This paper explores the use of $L/E$ oscillation probability distributions to compare experimental measurements and to evaluate oscillation models. In this case, $L$ is the distance of neutrino travel and $E$ is a measure of the interacting neutrinos
energy. While comparisons using allowed and excluded regions for oscillation model parameters are likely the only rigorous method for these comparisons, the $L/E$ distributions are shown to give qualitative information on the agreement of an experiments data with a simple two-neutrino oscillation model. In more detail, this paper also outlines how the $L/E$ distributions can be best calculated and used for model comparisons. Specifically, the paper presents the $L/E$ data points for the final MiniBooNE data samples and, in the Appendix, explains and corrects the mistaken analysis published by the ICARUS collaboration.
There exists a need to address and resolve the growing evidence for short-baseline neutrino oscillations and the possible existence of sterile neutrinos. Such non-standard particles require a mass of $sim 1$ eV/c$^2$, far above the mass scale associa
ted with active neutrinos, and were first invoked to explain the LSND $bar u_mu rightarrow bar u_e$ appearance signal. More recently, the MiniBooNE experiment has reported a $2.8 sigma$ excess of events in antineutrino mode consistent with neutrino oscillations and with the LSND antineutrino appearance signal. MiniBooNE also observed a $3.4 sigma$ excess of events in their neutrino mode data. Lower than expected neutrino-induced event rates using calibrated radioactive sources and nuclear reactors can also be explained by the existence of sterile neutrinos. Fits to the worlds neutrino and antineutrino data are consistent with sterile neutrinos at this $sim 1$ eV/c$^2$ mass scale, although there is some tension between measurements from disappearance and appearance experiments. In addition to resolving this potential major extension of the Standard Model, the existence of sterile neutrinos will impact design and planning for all future neutrino experiments. It should be an extremely high priority to conclusively establish if such unexpected light sterile neutrinos exist. The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory, built to usher in a new era in neutron research, provides a unique opportunity for US science to perform a definitive world-class search for sterile neutrinos.
This paper reviews the results of the LSND and MiniBooNE experiments. The primary goal of each experiment was to effect sensitive searches for neutrino oscillations in the mass region with $Delta m^2 sim 1$ eV$^2$. The two experiments are complementa
ry, and so the comparison of results can bring additional information with respect to models with sterile neutrinos. Both experiments obtained evidence for $bar u_mu rightarrow bar u_e$ oscillations, and MiniBooNE also observed a $ u_mu rightarrow u_e$ excess. In this paper, we review the design, analysis, and results from these experiments. We then consider the results within the global context of sterile neutrino oscillation models. The final data sets require a more extended model than the simple single sterile neutrino model imagined at the time that LSND drew to a close and MiniBooNE began. We show that there are apparent incompatibilities between data sets in models with two sterile neutrinos. However, these incompatibilities may be explained with variations within the systematic error. Overall, models with two (or three) sterile neutrinos seem to succeed in fitting the global data, and they make interesting predictions for future experiments.
The growing evidence for short-baseline neutrino oscillations and the possible existence of sterile neutrinos necessitates the development of a cost-effective experiment that can resolve these mysteries. The OscSNS cite{1} experiment, located at the
Spallation Neutron Source (SNS), Oak Ridge Laboratory, is ideal for this purpose.
The MiniBooNE experiment at Fermilab reports results from an analysis of $bar u_e$ appearance data from $11.27 times 10^{20}$ protons on target in antineutrino mode, an increase of approximately a factor of two over the previously reported results.
An event excess of $78.4 pm 28.5$ events ($2.8 sigma$) is observed in the energy range $200<E_ u^{QE}<1250$ MeV. If interpreted in a two-neutrino oscillation model, $bar{ u}_{mu}rightarrowbar{ u}_e$, the best oscillation fit to the excess has a probability of 66% while the background-only fit has a $chi^2$-probability of 0.5% relative to the best fit. The data are consistent with antineutrino oscillations in the $0.01 < Delta m^2 < 1.0$ eV$^2$ range and have some overlap with the evidence for antineutrino oscillations from the Liquid Scintillator Neutrino Detector (LSND). All of the major backgrounds are constrained by in-situ event measurements so non-oscillation explanations would need to invoke new anomalous background processes. The neutrino mode running also shows an excess at low energy of $162.0 pm 47.8$ events ($3.4 sigma$) but the energy distribution of the excess is marginally compatible with a simple two neutrino oscillation formalism. Expanded models with several sterile neutrinos can reduce the incompatibility by allowing for CP violating effects between neutrino and antineutrino oscillations.
The MiniBooNE experiment at Fermilab reports results from an analysis of the combined $ u_e$ and $bar u_e$ appearance data from $6.46 times 10^{20}$ protons on target in neutrino mode and $11.27 times 10^{20}$ protons on target in antineutrino mode.
A total excess of $240.3 pm 34.5 pm 52.6$ events ($3.8 sigma$) is observed from combining the two data sets in the energy range $200<E_ u^{QE}<1250$ MeV. In a combined fit for CP-conserving $ u_mu rightarrow u_e$ and $bar{ u}_{mu}rightarrowbar{ u}_e$ oscillations via a two-neutrino model, the background-only fit has a $chi^2$-probability of 0.03% relative to the best oscillation fit. The data are consistent with neutrino oscillations in the $0.01 < Delta m^2 < 1.0$ eV$^2$ range and with the evidence for antineutrino oscillations from the Liquid Scintillator Neutrino Detector (LSND).
Several mistakes have been found in recent papers that purport to reanalyze the backgrounds to the LSND neutrino oscillation signal. Once these mistakes are corrected, then it is determined that the background estimates in the papers are close to (if not lower than) the LSND background estimate.
The MiniBooNE experiment at Fermilab reports results from a search for $bar u_mu rightarrow bar u_e$ oscillations, using a data sample corresponding to $5.66 times 10^{20}$ protons on target. An excess of $20.9 pm 14.0$ events is observed in the en
ergy range $475<E_ u^{QE}<1250$ MeV, which, when constrained by the observed $bar u_mu$ events, has a probability for consistency with the background-only hypothesis of 0.5%. On the other hand, fitting for $bar{ u}_{mu}rightarrowbar{ u}_e$ oscillations, the best-fit point has a $chi^2$-probability of 8.7%. The data are consistent with $bar u_mu rightarrow bar u_e$ oscillations in the 0.1 to 1.0 eV$^2$ $Delta m^2$ range and with the evidence for antineutrino oscillations from the Liquid Scintillator Neutrino Detector at Los Alamos National Laboratory.
The MiniBooNE Collaboration observes unexplained electron-like events in the reconstructed neutrino energy range from 200 to 475 MeV. With $6.46 times 10^{20}$ protons on target, 544 electron-like events are observed in this energy range, compared to
an expectation of $415.2 pm 43.4$ events, corresponding to an excess of $128.8 pm 20.4 pm 38.3$ events. The shape of the excess in several kinematic variables is consistent with being due to either $ u_e$ and $bar u_e$ charged-current scattering or to $ u_mu$ neutral-current scattering with a photon in the final state. No significant excess of events is observed in the reconstructed neutrino energy range from 475 to 1250 MeV, where 408 events are observed compared to an expectation of $385.9 pm 35.7$ events.
The MiniBooNE Collaboration reports first results of a search for $ u_e$ appearance in a $ u_mu$ beam. With two largely independent analyses, we observe no significant excess of events above background for reconstructed neutrino energies above 475 Me
V. The data are consistent with no oscillations within a two neutrino appearance-only oscillation model.
