(3+1)-spectrum of neutrino masses: A chance for LSND?
O. L. G. Peres, A. Yu. Smirnov
TL;DR
The paper analyzes whether LSND can be reconciled with solar and atmospheric neutrino data within four-neutrino scenarios, focusing on (2+2) versus (3+1) schemes and introducing η_s^{sun} and η_s^{atm} to quantify sterile participation. It shows that a (2+2) interpretation would impose η_s^{sun}+η_s^{atm}=1, a relation that can be tested with solar and atmospheric data, while the (3+1) scheme isolates a LSND-scale sterile state, allowing flexible sterile involvement and potential compatibility with existing disappearance bounds. The LSND signal in a (3+1) framework yields sin^2 2θ_{eμ}=4 U_{e4}^2 U_{μ4}^2, and a probabilistic treatment indicates some LSND parameter space remains allowed at 95–99% CL for Δm^2_{LSND}≈(0.4–2) eV^2, though tighter future bounds could challenge this. The work further discusses experimental prospects (Mini-BooNE, KEK front detectors, near-reactor experiments) and broad phenomenological implications for neutrinoless double beta decay, atmospheric and SN neutrinos, and nucleosynthesis, outlining concrete tests to discriminate between schemes and reveal or constrain sterile neutrinos.
Abstract
If active to active neutrino transitions are dominant modes of the atmospheric ($ν_μ \to ν_τ$) and the solar neutrino oscillations ($ν_{e}\to ν_μ/ν_τ$), as is indicated by recent data, the favoured scheme which accommodates the LSND result - the so called (2+2)-scheme - should be discarded. We introduce the parameters $η_s^{atm}$ and $η_s^{sun}$ which quantify an involvement of the sterile component in the solar and atmospheric neutrino oscillations. The (2+2)-scheme predicts $η_s^{atm} + η_s^{sun} = 1$ and the experimental proof of deviation from this equality will discriminate the scheme. In this connection the (3+1)-scheme is revisited in which the fourth (predominantly sterile) neutrino is isolated from a block of three flavour neutrinos by the mass gap $Δm^2_{LSND} \sim (0.4-10)$ eV$^2$. We find that in the (3+1)-scheme the LSND result can be reconciled with existing bounds on $ν_e$- and $ν_μ$ - disappearance at 95-99 % C.L.. The generic prediction of the scheme is the $ν_e$- and $ν_μ$ - disappearance probabilities at the level of present experimental bounds. The possibility to strengthen the bound on $ν_μ$- disappearance in the KEK - front detector experiment is studied. We consider phenomenology of the (3 + 1)-scheme, in particular, its implications for the atmospheric neutrinos, neutrinoless double beta decay searches, supernova neutrinos and primordial nucleosynthesis.