two of them both sterile neutrinos are heavier than the three active ones. In the next two scenarios both sterile neutrinos are lighter than the three active ones. The remaining four scenarios have one sterile neutrino heavier and another lighter than the three active ones. We analyze all scenarios with respect to their predictions for mass-related observables. These are the sum of neutrino masses as constrained by cosmological observations, the kinematic mass parameter as measurable in the KATRIN experiment, and the effective mass governing neutrinoless double beta decay. It is investigated how these non-oscillation probes can distinguish between the eight scenarios. Six of the eight possible mass orderings predict positive signals in the KATRIN and future neutrinoless double beta decay experiments. We also remark on scenarios with three sterile neutrinos. In addition we make some comments on the possibility of using decays of high energy astrophysical neutrinos to discriminate between the mass orderings in presence of two sterile neutrinos.

Figures (8)

• Figure 1: Allowed 2+3 mass orderings which are defined by having two sterile neutrinos heavier than the three active neutrinos. (Not to scale).
• Figure 2: Allowed 3+2 mass orderings which are defined by having two sterile neutrinos lighter than the three active neutrinos. (Not to scale).
• Figure 3: Allowed 1+3+1 mass orderings which are defined by having one sterile neutrino heavier than the three active ones which in turn are heavier than the second sterile neutrino. (Not to scale). Note that not necessarily $\hbox{$\Delta \tilde{m}^2_{\rm s1}$} = \hbox{$\Delta m^2_{\rm s1}$}$ and $\hbox{$\Delta \tilde{m}^2_{\rm s2}$} = \hbox{$\Delta m^2_{\rm s2}$}$ holds.
• Figure 4: Scenarios with three active and two sterile neutrinos: the individual neutrino masses as a function of the smallest neutrino mass for scenarios SSN, SSI, NSS and SNSa. For the mass-squared differences related to the sterile neutrinos the best-fit point given in Eq. (\ref{['eq:stBF']}) is used and we assumed that $\hbox{$\Delta m^2_{\rm s1}$} = \hbox{$\Delta \tilde{m}^2_{\rm s1}$}$ and $\hbox{$\Delta m^2_{\rm s2}$} = \hbox{$\Delta \tilde{m}^2_{\rm s2}$}$. Scenario ISS is indistinguishable from case NSS and SISa from SNSa. The schemes SNSb and SISb are very similar to NSS.
• Figure 5: The sum of neutrino masses $\Sigma$ and the kinematic neutrino mass $m_\beta$ for scenarios SSN (top left), SSI (top right), NSS (bottom left) and SNSa (bottom right). The solid lines give the values of the respective observable at the best-fit point Eq. (\ref{['eq:stBF']})while the shaded regions are obtained by varying the parameters involved in their corresponding ranges from Eqs. (\ref{['eq:data']}) and (\ref{['eq:rangeUe45']}). We assumed that $\hbox{$\Delta m^2_{\rm s1}$} = \hbox{$\Delta \tilde{m}^2_{\rm s1}$}$ and $\hbox{$\Delta m^2_{\rm s2}$} = \hbox{$\Delta \tilde{m}^2_{\rm s2}$}$. Scenario ISS is indistinguishable from case NSS, SISa is indistinguishable from SNSa, and SNSb/SISb are indistinguishable from NSS. For these two observables SSN and SSI give identical results. Also indicated is the KATRIN sensitivity on $m_\beta$ of 0.3 eV.