A combined analysis of short-baseline neutrino experiments in the (3+1) and (3+2) sterile neutrino oscillation hypotheses

TL;DR

This study jointly analyzes one- and two-sterile-neutrino (3+1 and 3+2) hypotheses against seven short-baseline experiments, including LSND, to assess compatibility and identify favored mass-mixing regions. By separating NSBL constraints from LSND and performing combined fits, the authors quantify incompatibilities with four statistical tests and demonstrate that 3+2 models fit the data significantly better than 3+1 models. The analysis highlights that NSBL+LSND compatibility is marginal for 3+1 but notably improved for 3+2, with best-fit regions specified in terms of $\Delta m^2$ values and mixing parameters. Additional constraints from atmospheric data, tritium beta decay, and cosmology are discussed, but the primary conclusion is that a 3+2 sterile neutrino framework offers a more plausible explanation for short-baseline oscillation results, pending confirmation from upcoming experiments.

Abstract

We investigate adding two sterile neutrinos to resolve the apparent tension existing between short-baseline neutrino oscillation results and CPT-conserving, four-neutrino oscillation models. For both (3+1) and (3+2) models, the level of statistical compatibility between the combined dataset from the null short-baseline experiments Bugey, CHOOZ, CCFR84, CDHS, KARMEN, and NOMAD, on the one hand; and the LSND dataset, on the other, is computed. A combined analysis of all seven short-baseline experiments, including LSND, is also performed, to obtain the favored regions in neutrino mass and mixing parameter space for both models. Finally, four statistical tests to compare the (3+1) and the (3+2) hypotheses are discussed. All tests show that (3+2) models fit the existing short-baseline data significantly better than (3+1) models.

Figures (8)

• Figure 1: Flavor content of neutrino mass eigenstates in (3+1) models (a), and (3+2) models (b). Neutrino masses increase from bottom to top. The $\nu_e$ fractions are indicated by right-leaning hatches, the $\nu_{\mu}$ fractions by left-leaning hatches, the $\nu_{\tau}$ fractions by crosshatches, and the $\nu_s$ fractions by no hatches. The flavor contents shown are schematic only.
• Figure 2: Compatibility between the NSBL and LSND datasets in (3+1) models. Fig. \ref{['fig:fig2']}a shows the 90% (grey solid line), 95% (black dotted line), and 99% (black solid line) CL exclusion curves in $(\sin^2 2\theta_{\mu e} ,\Delta m^2)$ space for (3+1) models, considering the null short-baseline (NSBL) experiments Bugey, CCFR84, CDHS, CHOOZ, KARMEN, and NOMAD. Fig. \ref{['fig:fig2']}a also shows the 90%, 95%, and 99% CL allowed regions by our analysis of LSND data. Fig. \ref{['fig:fig2']}b) is as Fig. \ref{['fig:fig2']}a, but in $(p_{\hbox{\tiny LSND}},\Delta m^2)$ space, where $p_{\hbox{\tiny LSND}}$ is the LSND oscillation probability (see text for the definition). Fig. \ref{['fig:fig2']}c) and d) show the minimum $\chi^2$ values as a function of $\Delta m^2$ for the NSBL and LSND datasets (143 and 3 d.o.f., respectively).
• Figure 3: a)$\chi^2$ differences $\Delta\chi^2_{\hbox{\tiny NSBL}}$, $\Delta\chi^2_{\hbox{\tiny LSND}}$, and b) individual confidence levels $\delta_{\hbox{\tiny NSBL}}$, $\delta_{\hbox{\tiny LSND}}$, as a function of the LSND oscillation probability $p_{\hbox{\tiny LSND}}$, for the NSBL and LSND datasets. The curves are for (3+1) models with the neutrino mass splitting $\Delta m^2$ fixed to the best-fit value $\Delta m^2=0.92\ \hbox{eV}^2$ from the combined NSBL+LSND analysis, and variable mixing matrix elements $U_{\mu 4}$, $U_{e4}$. The solid curves refer to the NSBL dataset, the dotted ones to the LSND dataset. The dashed horizontal lines in Fig. \ref{['fig:fig3']}b refer to the 90%, 95%, 99% individual confidence levels, the dotted horizontal line gives the combined confidence level $\delta =\delta_{\hbox{\tiny NSBL}}(\delta_{\hbox{\tiny LSND}}+ (1-\delta_{\hbox{\tiny LSND}})/2)$ for which the NSBL and LSND datasets are incompatible.
• Figure 4: Allowed regions in parameter space from a combined analysis of NSBL and LSND data, in (3+1) models, assuming statistical compatibility of the NSBL and LSND datasets. Fig. \ref{['fig:fig4']}a shows the 90%, 95%, and 99% CL allowed regions in $(\sin^2 2\theta_{\mu e},\Delta m^2)$ space, together with the best-fit point, indicated by the star; b) shows the same allowed regions in $(p_{\hbox{\tiny LSND}},\Delta m^2)$ space; c) shows the minimum $\chi^2$ value obtained in the combined analysis as a function of $\Delta m^2$. The number of degrees of freedom is 148.
• Figure 5: Allowed regions in the parameter spaces relevant for $\nu_e$ and $\nu_{\mu}$ disappearance from a combined analysis of NSBL and LSND data, in (3+1) models, assuming statistical compatibility of the NSBL and LSND datasets. Fig. \ref{['fig:fig5']}a shows the 90%, 95%, and 99% CL allowed regions in $(\sin^2 2\theta_{e e},\Delta m^2)$ space, together with the best-fit point, indicated by the star; b) shows the same allowed regions in $(\sin^2 2\theta_{\mu\mu},\Delta m^2)$ space. Mixings to the right of the dashed vertical line in Fig.\ref{['fig:fig5']}b are excluded at 90% CL by atmospheric neutrino results Maltoni:2001mt, which are not included in this analysis.