# Horton Hears a Sterile Neutrino?

Article: Limits on Active to Sterile Neutrino Oscillations from Disappearance Searches in the MINOS, Daya Bay, and Bugey-3 Experiments
Authors:  Daya Bay and MINOS collaborations
Reference: arXiv:1607.01177v4

So far, the hunt for sterile neutrinos has come up empty. Could a joint analysis between MINOS, Daya Bay and Bugey-3 data hint at their existence?

Neutrinos, like the beloved Whos in Dr. Seuss’ “Horton Hears a Who!,” are light and elusive, yet have a large impact on the universe we live in. While neutrinos only interact with matter through the weak nuclear force and gravity, they played a critical role in the formation of the early universe. Neutrino physics is now an exciting line of research pursued by the Hortons of particle physics, cosmology, and astrophysics alike. While most of what we currently know about neutrinos is well described by a three-flavor neutrino model, a few inconsistent experimental results such as those from the Liquid Scintillator Neutrino Detector (LSND) and the Mini Booster Neutrino Experiment (MiniBooNE) hint at the presence of a new kind of neutrino that only interacts with matter through gravity. If this “sterile” kind of neutrino does in fact exist, it might also have played an important role in the evolution of our universe.

The three known neutrinos come in three flavors: electron, muon, or tau. The discovery of neutrino oscillation by the Sudbury Neutrino Observatory and the Super-Kamiokande Observatory, which won the 2015 Nobel Prize, proved that one flavor of neutrino can transform into another. This led to the realization that each neutrino mass state is a superposition of the three different neutrino flavor states. From neutrino oscillation measurements, most of the parameters that define the mixing between neutrino states are well known for the three standard neutrinos.

The relationship between the three known neutrino flavor states and mass states is usually expressed as a 3×3 matrix known as the PMNS matrix, for Bruno Pontecorvo, Ziro Maki, Masami Nakagawa and Shoichi Sakata. The PMNS matrix includes three mixing angles, the values of which determine “how much” of each neutrino flavor state is in each mass state. The distance required for one neutrino flavor to become another, the neutrino oscillation wavelength, is determined by the difference between the squared masses of the two mass states. The values of mass splittings $m_2^2-m_1^2$ and $m_3^2-m_2^2$ are known to good precision.

A fourth flavor? Adding a sterile neutrino to the mix

A “sterile” neutrino is referred to as such because it would not interact weakly: it would only interact through the gravitational force. Neutrino oscillations involving the hypothetical sterile neutrino can be understood using a “four-flavor model,” which introduces a fourth neutrino mass state, $m_4$, heavier than the three known “active” mass states. This fourth neutrino state would be mostly sterile, with only a small contribution from a mixture of the three known neutrino flavors. If the sterile neutrino exists, it should be possible to experimentally observe neutrino oscillations with a wavelength set by the difference between $m_4^2$ and the square of the mass of another known neutrino mass state. Current observations suggest a squared mass difference in the range of 0.1-10 eV$^2$.

Oscillations between active and sterile states would result in the disappearance of muon (anti)neutrinos and electron (anti)neutrinos. In a disappearance experiment, you know how many neutrinos of a specific type you produce, and you count the number of that type of neutrino a distance away, and find that some of the neutrinos have “disappeared,” or in other words, oscillated into a different type of neutrino that you are not detecting.

A joint analysis by the MINOS and Daya Bay collaborations

The MINOS and Daya Bay collaborations have conducted a joint analysis to combine independent measurements of muon (anti)neutrino disappearance by MINOS and electron antineutrino disappearance by Daya Bay and Bugey-3. Here’s a breakdown of the involved experiments:

• MINOS, the Main Injector Neutrino Oscillation Search: A long-baseline neutrino experiment with detectors at Fermilab and northern Minnesota that use an accelerator at Fermilab as the neutrino source
• The Daya Bay Reactor Neutrino Experiment: Uses antineutrinos produced by the reactors of China’s Daya Bay Nuclear Power Plant and the Ling Ao Nuclear Power Plant
• The Bugey-3 experiment: Performed in the early 1990s, used antineutrinos from the Bugey Nuclear Power Plant in France for its neutrino oscillation observations

Assuming a four-flavor model, the MINOS and Daya Bay collaborations put new constraints on the value of the mixing angle $\theta_{\mu e}$, the parameter controlling electron (anti)neutrino appearance in experiments with short neutrino travel distances. As for the hypothetical sterile neutrino? The analysis excluded the parameter space allowed by the LSND and MiniBooNE appearance-based indications for the existence of light sterile neutrinos for $\Delta m_{41}^2$ < 0.8 eV$^2$ at a 95% confidence level. In other words, the MINOS and Daya Bay analysis essentially rules out the LSND and MiniBooNE inconsistencies that allowed for the presence of a sterile neutrino in the first place. These results illustrate just how at odds disappearance searches and appearance searches are when it comes to providing insight into the existence of light sterile neutrinos. If the Whos exist, they will need to be a little louder in order for the world to hear them.