The Physical Significance of Confidence Intervals

We define some appropriate statistical quantities that indicate the physical significance (reliability) of confidence intervals in the framework of both Frequentist and Bayesian statistical theories. We consider the expectation value of the upper limit in the absence of a signal (that we propose to call "exclusion potential", instead of "sensitivity" as done by Feldman and Cousins) and its standard deviation, we define the "Pull" of a null result, expressing the reliability of an experimental upper limit, and the "upper and lower detection functions", that give information on the possible outcome of an experiment if there is a signal. We also give a new appropriate definition of "sensitivity", that quantifies the capability of an experiment to reveal the signal that is searched for at the given confidence level.Comment: 16 page

The Power of Confidence Intervals

We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter bounded to be non-negative. We show that the confidence intervals (upper limits) obtained with a (biased) method that near the boundary has large power in testing the parameter against larger alternatives and small power in testing the parameter against smaller alternatives are physically more significant. Considering the recently proposed methods with correct coverage, we show that the physical significance of upper limits is smallest in the Unified Approach and highest in the Maximum Likelihood Estimator method. We illustrate our arguments in the specific cases of a bounded Gaussian distribution and a Poisson distribution with known background.Comment: 13 pages, 5 figure

Light Sterile Neutrinos in Cosmology and Short-Baseline Oscillation Experiments

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.Comment: 12 pages; final version published in JHEP 1311 (2013) 21

Short-Baseline Electron Neutrino Disappearance, Tritium Beta Decay and Neutrinoless Double-Beta Decay

We consider the interpretation of the MiniBooNE low-energy anomaly and the Gallium radioactive source experiments anomaly in terms of short-baseline electron neutrino disappearance in the framework of 3+1 four-neutrino mixing schemes. The separate fits of MiniBooNE and Gallium data are highly compatible, with close best-fit values of the effective oscillation parameters Delta m^2 and sin^2 2 theta. The combined fit gives Delta m^2 >~ 0.1 eV^2 and 0.11 < sin^2 2 theta < 0.48 at 2 sigma. We consider also the data of the Bugey and Chooz reactor antineutrino oscillation experiments and the limits on the effective electron antineutrino mass in beta-decay obtained in the Mainz and Troitsk Tritium experiments. The fit of the data of these experiments limits the value of sin^2 2 theta below 0.10 at 2 sigma. Considering the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data as a statistical fluctuation, we perform a combined fit which gives Delta m^2 \simeq 2 eV and 0.01 < sin^2 2 theta < 0.13 at 2 sigma. Assuming a hierarchy of masses m_1, m_2, m_3 << m_4, the predicted contributions of m_4 to the effective neutrino masses in beta-decay and neutrinoless double-beta-decay are, respectively, between about 0.06 and 0.49 and between about 0.003 and 0.07 eV at 2 sigma. We also consider the possibility of reconciling the tension between the neutrino MiniBooNE and Gallium data and the antineutrino reactor and Tritium data with different mixings in the neutrino and antineutrino sectors. We find a 2.6 sigma indication of a mixing angle asymmetry.Comment: 14 pages; final version published in Phys.Rev.D82:053005,201

Light Sterile Neutrinos and Inflationary Freedom

We perform a cosmological analysis in which we allow the primordial power spectrum of scalar perturbations to assume a shape that is different from the usual power-law predicted by the simplest models of cosmological inflation. We parameterize the free primordial power spectrum with a "piecewise cubic Hermite interpolating polynomial" (PCHIP). We consider a 3+1 neutrino mixing model with a sterile neutrino having a mass at the eV scale, which can explain the anomalies observed in short-baseline neutrino oscillation experiments. We find that the freedom of the primordial power spectrum allows to reconcile the cosmological data with a fully thermalized sterile neutrino in the early Universe. Moreover, the cosmological analysis gives us some information on the shape of the primordial power spectrum, which presents a feature around the wavenumber $k=0.002\,\text{Mpc}^{-1}$.Comment: 19 pages; corrected Fig.4 and added Ref.[35

The flavor of neutrinos in muon decays at a neutrino factory and the LSND puzzle

The accurate prediction of the neutrino beam produced in muon decays and the absence of opposite helicity contamination for a particular neutrino flavor make a future neutrino factory the ideal place to look for the lepton flavor violating (LFV) decays of the kind \mu^+\ra e^+\nuebar\numu and lepton number violating (LNV) processes like \mu^-\ra e^-\nue\numu. Excellent sensitivities can be achieved using a detector capable of muon and/or electron identification with charge discrimination. This would allow to set experimental limits that improve current ones by more than two orders of magnitude and test the hypothesis that the LSND excess is due to such anomalous decays, rather than neutrino flavor oscillations in vacuum.Comment: 19 pages, 4 figure

Updated Global 3+1 Analysis of Short-BaseLine Neutrino Oscillations

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 $\nu_e$ and $\bar\nu_e$ disappearance in the light of the Gallium and reactor anomalies. We discuss the implications of the recent measurement of the reactor $\bar\nu_e$ spectrum in the NEOS experiment, which shifts the allowed regions of the parameter space towards smaller values of $|U_{e4}|^2$. The beta-decay constraints allow us to limit the oscillation length between about 2 cm and 7 m at $3\sigma$ for neutrinos with an energy of 1 MeV. We then consider the global fit of the data in the light of the LSND anomaly, taking into account the constraints from $\nu_e$ and $\nu_\mu$ disappearance experiments, including the recent data of the MINOS and IceCube experiments. The combination of the NEOS constraints on $|U_{e4}|^2$ and the MINOS and IceCube constraints on $|U_{\mu4}|^2$ 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 $\chi^2$ in the space of the four mixing parameters $\Delta{m}^2_{41}$, $|U_{e4}|^2$, $|U_{\mu4}|^2$, and $|U_{\tau4}|^2$ leads to three allowed regions with narrow $\Delta{m}^{2}_{41}$ widths at $\Delta m^2_{41} \approx 1.7$ (best-fit), 1.3 (at $2\sigma$), 2.4 (at $3\sigma$) eV$^2$. 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.Comment: 39 pages; improved treatment of the reactor flux uncertainties and other minor correction