# Joachim Kopp: Status of Sterile Neutrino Scenarios

Kopp started by mentioning that sterile is “lacking in stimulating emotional or intellectual quality”, but this is not the case of a sterile neutrino, because this is a very general extension of the SM, a singlet under the gauge group of the SM, and can be anything, a leftover of extended gauge multiplets such as those from GUT. Steriles can explain several observed anomalies in neutrino experiments in the past.

If there is a mixing between active and sterile neutrinos, we expect disappearance of active neutrinos, i.e. oscillations, and other anomalous transitions. With steriles, there is a complicated dependence of observable oscillation probabilities on the fundamental parameters of the theory. One can try and understand the probabilities analytically, determine the relevant parameters for each experiment, and the analytic knowledge can be used with theoretical input to simplify the calculations. A global fit can then constrain the parameters.

The two main anomalies are those of LSND and MiniBooNE. Both see antineutrino appearance in antineutrinos from muons. MiniBooNE has a low-energy excess that is not understood.

Reactor and gallium experiments have also observed anomalies. Reactor exps. see electron antineutrino fluxes which are 3.5% higher than predictions. The gallium anomaly came from intense radioactive electron neutrino sources, observing a deficit. Also a 3-sigma effect.

Kopp described the fit that they perform, which includes all the relevant experimental input. There are electron antineutrino disappearance ()SBL, LBL…) and appearance experiments, and muon neutrino disappearance experiments (from atmospheric sources, MiniBooNE, MINOS, and CDHS).

From short baseline reactors as a function of the distance one sees a varying set of points lower than expected fluxes (see figure below). One can fit this in the 3+1 scenario (three active and one sterile neutrino). This produces a measurement of allowed regions of the dm^2_14 vs sin^2(theta_14), which has a best solution at sin^2 theta_14 = 0.10, with a dm^2_14=1.75 eV^2.

Including everything as far as disappearance measurements are concerned (Gallium, Bugey3) one finds a compatible result, with best fit at (0.09,1.78). Such a scenario would not impact the theta_13 measurement; a non-zero theta_13 also does not impact sterile neutrino searches.

For muon neutrino disappearance experiments,the parameter regions favored by the tentative hints are in tension with null results, in the 3+1 scenario. Constraints on sin_theta_34 are also possible due to neutral current events and matter effects. Kopp showed plots of allowed regions in U(tau,4) vs U(mu,4) which see an allowed region in the lower left quadrant, i.e. for small values of both parameters (I will add the plot here later if I find the time!).

For electron neutrino appearance searches, the data comes from LSND, MiniBooNE, E776, Karmen, Nomad, and ICARUS most recently. A plot of mixing angle versus mass difference was shown, where the mixing angle is a composite of muon-electron neutrino mixing, sin^2 theta_mu-e. The fit is reasonable in chisquared, and there is a reasonably sized region of parameter space which accommodates all inputs. The data was also analyzed in the 3+2 scenario and in the 1+3+1 scenario. There is significant improvement in the goodness of fit by using the 3+2 scenario.

Putting everything together one can do a global oscillation fit, which shows severe tension between the two sets of experiments. This is not obvious from a simple analysis of the chisquare per degree of freedom: this is due to the fact that many of the inputs have no sensitivity to sterile neutrinos, and dilute the chisquared. If one compares the minimum chisquare from global and separate fits, one sees that there is a p-value at the level of 10^-4.

The conclusion is that the models cannot explain the full sets of data.

Kopp then spoke for a while of sterile neutrinos in cosmology. The constraints come from a sum of neutrino masses below 0.5 eV, and the number of relativistic species, with N>3 slightly preferred. Ways out are a large lepton asymmetry (>0.01) which would lead to a suppressed production. See e.g. hep-ph/9508275, or astro-ph/0608206. Or one could have more than one relativistic degree of freedom, or a coupling to a Majoron field, also leading to suppressed production (hep-ph/0108064).

Also a combined fit of SBL data and cosmology inputs has been tried, see arxiv:1302.6720. The cosmological input comes from Wmap9, plus results from the hubble space telescope and baryon acoustic oscillations. The combination yields a value of m4 in the 1.3 eV range and this is only if the detected number of degrees of freedom N4 is of about a half. The graph below shows the best-fit region in green.

In conclusion, sterile neutrinos are theoretically well motivated. Global fits show severe tension between appearance and disappearance searches; this also leads to different groups getting to slightly different conclusions on the whole picture. Cosmological inputs are strong but they do not add much.

One is bound to ask whether one or all of the positive results may be due to something else than neutrino oscillations. But more than one result should be wrong in order to reconcile experiments with the absence of steriles. Maybe the answer is that there are more than two steriles, or that there is also something else. We just can’t say yet.

Carlo Rubbia commented that the problem is an experimental one, while the speaker made the implicit assumption that every experiment is right. He mentioned that the disappearance experiments all assume that the spectrum from the reactor material is known and the same. Also the lifetime of the neutron has changed with respect to what was before. So the results cannot be combined as if they were independent. To him the combination is not correct as it is done. The second point he made was about neutrino appearance experiments. The low-energy excess in MiniBooNE is certainly an experimental problem to Rubbia. Icarus has a low-energy peak which is instrumental. So if one uses this result as a genuine result one will certainly reach inconsistent conclusions. Rubbia made the wish that the experimental input is more carefully treated.

The speaker answered that the datasets certainly need more experimental scrutiny, but it is definitely justified to use these results from a theoretical point of view. About the combination of short baseline disappearance results, he mentioned that there is an accurate evaluation of the covariance matrix between all the results which accounts for all the known features.