Alexei Smirnov: Mass Hierarchy and Matter Effects
Mixing and mass splitting parameters that are responsible of neutrino oscillations depend on the density of matter and energy and these depend on the mass hierarchy. THe mass states of neutrinos can be marked by the amount of electron flavour, so that there is no ambiguity of which is the state 1,2,3. For non-zero delta_CP the antineutrino spectrum is different (distribution of nu_mu and nu_tau flavour in nu_1 and nu_2).
Flavour in matter is determined by the eigenstates of neutrinos in matter. In matter the hamiltonian needs to include a potential, so the mixing in vacuum and the mixing in matter have different eigenstates. The potential depends on the medium density, and so the mixing also depends on this and on the energy.
As density increases, the spectrum is modified. If one hypothesizes a normal hierarchy, there are resonances between the nu_1 and nu_2 as one increases density, and then a nu_2-nu_3 resonance. With an inverted hierarchy things change.
One can take a two-neutrino system to clarify the situation. In matter, when we move from nu’s to anti-nu’s, the potential changes sign. What happens is that delta m^2 also changes sign. But under a simultaneous change of the potential and dm^2 signs, the mixing does not change, and the moduli of the oscillation phase also do not change. This means that going from a normal to a inverted hierarchy and from neutrinos to antineutrinos there is this invariance. Hierarchy asymmetries for neutrinos and antineutrinos have opposite signs.
So if you do not distinguish neutrinos from antineutrinos, you have a cancellation of asymmetries which makes you blind from the relevant effects.
The 1-2 mixing is already determined from solar neutrino data. One has different suppressions at low and high energy due to matter effects. One can try to use solar neutrinos to have hints about the 1-3 hierarchy, but the modifications are small for the 1-3 ordering: the matter effect is small on 1-3 mixing.
Using matter effects on 1-3 mixing we can determine the mass hierarchy using the atmospheric neutrinos, long-baseline, and SN neutrinos. For the latter, matter effects actually dominate. These neutrinos, produced in the center of the dying star, undergo MSW conversion inside the star, and this can be affected by the shock wave that propagates outward. Then one has propagation in vacuum and oscillations inside the earth. For the shock wave effect, this is mostly for a normal hierarchy. Neutrino collecive effects are more prominent in the inverted hierarchy case instead. A time rise of the anti-nu burst in the initial phase can point to a inverted hierarchy, while a strong suppression of the peak of nu_e points to normal hierarchy.
One can derive probabilities for the normal and inverted hierarchy of neutrinos and antineutrino oscillations, for different zenith angles of arrival of neutrinos from SN sources. These differences are not huge, but the speaker did not seem to convey the significance of the graphs showed. Or maybe I was distracted…
One can investigate the situation with muon neutrino events. One measures the energy of the muon in a CC event, the angle of the muon, and the hadronic recoil energy, determining the energy and angle of the neutrino. The estimated sensitivity depends on angular and energy resolution, but depends on the asymmetry and on the square number of the number of events. There can be a 3-sigma identification of the mass hierarchy, but this depends on the particular points of parameter space; in some points there is a cancellation that makes the determinations insensitive to the hierarchy.
One can try to improve the sensitivity to the mass hierarchy. The challenges are flavor identification, the smearing over energy and direction, the degeneracy of parameter and uncertainties in the parameters. Crucially one needs to distinguish neutrinos and antineutrinos. One can improve the sensitivity by measuring the inelasticity, y, and its 3-Dimensional distribution; one can also use cascades of electron neutrinos. Inelasticity is the energy transferred into hadrons. For each bin the y distribution can allow the extractions of fractions of neutrinos and antineutrinos. One therefore needs to reconstruct oscillograms as a function of y.
He showed studies of experimental smearing, considering the hierarchy-asymmetry for different inelasticity values, showing how the picture varies as one worsens the experimental precision. At the end of the day, the significances do not exceed two standard deviations.
In summary, matter effects change the mixing and mass splitting in a way which depends on the mass hierarchy. So the oscillation pattern also depends on it. In a multilayer medium resonance enhancement of oscillation can occur. Multi-megaton scale under ice (or water) detecting atmospheric neutrinos with low energy threshold may establish the mass hierarchy with high confidence level in few years. There are many challenges: the identification of the events, and the accuracy of energy and direction of the neutrino. There are various ways to improve the sensitivity, in particular by measuring the inelasticity.