This paper reviews short-baseline oscillation experiments as interpreted within the context of one, two, and
three sterile neutrino models associated with additional neutrino mass states in the
Over the past 15 years, neutrino oscillations associated with small splittings between the neutrino mass states have become well established [
Despite its success, the model does not address fundamental questions such as how neutrino masses should be incorporated into an SM Lagrangian or why the neutrino sector has small masses and large mixing angles compared to the quark sector. As a result, while this structure makes successful predictions, one would like to gain a deeper understanding of neutrino phenomenology. This has led to searches for other unexpected properties of neutrinos that might lead to clues towards a more complete theory governing their behavior.
Recalling that the mass splitting is related to the frequency of oscillation, short-baseline (SBL) experiments search for evidence of “rapid” oscillations above the established solar (~10−5
This paper examines these results within the context of models describing oscillations with sterile neutrinos. An oscillation formalism that introduces multiple sterile neutrinos is described in the next section. Following this, we review the SBL datasets used in the fits presented in this paper, which include both positive signals and stringent limits. We then detail the analysis approach, which we have developed in a series of past papers [
Sterile neutrinos are additional states beyond the standard electron, muon, and tau flavors, which do not interact via the exchange of
Within the expanded oscillation phenomenology, sterile neutrinos are handled as additional noninteracting flavors, which are connected to additional mass states via an extended mixing matrix with extra mixing angles and CP violating phases. These additional mass states must be mostly sterile, with only a small admixture of the active flavors, in order to accommodate the limits on oscillations to sterile neutrinos from the atmospheric and solar neutrino data. Experimental evidence for these additional mass states would come from the disappearance of an active flavor to a sterile neutrino state or additional transitions from one active flavor to another through the sterile neutrino state.
The number of light sterile neutrinos is not predicted by theory. However, a natural tendency is to introduce three sterile states. Depending on how the states are distributed in mass scale, one, two, or all three states may be involved in SBL oscillations. These are referred to as (
Introducing sterile neutrinos can have implications in cosmological observations, especially measurements of the radiation density in the early universe. These are compounded if the extra neutrinos have significant mass (
Before considering the phenomenology of light sterile neutrinos, it is useful to introduce the idea of oscillations within a simpler model. In this section, we first consider the two-neutrino formalism. We then extend these ideas to form the well-established three-active-flavor neutrino model. Based on these concepts, we expand the discussion to include more states in the following section.
Neutrino oscillations require that (1) neutrinos have mass; (2) the difference between the masses is small; (3) the mass eigenstates are rotations of the weak interaction eigenstates. These rotations are given in a simple two-neutrino model as follows:
From (
In the case where
The exercise of generalizing to a three-neutrino model is useful, since the inclusion of more states follows from this procedure. Within a three-neutrino model, the mixing matrix is written as follows:
The oscillation probability for three-neutrino oscillations is typically written as the following:
Three different
The sterile neutrino oscillation formalism followed in this paper assumes up to three additional neutrino mass eigenstates, beyond the established three SM neutrino species. We know, from solar and atmospheric oscillation observations, that three of the mass states must be mostly active. Experimental hints point toward the existence of additional mass states that are mostly sterile, in the range of
Introducing extra mass states results in a large number of extra parameters in the model. Approximation is required to allow for efficient exploration of the available parameters. To this end, in our model we assume that the three lowest states,
The active
In this formalism, the probabilities for
To be explicit, for the (
We have discussed the formulas for (
For a (
In principle, the probability for neutrino oscillation is modified in the presence of matter. “Matter effects” arise because the electron neutrino flavor experiences both Charged-Current (CC) and Neutral-Current (NC) elastic forward scattering with electrons as it propagates through matter, while the
This section provides an overview of the various types of past and current neutrino sources and detectors used in SBL experiments. After introducing the experimental concepts, the specific experimental datasets used in this analysis are discussed.
The data fall into two overall categories: disappearance, where the active flavor is assumed to have oscillated into a sterile neutrino and/or another flavor which is kinematically not allowed to interact or leaves no detectable signature, and appearance, where the transition is between active flavors, but with mass splittings corresponding to the mostly sterile states. Appearance and disappearance are natural divisions for testing the compatibility of datasets. If
CPT conservation, which is assumed in the analysis, demands that neutrino and antineutrino disappearance probabilities are the same after accounting for cp violating effects. To test this, we divide the data into antineutrino and neutrino sets and fit each set separately. If CP violation is already allowed in the oscillation formalism, then any incompatibility found between respective neutrino and antineutrino fits could imply effective CPT violation, as discussed in [
Figures
Summary of
Summary of
Summary of
Before considering the datasets in detail, we provide an overview of how SBL experiments are typically designed.
