The MINOS results from the Neutrino 2014 conference in Boston have been replicated almost exactly by the Chinese Daya Bay neutrino experiment using similar methods (i.e. a set of several neutrino detectors hundreds of miles from each other and from the reactor neutrino source) which were reported at the same conference. The fact that the conclusions have been simultaneously and independently confirmed gives us considerable confidence that they are correct.
Fortunately, the data necessary to measure differences in mass and mixing angles for a fourth or fifth sterile neutrino with the three Standard Model neutrinos in the MINOS and Daya Bay experiments does not impact the determination of Theta 13, the squared mass difference between states one and three, or some of the other key parameters of the model which would complicate the analysis if they were strongly interdependent upon each other in fits of experimental data from these experiments to neutrino oscillation models with sterile neutrinos.
According to the new data from MINOS and Daya Bay, any sterile neutrino would have to be either at least 100 meV heavier than the heaviest of the three "fertile neutrinos" or less than 1 meV different in mass from the three fertile neutrinos
The Three Light "Fertile" Neutrinos of the Standard Model
Multiple experimental sources have confirmed in experiments measuring neutrino oscillations and in cosmology observations, that there are at least the three Standard Model fertile neutrino flavors that have been observed in weak force decays. Precision electroweak data, for example from the LEP experiment, rule out the existence of additional "fertile neutrinos" with a mass of less than 45,000,000 eV.
The absolute value of the mass difference between the first and second neutrino mass eigenstates is about 8 meV. The absolute value of the mass difference between the second and third neutrino mass eigenstates is about 50 meV.
The sum of the three neutrino mass eigenstates is at least 0.058 eV in a "normal" mass hierarchy, and at least 0.108 in an inverted mass hiearchy.
The latest direct experimental measurements reported at Neutrino 2014 merely confirm that the electron neutrino's most favored mass eigenstate has a mass of under about 0.225 eV (which would imply a sum of the three fertile neutrino mass eigenstates no higher 0.303 eV given the experimentally measured mass differences between these neutrino mass states). The highest credible prediction that I've seen of this sum of mass states based in theory, which assumes a near degenerate inverted mass hierachy is 0.254 eV. Direct experimental measurements of other flavors of neutrinos add no meaningful insight at all because they are even less precise and absurdly exceed what other well motivated theoretical and observational considerations permit.
Thus, the highest possible absolute sum of the three masses is about five times as large as the lowest possible value. The absolute value of the neutrino masses is certainly still an open question, but it has been narrowed to less than a single order of magnitude when measured on a sum of fertile neutrino mass states basis.
The Possibility of Light "Reactor Anomaly" Sterile Neutrinos
The "reactor anomaly" suggest a less than definitive possibility that there is another "sterile neutrino" that oscillates with the three fertile neutrinos. But there are tensions between the various data points suggesting this possibility, particularly between appearance and disappearance data at some reactors, which should be functions of each other.
Best fits for reactor anomaly sterile neutrino models have pointed to a single sterile neutrino of about 1 eV or more in rest mass that mixes only infrequently with fertile neutrinos (compared to the rates at which they mix with each other, specifically, for sterile neutrinos of more than 0.1 eV not more than 2.2% of the time for an electron neutrino). As the Daya Bay pre-print linked earlier in this post explains:
At the moment, there are three experimental results from neutrino oscillation experiments, which give hints that sterile neutrinos could exist. These three results, usually referred to as anomalies, are the LSND (and MiniBooNE) anomaly, the Gallium anomaly, and the reactor anomaly, which all point to sterile neutrinos with mass of the order of 1 eV and small mixing. It should be noted that if such sterile neutrinos exist, they could be produced in the early Universe, and have played an important role in the cosmological evolution. Global ﬁts to data from short-baseline neutrino oscillation experiments suggest that the data can be described by either three active and one sterile (3+1) neutrinos or three active and two sterile (3+2) neutrinos. However signiﬁcant constraints come from experiments which would appear to disfavor these anomalies.In general, while the reactor anomaly remains one of the more important unsolved questions in physics at this point, the significance of the data supporting it has declined somewhat over time. One recent study estimated the statistical significance of the reactor anomaly to be just 1.4 standard deviations. Systemic error and flawed theoretical calculations may account for much of it.
Best fits for 1+3+1 models, with one sterile neutrino lighter than any of the three Standard Model neutrinos, and one heavier, suggest a best fit mass of 3.2 eV for the five neutrino flavors combined.
Cosmology Data Regarding The Number Of Neutrino Flavors And Their Mass
Cosmological estimates of the number of effective neutrino species from cosmic background radiation observations and similar data have also pointed, but less than definitively, to the possibility of a light sterile neutrino in addition to the three Standard Model neutrinos.
Cosmology measurements favor a combined sum of the three neutrino masses that is less than about 0.3 eV, subject to a number of model dependent considerations (after the final Planck data on that point). A reactor anomaly sterile neutrino is not forbidden by cosmology data on the number of effective neutrino species (Neff) but is disfavored by data on the estimated sum of the masses of the respective neutrino flavors at a value of 1 eV of rest mass, which exceeds best estimates for the sum of all of the neutrino flavor masses combined. Best fits for 1+3+1 models are strongly at odds with cosmology data on the sum of the neutrino masses in all possible flavors.
However, it is important to note that neutrinos are defined for cosmology purposes, however, to have masses on the order of 1 eV or less, even if they would be considered neutrinos for other purposes in fundamental physics. So, for example, a 2500 eV sterile neutrino dark matter candidate would not count as a neutrino for cosmology observation purposes. Even a 3.1 eV sterile neutrino pushes the boundaries of what would be considered a neutrino for cosmology model purposes.
Cosmology data regarding Neff favor 3+1 models (i.e. a single sterile neutrino models) strongly relative to 3+2 models (i.e. models with two sterile neutrinos), the Chi-square fits to reactor data, given the respective numbers of degrees of freedom in each model, are not substantially improved by using 3+2 models rather than 3+1 models. Reactor data tends to do the same thing, although 1+3+1 models are disfavored far less strongly than 3+2 models.
Significance of Findings
The exclusion of degenerate sterile neutrinos is not unexpected. But, it largely rules out a possibility that experiments without multiple detectors spaced hundreds of miles apart and from a source reactor could not exclude. This allows data from other experiments to be fit to less exotic sterile neutrino parameter spaces that other experiments cannot distinguish themselves, without loss of rigor.
A reactor anomaly sterile neutrino mass would be too light to be a warm dark matter or cold dark matter candidate if it is a thermal relic (if it were a thermal relic, it would be "hot dark matter" which is excluded as a explanation for dark matter phenomena experimentally). But, obviously, any experimental evidence for a non-Standard Model fundamental particle, even if it is not definitive, is a big deal.
In the end, my prediction is that the reactor anomaly will evaporate as systemic errors and theoretical calculation issues are clarified, eventually ruling out the possibility of a light sterile neutrino. There is too much tension between the weak evidence in favor of sterile neutrinos for it to be likely that it will stand the test of time, and too little theoretical motivation for their existence. But, it is too early to rule their existence out at this point based upon observational evidence alone at this point.