Addressing the short-baseline neutrino anomalies with energy-dependent mixing parameters

Several neutrino experiments have reported results that are potentially inconsistent with our current understanding of the lepton sector. A candidate solution to these so-called short-baseline anomalies is postulating the existence of new, eV-scale, mostly sterile neutrinos that mix with the active neutrinos. This hypothesis, however, is strongly disfavored once one considers all neutrino data, especially those that constrain the disappearance of muon and electron neutrinos at short baselines. Here, we show that if the sterile-active mixing parameters depend on the energy scales that characterize neutrino production and detection, then the sterile-neutrino hypothesis may provide a reasonable fit to all neutrino data. The reason for the improved fit is that the stringent disappearance constraints on the different elements of the extended neutrino mixing matrix are associated to production and detection energy scales that are different from those that characterize the anomalous appearance data at MiniBooNE. We show, via a concrete example, that secret interactions among the sterile neutrinos can lead to the results of interest.

Figure 1

Renormalization group evolution of ${\sin }^2{\theta }_{14}$ and ${\sin }^2{\theta }_{24}$. Here, $g^{\prime }({\mu }_0)=1.41$ and $\mathrm{\Delta }{m}_{41}^2=1{\mathrm{eV}}^2$. See text for details. The dashed horizontal lines indicate the constraints on ${\sin }^2{\theta }_{14}$ and ${\sin }^2{\theta }_{24}$ in the absence of quantum corrections. The energy scales associated to neutrino detection at LSND, MiniBooNE, and MINOS are also indicated.

Figure 2

Disappearance probability of TeV-scale muon antineutrinos in the standard (blue) and energy-dependent frameworks (green), assuming only two-flavors (muon and sterile neutrino) and that the antineutrinos go through the Earth. $\sqrt{\mathrm{\Delta }{m}^2}=0.35\mathrm{eV}$ and $E_{\nu }$ is set to the resonant energy. In both curves, the mixing angles are chosen such that the amplitude of ${\nu }_{\mu }\to {\nu }_e$ oscillations at MiniBooNE is $3\times {10}^{-3}$. In the energy-dependent framework, relative to the standard scenario, the resonance is shifted towards larger values of $L$, often exceeding the Earth’s diameter for the values of the parameters of interest.

Figure 3

“Standard”: combined constraints on ${\sin }^{2}2{\theta }_{\mu e}$ as a function of $\mathrm{\Delta }{m}_{41}^2$, assuming the standard $3+1$ scenario. “Renormalization group evolution” (RGE): combined constraints on the effective ${\sin }^{2}2{\theta }_{\mu e}$ at MiniBooNE as a function of $\mathrm{\Delta }{m}_{41}^2$ in the model of interest. We include bounds from solar experiments (using the AGSS09 model), MicroBooNE, and ${\nu }_{\mu }$ disappearance experiments, including MINOS. The region of parameter space preferred by MiniBooNE is depicted in gray. The dashed, purple line is the $3\sigma$ C.L. sensitivity of the SBN program to ${\nu }_e$ appearance. See text for details.

Figure 4

Same as Fig. 3, except the GS98 solar model is used to extract the bounds from solar data.

Figure 5

Same as Fig. 3, for LSND instead of MiniBooNE. The region of parameter space preferred by LSND is depicted in gray. Detection energies are smaller at LSND and the distinction between the two red curves is not as pronounced as in the MiniBooNE case (Fig. 3).