The neutrino sources used in SBL experiments range in energy from a few MeV to hundreds of GeV and include manmade radioactive sources, reactors, and accelerator-produced beams. While the higher energy accelerator sources are mixtures of different neutrino flavors, the <10 MeV sources rely on beta decay and are thus pure electron neutrino flavor.
At the low-energy end of the spectrum, the rate of electron neutrino interactions from the beta decay of the ~1 MCi sources
Moving up in energy by a few MeV, nuclear reactors are powerful sources of ~2−8 MeV
The lowest neutrino energy (up to 53 MeV) accelerator sources used in existing SBL experiments are based on pion- and muon-decay-at-rest (DAR). The neutrino flux comes from the stopped pion decay chain:
In a conventional high-energy (from ~100 MeV to hundreds of GeV) accelerator-based neutrino beam, protons impinge on a target (beryllium and carbon are typical) to produce secondary mesons. The boosted mesons enter and subsequently decay inside a long, often evacuated, pipe. Neutrinos are primarily produced by
In contrast to lower-energy neutrino sources (DAR, reactor, and isotope sources), high-energy accelerator-based neutrino sources are subject to significant energy-dependent neutrino flux uncertainties, often at the level of 10–15%, due to in-target meson production uncertainties. These uncertainties can affect the energy distribution, flavor content, and absolute normalization of a neutrino beam. Typically, meson production systematics are constrained with dedicated measurements by experiments such as HARP [
Because low-energy neutrino interaction cross-sections are very small, the options for SBL detectors are typically limited to designs which can be constructed on a massive scale. There are several generic neutrino detection methods in use today: unsegmented scintillator detectors, unsegmented Cerenkov detectors, segmented scintillator-and-iron calorimeters, and segmented trackers.
Neutrino oscillation experiments usually require sensitivity to CC neutrino interactions, whereby one can definitively identify the flavor of the interacting neutrino by the presence of a charged lepton in the final state. However, in the case of sterile neutrino oscillation searches, NC interactions can also provide useful information, as they are directly sensitive to the sterile flavor content of the neutrino mass eigenstate,
Unsegmented scintillator detectors are typically used for few-MeV-scale SBL experiments, which require efficient electron neutrino identification and reconstruction. These detectors consist of large tanks of oil-based (
The CC interaction with the carbon in the oil (which produces either nitrogen or boron depending on whether the scatterer is a neutrino or antineutrino) has a significantly higher energy threshold than the free proton target-scattering process. The CC quasielastic interaction
Unsegmented Cerenkov detectors make use of a target which is a large volume of clear medium (undoped oil or water is typical) surrounded by, or interspersed with, phototubes. Undoped oil has a larger refractive index, leading to a larger Cerenkov opening angle. Water is the only affordable medium once the detector size surpasses a few kilotons. In this paper, the only unsegmented Cerenkov detector that is considered is the 450-ton oil-based MiniBooNE detector. In such a detector, a track will project a ring with a sharp inner and outer edge onto the phototubes. Consider an electron produced in a
Scintillator and iron calorimeters provide an affordable detection technique for ~1 GeV and higher
To address the problem of running at ~1 GeV, where hadron track reconstruction is desirable, highly segmented tracking designs have been developed. The best resolution comes from stacks of wire chambers, where the material enclosing the gas provides the target. However, a more practical alternative has been stacks of thin extruded scintillator bars that are read out using wavelength-shifting fibers.
