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Register a new userThe impact of hierarchy upon the values of neutrino mixing parameters
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A neutrino-oscillation analysis is performed of the more finely binned Super-K atmospheric, MINOS, and CHOOZ data in order to examine the impact of neutrino hierarchy in this data set upon the value of $theta_{13}$ and the deviation of $theta_{23}$ from maximal mixing. Exact oscillation probabilities are used, thus incorporating all powers of $theta_{13}$ and $epsilon :=theta_{23}-pi/4$. The extracted oscillation parameters are found to be dependent on the hierarchy, particularly for $theta_{13}$. We find at 90% CL are $Delta_{32} = 2.44^{+0.26}_{-0.20}$ and $2.48^{+0.25}_{-0.22}times 10^{-3} {rm eV}^2$, $epsilon=theta_{23}-pi/4=0.06^{+0.06}_{-0.16}$ and $0.06^{+0.08}_{-0.17}$, and $theta_{13}=-0.07^{+0.18}_{-0.11}$ and $-0.13^{+0.23}_{-0.16}$, for the normal and inverted hierarchy respectively. The inverted hierarchy is preferred at a statistically insignificant level of 0.3 $sigma$.
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One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best fit values of these constants but also their errors. Some of the neutrino oscillation data is statistically poor and cannot be treated by normal (Gaussian) statistics. To extract confidence intervals when the statistics are not normal, one should not utilize the value for chisquare versus confidence level taken from normal statistics. Instead, we propose that one should use the normalized likelihood function as a probability distribution; the relationship between the correct chisquare and a given confidence level can be computed by integrating over the likelihood function. This allows for a definition of confidence level independent of the functional form of the !2 function; it is particularly useful for cases in which the minimum of the !2 function is near a boundary. We present two pedagogic examples and find that the proposed method yields confidence intervals that can differ significantly from those obtained by using the value of chisquare from normal statistics. For example, we find that for the first data release of the T2K experiment the probability that chisquare is not zero, as defined by the maximum confidence level at which the value of zero is not allowed, is 92%. Using the value of chisquare at zero and assigning a confidence level from normal statistics, a common practice, gives the over estimation of 99.5%.
The Daya Bay, RENO, and Double Chooz experiments have discovered a large non-zero value for $theta_{13}$. We present a global analysis that includes these three experiments, Chooz, the Super-K atmospheric data, and the $ u_mu rightarrow u_e$ T2K and MINOS experiments that are sensitive to the hierarchy and the sign of $theta_{13}$. We report preliminary results in which we fix the mixing parameters other than $theta_{13}$ to those from a recent global analysis. Given there is no evidence for a non-zero CP violation, we assume $delta=0$. T2K and MINOS lie in a region of $L/E$ where there is a hierarchy degeneracy in the limit of $theta_{13}rightarrow 0$ and no matter interaction. For non-zero $theta_{13}$, the symmetry is partially broken, but a degeneracy under the simultaneous exchange of both hierarchy and the sign of $theta_{13}$ remains. Matter effects break this symmetry such that the positions of the peaks in the oscillation probabilities maintain the two-fold symmetry, while the magnitude of the oscillations is sensitive to the hierarchy. This renders T2K and NO$ u$A, with different baselines and different matter effects, better able in combination to distinguish the hierarchy and the sign of $theta_{13}$. The large value of $theta_{13}$ yields effects from atmospheric data that distinguish hierarchies. We find for normal hierarchy, positive $theta_{13}$, $sin^22theta_{13}=0.090pm0.020$ and is 0.2% probable it is the correct combination; for normal hierarchy, negative $theta_{13}$, $sin^22theta_{13}=0.108pm0.023$ and is 2.2% probable; for inverse hierarchy, positive $theta_{13}$, $sin^22theta_{13}=0.110pm0.022$ and is 7.1% probable; for inverse hierarchy, negative $theta_{13}$, $sin^22theta_{13}=0.113pm0.022$ and is 90.5% probable, results that are inconsistent with two similar analyses.
We use a Bayesian inference analysis to explore the sensitivity of Taylor expansion parameters of the nuclear equation of state (EOS) to the neutron star dimensionless tidal deformability ($Lambda$) on 1 to 2 solar masses neutron stars. A global power law dependence between tidal deformability and compactness parameter (M/R) is verified over this mass region. To avoid superfluous correlations between the expansion parameters, we use a correlation-free EOS model based on a recently published meta-modeling approach. We find that assumptions in the prior distribution strongly influence the constraints on $Lambda$. The $Lambda$ constraints obtained from the neutron star merger event GW170817 prefer low values of $L_text{sym}$ and $K_text{sym}$, for a canonical neutron star with 1.4 solar mass. For neutron star with mass $<1.6$ solar mass, $L_text{sym}$ and $K_text{sym}$ are highly correlated with the tidal deformability. For more massive neutron stars, the tidal deformability is more strongly correlated with higher order Taylor expansion parameters.
We introduce a hybrid method to determine the neutrino mass hierarchy by simultaneous measurements of responses of at least two detectors to antineutrino and neutrino fluxes from accretion and cooling phases of core-collapse supernovae. The (anti)neutrino-nucleus cross sections for $^{56}$Fe and $^{208}$Pb are calculated in the framework of the relativistic nuclear energy density functional and weak interaction Hamiltonian, while the cross sections for inelastic scattering on free protons $mathrm{p}(bar{ u}_mathrm{e},mathrm{e}^{+})mathrm{n}$ are obtained using heavy-baryon chiral perturbation theory. The modelling of (anti)neutrino fluxes emitted from a protoneutron star in a core-collapse supernova include collective and Mikheyev-Smirnov-Wolfenstein effects inside the exploding star. The particle emission rates from the elementary decay modes of the daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material allows to determine the neutrino mass hierarchy from the ratios of $ u_mathrm{e}$- and $bar{ u}_mathrm{e}$-induced particle emissions. This hybrid method favors neutrinos from the supernova cooling phase and the implementation of detectors with heavier target nuclei ($^{208}$Pb) for the neutrino sector, while for antineutrinos the use of free protons in mineral oil or water is the appropriate choice.
We suggest that superscaling in electroweak interactions with nuclei, namely the observation that the reduced electron-nucleus cross sections are to a large degree independent of the momentum transfer and of the nuclear species, can be used as a tool to obtain precise predictions for neutrino-nucleus cross sections in both charged and neutral current-induced processes.
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