Neutrino Oscillation - Observed Values of Oscillation Parameters

Observed Values of Oscillation Parameters

• sin2(2θ₁₃) = 0.092±0.017
• tan2(θ₁₂) = 0.457+0.040
  −0.029. This corresponds to θ₁₂ ≡ θ_sol = 34.06+1.16
  −0.84° ("sol" stands for solar)
• sin2(2θ₂₃) > 0.92 at 90% confidence level, corresponding to θ₂₃ ≡ θ_atm = 45±7.1° ("atm" stands for atmospheric)
• Δm2
  21 ≡ Δm2
  sol = 7.59+0.20
  −0.21×10−5 eV2
• |Δm2
  31| ≈ |Δm2
  32| ≡ Δm2
  atm = 2.43+0.13
  −0.13×10−3 eV2

• δ, α₁, α₂, and the sign of Δm2
  32 are currently unknown

Solar neutrino experiments combined with KamLAND have measured the so-called solar parameters Δm2
sol and sin2θ_sol. Atmospheric neutrino experiments such as Super-Kamiokande together with the K2K and MINOS long baseline accelerator neutrino experiment have determined the so-called atmospheric parameters Δm2
atm and sin2θ_atm. The last mixing angle, θ₁₃, has been measured by the Daya Bay Experiment as sin22θ₁₃.

For atmospheric neutrinos (where the relevant difference of masses is about Δm2 = 2.4×10−3 eV2 and the typical energies are ~1 GeV), oscillations become visible for neutrinos traveling several hundred km, which means neutrinos that reach the detector from below the horizon.

The mixing parameter sin22θ₁₃ is measured using electron anti-neutrinos from nuclear reactors. The rate of anti-neutrino interactions is measured in detectors sited near the reactors to determine the flux prior to any significant oscillations and then it is measured in far detectors (sited about 2 km from the reactors). The oscillation is observed as an apparent disappearance of electron anti-neutrinos in the far detectors (i.e. the interaction rate at the far site is lower than predicted from the observed rate at the near site).

From atmospheric and solar neutrino oscillation experiments, it is known that two mixing angles of the MNS matrix are large and the third is smaller. This is in sharp contrast to the CKM matrix in which all three angles are small and hierarchically decreasing. Nothing is known about the CP-violating phase of the MNS matrix.

If the neutrino mass proves to be of Majorana type (making the neutrino its own antiparticle), it is possible that the MNS matrix has more than one phase.

Since experiments observing neutrino oscillation measure the squared mass difference and not absolute mass, one can claim that the lightest neutrino mass is exactly zero, without contradicting observations. This is however regarded as unlikely by theorists.