There are many SBL datasets that can be included in this analysis. In this work, we have substantially expanded the number of datasets used beyond those in our past papers [
In past sterile neutrino studies [
This dataset is referred to as LSND in the analysis below and indicates a signal at 95% CL, as shown in Figure
The center of the approximately cubic segmented scintillator detector was located at 17.7 m. Thus, this detector was 60% of the distance from the source compared to LSND. The liquid scintillator target volume was 56 m3 and consisted of 512 optically independent modules (17.4 cm
This dataset is referred to as KARMEN in the analysis below and indicates a limit at 95% CL, as shown in Figure
The cross-section is measured by both experiments under the assumption that the
This dataset is referred to as KARMEN/LSND(
The MiniBooNE experiment provides multiple results from a single detector. This oil-based 450 t fiducial volume Cerenkov detector was exposed to two conventional beams, the Booster Neutrino Beam (BNB) and the off-axis NuMI beam. The primary goal of MiniBooNE was to search for
The MiniBooNE datasets included in our analysis have increased throughout the period that our group has been performing fits. Reference [
In our fits to MiniBooNE appearance data, when drawing allowed regions and calculating compatibilities, which make use of
The global fits presented here use the full statistics of the MiniBooNE
We include the BNB-MB(
The dataset results in a signal at 95% CL, as shown in Figure
The global fits presented here use the full statistics of the MiniBooNE
As in neutrino mode, we fit the full
The dataset results in a signal at 95% CL, as shown in Figure
This dataset is referred to as NuMI-MB(
The fit to the
This dataset is referred to as BNB-MB(
The set of multi-GeV conventional SBL
This dataset is referred to as NOMAD in the analysis below. This dataset contributes 30 energy bins to the global fit. The statistical and systematic errors are added in quadrature. This experiment sets a limit at 95% CL, as seen in Figure
This dataset is referred to as CCFR84 in the analysis below. The data were published as the double ratios of the observed-to-expected rates in a near-to-far ratio. For each secondary mean setting, the data are divided into three energy bins. The systematic uncertainty is assumed to be energy independent and fully correlated between the energy bins. Due to the high beam energies and short baselines, this experiment sets a limit at high
This dataset is referred to as CDHS in the analysis below. CDHS provides data and errors in 15 bins of muon energy, as seen in in Table 1 of [
The reactor experiment dataset has been updated to reflect recent changes in the predicted neutrino fluxes, as discussed below. The source-based experimental datasets are both new to this paper, and have been published since our last set of fits [
Recently, a reanalysis of reactor
There are many other SBL reactor datasets in existence. However, we have chosen to use only Bugey in these fits as the measurement has the lowest combined errors. Also, any global fit to multiple reactor datasets must correctly account for the correlated systematics between them, which is beyond the scope of our fits at present.
This dataset is referred to as Bugey in the analysis below. As shown in Figure
While this study concentrates mainly on results from SBL experiments, the data from experiments with baselines of hundreds of kilometers can be valuable. At such long baselines, the ability to identify the
We note two long-baseline results not included in this analysis. First, we have dropped the Chooz dataset that was included in previous fits [
MINOS ran in both neutrino and antineutrino mode. We employ the antineutrino data in our fits as it constrains the allowed region for muon antineutrino disappearance when we divide the datasets into neutrino versus antineutrino fits. The MINOS neutrino mode disappearance limit is not as restrictive as the atmospheric result, and so only the antineutrino dataset is utilized.
This result is referred to as MINOS-CC in the analysis below. The data present a limit at 95% CL as discussed above and shown in Figure
As with our past fits, we include atmospheric constraints following the prescription of [
The analysis method follows the formalism described in Section
The independent parameters considered in the (
The fitting method closely follows what has been done in [
In any given fit, we define possible signal indications at 90% and 99% CL by marginalizing over the full parameter space, and looking for closed contours formed about a global minimum,
In any given fit, in addition to a standard
This section presents the results of the analysis for the (
Datasets used in the fits and their corresponding use in the analysis. Column 1 provides the tag for the data. Column 2 references the description in Section
Tag | Section | Process |
|
App versus Dis |
---|---|---|---|---|
LSND |
|
|
|
App |
KARMEN |
|
|
|
App |
KARMEN/LSND( |
