One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many ...analyses involving open likelihoods are affected by the eternal dilemma of choosing between linear and logarithmic prior, and in particular in the latter case the situation is worsened by the dependence on the prior range under consideration. In this letter, we revive a simple method to obtain constraints that depend neither on the prior shape nor range and, using the tools of Bayesian model comparison, extend it to overcome the possible dependence of the bounds on the choice of free parameters in the numerical analysis. An application to the case of cosmological bounds on the sum of the neutrino masses is discussed as an example.
A
bstract
We present the results of an updated fit of short-baseline neutrino oscillation data in the framework of 3+1 active-sterile neutrino mixing. We first consider
ν
e
and
ν
¯
e
disappearance in ...the light of the Gallium and reactor anomalies. We discuss the implications of the recent measurement of the reactor
ν
¯
e
spectrum in the NEOS experiment, which shifts the allowed regions of the parameter space towards smaller values of |
U
e
4
|
2
. The
β
-decay constraints of the Mainz and Troitsk experiments allow us to limit the oscillation length between about 2 cm and 7 m at 3
σ
for neutrinos with an energy of 1 MeV. The corresponding oscillations can be discovered in a model-independent way in ongoing reactor and source experiments by measuring ν
e
and
ν
¯
e
disappearance as a function of distance. We then consider the global fit of the data on short-baseline
ν
μ
−
→
ν
e
−
transitions in the light of the LSND anomaly, taking into account the constraints from
ν
e
−
and
ν
μ
−
disappearance experiments, including the recent data of the MINOS and IceCube experiments. The combination of the NEOS constraints on |
U
e
4
|
2
and the MINOS and IceCube constraints on |
U
μ
4
|
2
lead to an unacceptable appearance-disappearance tension which becomes tolerable only in a pragmatic fit which neglects the MiniBooNE low-energy anomaly. The minimization of the global
χ
2
in the space of the four mixing parameters Δ
m
41
2
, |
U
e
4
|
2
, |
U
μ
4
|
2
, and |
U
τ
4
|
2
leads to three allowed regions with narrow Δ
m
41
2
widths at Δ
m
41
2
≈ 1.7 (best-fit), 1.3 (at 2
σ
), 2.4 (at 3
σ
) eV
2
. The effective amplitude of short-baseline
ν
μ
−
→
ν
e
−
oscillations is limited by 0.00048 ≲ sin
2
2
ϑ
eμ
≲ 0.0020 at 3
σ
. The restrictions of the allowed regions of the mixing parameters with respect to our previous global fits are mainly due to the NEOS constraints. We present a comparison of the allowed regions of the mixing parameters with the sensitivities of ongoing experiments, which show that it is likely that these experiments will determine in a definitive way if the reactor, Gallium and LSND anomalies are due to active-sterile neutrino oscillations or not.
A
bstract
We present an updated global fit of neutrino oscillation data in the simplest three-neutrino framework. In the present study we include up-to-date analyses from a number of experiments. ...Concerning the atmospheric and solar sectors, besides the data considered previously, we give updated analyses of IceCube DeepCore and Sudbury Neutrino Observatory data, respectively. We have also included the latest electron antineutrino data collected by the Daya Bay and RENO reactor experiments, and the long-baseline T2K and NO
ν
A measurements, as reported in the Neutrino 2020 conference. All in all, these new analyses result in more accurate measurements of
θ
13
,
θ
12
,
Δ
m
21
2
and
Δ
m
31
2
. The best fit value for the atmospheric angle
θ
23
lies in the second octant, but first octant solutions remain allowed at ∼ 2
.
4
σ
. Regarding CP violation measurements, the preferred value of
δ
we obtain is 1.08
π
(1.58
π
) for normal (inverted) neutrino mass ordering. The global analysis still prefers normal neutrino mass ordering with 2.5
σ
statistical significance. This preference is milder than the one found in previous global analyses. These new results should be regarded as robust due to the agreement found between our Bayesian and frequentist approaches. Taking into account only oscillation data, there is a weak/moderate preference for the normal neutrino mass ordering of 2
.
00
σ
. While adding neutrinoless double beta decay from the latest Gerda, CUORE and KamLAND-Zen results barely modifies this picture, cosmological measurements raise the preference to 2
.
68
σ
within a conservative approach. A more aggressive data set combination of cosmological observations leads to a similar preference for normal with respect to inverted mass ordering, namely 2
.
70
σ
. This very same cosmological data set provides 2
σ
upper limits on the total neutrino mass corresponding to Σ
m
ν
<
0
.
12 (0
.
15) eV in the normal (inverted) neutrino mass ordering scenario. The bounds on the neutrino mixing parameters and masses presented in this up-to-date global fit analysis include all currently available neutrino physics inputs.
We consider the ratio of the spectra measured in the DANSS neutrino experiment at 12.7 and 10.7 m from a nuclear reactor. These data give a new model-independent indication in favor of short-baseline ...ν¯e oscillations which reinforce the model-independent indication found in the late 2016 in the NEOS experiment. The combined analysis of the NEOS and DANSS spectral ratios in the framework of 3+1 active–sterile neutrino mixing favor short-baseline ν¯e oscillations with a statistical significance of 3.7σ. The two mixing parameters sin22ϑee and Δm412 are constrained at 2σ in a narrow-Δm412 island at Δm412≃1.3eV2, with sin22ϑee=0.049±0.023 (2σ). We discuss the implications of the model-independent NEOS+DANSS analysis for the reactor and Gallium anomalies. The NEOS+DANSS model-independent determination of short-baseline ν¯e oscillations allows us to analyze the reactor rates without assumptions on the values of the main reactor antineutrino fluxes and the data of the Gallium source experiments with free detector efficiencies. The corrections to the reactor neutrino fluxes and the Gallium detector efficiencies are obtained from the fit of the data. In particular, we confirm the indication in favor of the need for a recalculation of the U235 reactor antineutrino flux found in previous studies assuming the absence of neutrino oscillations.
A
bstract
We analyze the most recent cosmological data, including Planck, taking into account the possible existence of a sterile neutrino with a mass at the eV scale indicated by short-baseline ...neutrino oscillations data in the 3+1 framework. We show that the contribution of local measurements of the Hubble constant induces an increase of the value of the effective number of relativistic degrees of freedom above the Standard Model value, giving an indication in favor of the existence of sterile neutrinos and their contribution to dark radiation. Furthermore, the measurements of the local galaxy cluster mass distribution favor the existence of sterile neutrinos with eV-scale masses, in agreement with short-baseline neutrino oscillations data. In this case there is no tension between cosmological and short-baseline neutrino oscillations data, but the contribution of the sterile neutrino to the effective number of relativistic degrees of freedom is likely to be smaller than one. Considering the Dodelson-Widrow and thermal models for the statistical cosmological distribution of sterile neutrinos, we found that in the Dodelson-Widrow model there is a slightly better compatibility between cosmological and short-baseline neutrino oscillations data and the required suppression of the production of sterile neutrinos in the early Universe is slightly smaller.
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