The minimal 3+2 neutrino model versus oscillation anomalies

TL;DR

The authors study a minimal extension of the Standard Model that adds two sterile Weyl fermions, yielding a $3+2$ neutrino spectrum with four massive states and one massless state ($3+2$ MM). They develop a beyond-Casas-Ibarra parametrization to handle significant light-heavy mixing and perform a global oscillation fit, finding that the $3+2$ MM can improve over the standard $3ν$ framework, especially for normal ordering, while remaining substantially predictive with constrained mixing patterns. The analysis shows the heavy-light mixings can accommodate LSND/MiniBooNE and reactor anomalies in a way similar to $3+2$ PM fits, but with tighter correlations among parameters and notable $ au$-sector predictions. For future experiments, the work highlights that near detectors (e.g., T2K near) and tau-appearance measurements could strongly constrain or reveal the predicted heavy-light mixing structures, clarifying the role of light sterile neutrinos in oscillations.

Abstract

We study the constraints imposed by neutrino oscillation experiments on the minimal extension of the Standard Model that can explain neutrino masses, which requires the addition of just two singlet Weyl fermions. The most general renormalizable couplings of this model imply generically four massive neutrino mass eigenstates while one remains massless: it is therefore a minimal 3+2 model. The possibility to account for the confirmed solar, atmospheric and long-baseline oscillations, together with the LSND/MiniBooNE and reactor anomalies is addressed. We find that the minimal model can fit oscillation data including the anomalies better than the standard $3ν$ model and similarly to the 3+2 phenomenological models, even though the number of free parameters is much smaller than in the latter. Accounting for the anomalies in the minimal model favours a normal hierarchy of the light states and requires a large reactor angle, in agreement with recent measurements. Our analysis of the model employs a new parametrization of seesaw models that extends the Casas-Ibarra one to regimes where higher order corrections in the light-heavy mixings are significant.

Figures (7)

• Figure 1: Minimum $\chi^2$ in the 3+2 MM as a function of the parameter $\gamma_{45}$ for NH (left) and IH (right), and for $M_1=\sqrt{\Delta m^2_{41}}$, $M_2=\sqrt{\Delta m^2_{51}}$ fixed to the best fit values of the 3+2 PM KMS fit (up) and to the GL fit (down). The dashed line corresponds to the minimum $\chi^2$ of the standard 3$\nu$ model. The band is the 2$\sigma$ band of the 3+2 PM KMS/GL best fit.
• Figure 2: Left: 3$\sigma$ ranges on the plane ($|U_{\alpha4}|$,$|U_{\alpha5}|$) for $\alpha=e$ (solid),$\mu$ (dashed) and $\tau$ (dotted) for the NH, with $M_1$ and $M_2$ fixed to the KMS values of Table 2. Right: same for the IH and with the GL values of $M_1$ and $M_2$. The symbols: circle (e) and square ($\mu$) correspond to the best fit points of the 3+2 PM fits from Table 2.
• Figure 3: Left: Projection of the mimimum $\chi^2$ as a function of the SBL phase, $\phi_{45}$, for NH and with $M_1$ and $M_2$ fixed to the KMS values of Table 2. Right: same for IH and for $M_1$ and $M_2$ fixed to the GL values of Table 2.
• Figure 4: Minimum $\chi^2$ as a function of the physical combinations $A_{ee}$, $2 |A_{\mu e}|$, $N_{\mu e}$, $|B_{\mu e}|$ for the NH(left) and IH (right). The heavy masses are fixed to the KMS values of Table 2 for NH and to the GL values for IH. The band in the top plots corresponds to the recent Daya Bay 3$\sigma$ limit.
• Figure 5: $\chi^2$ as a function of the non-conventional phase $\phi$ for NH (left) and IH (right). The heavy masses are fixed to the KMS choice of Table 2 for NH and to the GL choice for IH.