|
|
|
Dis |
BNB-MB( |
|
|
|
App |
BNB-MB( |
|
|
|
App |
NuMI-MB( |
|
|
|
App |
BNB-MB( |
|
|
|
Dis |
NOMAD |
|
|
|
App |
CCFR84 |
|
|
|
Dis |
CDHS |
|
|
|
Dis |
Bugey |
|
|
|
Dis |
Gallium |
|
|
|
Dis |
MINOS-CC |
|
|
|
Dis |
ATM |
|
|
|
Dis |
The
|
|
|
|
|
PG (%) | |
---|---|---|---|---|---|---|
|
||||||
| ||||||
All | 233.9 (237) | 286.5 (240) | 55% | 2.1% | 54.0 (24) | 0.043% |
App | 87.8 (87) | 147.3 (90) | 46% | 0.013% | 14.1 (9) | 12% |
Dis | 128.2 (147) | 139.3 (150) | 87% | 72% | 22.1 |
28% |
|
123.5 (120) | 133.4 (123) | 39% | 25% | 26.6 |
2.2% |
|
94.8 (114) | 153.1 (117) | 90% | 1.4% | 11.8 |
11% |
App versus Dis | — | — | — | — | 17.8 |
0.013% |
|
— | — | — | — | 15.6 |
0.14% |
| ||||||
|
||||||
| ||||||
All | 221.5 (233) | 286.5 (240) | 69% | 2.1% | 63.8 (52) | 13% |
App | 75.0 (85) | 147.3 (90) | 77% | 0.013% | 16.3 (25) | 90% |
Dis | 122.6 (144) | 139.3 (150) | 90% | 72% | 23.6 (23) | 43% |
|
116.8 (116) | 133.4 (123) | 77% | 25% | 35.0 (29) | 21% |
|
90.8 (110) | 153.1 (117) | 90% | 1.4% | 15.0 |
53% |
App versus Dis | — | — | — | — | 23.9 |
0.0082% |
|
— | — | — | — | 13.9 |
5.3% |
| ||||||
|
||||||
| ||||||
All | 218.2 (228) | 286.5 (240) | 67% | 2.1% | 68.9 (85) | 90% |
App | 70.8 (81) | 147.3 (90) | 78% | 0.013% | 17.6 (45) | 100% |
Dis | 120.3 (141) | 139.3 (150) | 90% | 72% | 24.1 (34) | 90% |
|
116.7 (111) | 133.4 (123) | 34% | 25% | 39.5 (46) | 74% |
|
90.6 (105) | 153 (117) | 84% | 1.4% | 18.5 (27) | 89% |
App versus Dis | — | — | — | — | 27.1 |
0.014% |
|
— | — | — | — | 10.9 (12) | 53% |
The oscillation parameter best-fit points in each scenario considered. The values of
|
|
|
|
---|---|---|---|
All | 0.92 | 0.17 | 0.15 |
App | 0.15 | 0.39 | 0.39 |
Dis | 18 | 0.18 | 0.18 |
|
7.8 | 0.059 | 0.26 |
|
0.92 | 0.23 | 0.13 |
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
All | 0.92 | 17 | 0.13 | 0.15 | 0.16 | 0.069 | 1.8 |
App | 0.31 | 1.0 | 0.31 | 0.31 | 0.17 | 0.17 | 1.1 |
Dis | 0.92 | 18 | 0.015 | 0.12 | 0.17 | 0.12 | N/A |
|
7.6 | 17.6 | 0.05 | 0.27 | 0.18 | 0.052 | 1.8 |
|
0.92 | 3.8 | 0.25 | 0.13 | 0.12 | 0.079 | 0.35 |
|
|
|
|
|
|
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|---|---|---|---|---|
All | 0.90 | 17 | 22 | 0.12 | 0.11 | 0.17 | 0.11 | 0.14 | 0.11 | 1.6 |
0.28 |
1.4 |
App | 0.15 | 1.8 | 2.7 | 0.37 | 0.37 | 0.12 | 0.12 | 0.12 | 0.12 | 1.4 |
0.32 |
0.94 |
Dis | 0.92 | 7.2 | 18 | 0.013 | 0.12 | 0.019 | 0.16 | 0.15 | 0.069 | N/A | N/A | N/A |
|
13 | 17 | 26 | 0.076 | 0.24 | 0.16 | 0.067 | 0.10 | 0.017 | 1.1 |
1.8 |
0.037 |
|
7.5 | 9.1 | 18 | 0.024 | 0.28 | 0.098 | 0.11 | 0.18 | 0.029 | 1.8 |
2.0 |
0.61 |
For a (
The
In order to understand the source of the poor compatibility, the datasets are subdivided, as shown in Table
The
The
As can be seen in Table
In a (
The
Adding a second mass eigenstate reduces the tension seen in the (
The need to introduce a CP-violating phase was established in previous studies of global fits [
Table
The
While the neutrino versus antineutrino discrepancy has been somewhat reduced, Table
The
For a (
It is interesting to note that the (
The one puzzling discrepancy for the (3 + 3) fits is the tension still exhibited by the appearance versus disappearance datasets, shown in Figures
The
The
The
A comparison of the BNB-MB(
Statistical issues could be addressed with more MiniBooNE neutrino data that may become available over the next few years. In addition, the MicroBooNE experiment, which is expected to start running in 2014, will provide more information on the low-energy excess events and will answer the question of whether the excess is associated with outgoing electrons or photons [
The sterile neutrino fits to global datasets show that a (
In summary, out of the three sterile neutrino oscillation hypotheses considered in the analysis, we find that the (
Establishing the existence of sterile neutrinos would have a major impact on particle physics. Motivated by this, there are a number of existing and planned experiments set to probe the parameter space indicative of one or more sterile neutrinos. Such experiments are necessary in order to confirm or refute the observed anomalies in the
Sterile neutrino oscillation models are based on oscillations associated with mixing between active and sterile states and demand the presence of both appearance and disappearance. It is therefore imperative that the future program explore both of these oscillation types. Establishing sterile neutrinos will require that both types of measurements are compatible with sterile neutrino oscillation models. Future experiments will search for evidence of sterile neutrino(s) using a variety of neutrino creation sources: (1) pion/muon DIF (e.g., [
Ultimately, in order to determine if there are zero, one, two, or three sterile states contributing to oscillations in SBL experiments, it will be necessary to observe the expected
The three models, (
The (
The (
The (
In Figures
In summary, it seems very unlikely that any
A summary of current and future sterile neutrino oscillation experiments.
