Neutrino Decay and Atmospheric Neutrinos

We reconsider neutrino decay as an explanation for atmospheric neutrino observations. We show that if the mass-difference relevant to the two mixed states νμ and ντ is very small (< 10 −4 eV), then a very good fit to the observations can be obtained with decay of a component of νμ to a sterile neutrino and a Majoron. We discuss how the K2K and MINOS long-baseline experiments can distinguish the decay and oscillation scenarios. Recently a neutrino decay explanation for the atmospheric neutrino observations of Super-Kamiokande was proposed [1]. To recapitulate briefly, in presence of a decaying neutrino state, the survival probability of νμ is given by P (νμ → νμ) = sin 4 θ + cos θe + 2 sin θ cos θe cos ( δm 23 L 2E ) (1) where we have considered only two state mixing for simplicity: δm 23 = m 2 −m 3 , α = m2/τ2 and νμ = cos θν2 + sin θν3. If the decay of ν2 is ν2 → ν̄3 + J , where J is a massless scalar, then the δm in the decay is the same as in Eq. (1) and it can be shown that this δm has to be larger than 0.73 eV to satisfy constraints from K → μ+neutrals decay [2]. Then the oscillating term in Eq. (1) averages to zero and P (νμ → νμ) simplifies to P (νμ → νμ) = sin 4 θ + cos θe (2) This decay scenario was analyzed in Ref. [1] and fit to the L/Eν dependence and the asymmetry of the contained events in Super-Kamiokande [3]. A satisfactory fit with cos θ ∼ 0.87 and α ∼ 1 GeV/DE (where DE is the diameter of the earth) was found. However, it has since been shown that the fit to the higher energy events in Super-K (especially the upcoming muons) is quite poor [4], [5]. Another possibility, mentioned in Ref. [1], is that the decay of ν2 is into a state with which it does not mix. For example, the three weak coupling states νμ, ντ , νs (where νs is a sterile neutrino) may be related to the mass eigenstates ν2, ν3, ν4 by the approximate mixing