Source | App/Dis | Channel | Experiment |
---|---|---|---|
Reactor | Dis |
|
Nucifer, Stereo, SCRAMM, NIST, Neutrino4, DANSS |
Radioactive | Dis |
|
Baksan, LENS, Borexino, SNO+, Ricochet, CeLAND, Daya Bay |
Accelerator-based isotope | Dis |
|
IsoDAR |
Pion/Kaon DAR | App and Dis |
|
OscSNS, DAE |
|
|||
Accelerator (Pion DIF) | App and Dis |
|
MINOS+, MicroBooNE, LAr1kton + MicroBooNE, CERN SPS |
|
|||
Low-energy |
App and Dis |
|
|
|
A summary of future sterile neutrino experiments is provided in Table
Muon neutrinos (antineutrinos) from positive (negative) pion DIF can be used to search for (anti)neutrino disappearance and electron (anti)neutrino appearance in the sterile neutrino region of interest. Given the usual neutrino energies for these experiments (
The BNB at Fermilab will provide pion-induced neutrinos to the MicroBooNE LArTPC-based detector starting in 2014 [
Another BNB-based idea calls for a significant upgrade to the MiniBooNE experiment in which the current MiniBooNE detector becomes the 540 m baseline far detector in a two detector configuration and a MiniBooNE-like oil-based near detector is installed at a baseline of 200 m [
A low-energy 3-4 GeV/c muon storage ring could deliver a precisely known flux of electron neutrinos for a muon neutrino appearance search in the parameter space of interest for sterile neutrinos [
As discussed above, neutrinos from pion DAR and subsequent daughter muon DAR, with their well-known spectrum, provide a source for an oscillation search. Notably, LSND employed muon antineutrinos from the pion daughter’s muon DAR in establishing their 3.8
The 1 MW Spallation Neutron Source at Oak Ridge National Laboratory, a pion and muon DAR neutrino source, in combination with an LSND-style detector could directly probe the LSND excess with a factor of 100 lower steady state background and higher beam power [
If higher energy proton beams are used, then positive kaon DAR and the resulting monoenergetic (235.5 MeV) muon neutrino can also be used to search for sterile neutrinos through an electron neutrino appearance search with a LArTPC-based device [
The disappearance of electron antineutrinos from radioactive isotopes is a direct probe of the reactor/gallium anomaly and an indirect probe of the LSND anomaly. As such neutrinos are in the ones-of-MeV range, the baseline for these experiments is generally on the order of tens of meters or so. Oscillation waves within a single detector can be observed if the neutrinos originate from a localized source, if the oscillation length is short enough, and if the detector has precise enough vertex resolution.
The IsoDAR concept [
Another unstable-isotope-based idea involves the deployment of a radioactive source inside an existing kiloton-scale detector [
A nuclear reactor can be used as a source for an electron antineutrino disappearance experiment with sensitivity to sterile neutrino(s). The Nucifer detector will likely be the first reactor-based detector to test the sterile neutrino hypothesis using antineutrino energy shape rather than just rate [
One of the challenges of a reactor-based search is the need for a relatively small reactor size given the baseline required for maximal sensitivity to
All of the future experiments discussed previously involve either disappearance or appearance of neutrinos and antineutrinos detected via the charged current. However, a NC-based disappearance experiment provides unique sensitivity to the sterile neutrino. If neutrino disappearance was observed in a NC experiment, one would know that the active flavor neutrino(s) in question had oscillated into the noninteracting sterile flavor. Particularly, such an experiment would provide a measure of
This paper has presented results of SBL experiments discussed within the context of oscillations involving sterile neutrinos. Fits to (
Several issues arise when comparing datasets in (
A 3 + 3 (3 + 2) model fit has a
While the indications of sterile neutrino oscillations have historically been associated with only appearance-based SBL experiments, the recently realized suppression in observed
The authors thank William Louis and Zarko Pavlovic for valuable discussions and the National Science Foundation for its support.