arXiv1995
In the light of the $ν_μ\toν_e$ neutrino oscillations which may have been observed at the LSND experiment we explore the consequences of two inverted mass schemes where solar neutrino oscillations occur between $ν_e$ and $ν_τ$. The favored LSND value $Δm^2=6\,\eV^2$ leads to $m_{ν_e}\approx m_{ν_τ}\approx 2.5\,\eV$ and $m_{ν_μ}\approx0$ so that cosmology can benefit from a recently proposed ``cold plus hot dark matter'' structure formation scenario with two equal mass light neutrinos (C$ν^2$DM). Solar neutrino oscillations ($ν_e\toν_τ$) can occur with one of the large mixing angle solutions so that a serious conflict with $ββ$ decay Majorana mass limits is avoided without invoking Dirac masses. However, there is a problem with the SN~1987A signal because of resonant $\antiν_e\leftrightarrow\antiν_μ$ oscillations which are expected to cause far higher $\antiν_e$ energies at the IMB and Kamiokande~II detectors than have been observed. A small value $Δm^2=0.5\,\eV^2$ at LSND, which allows for a relatively large $ν_e$-$ν_μ$ mixing angle without conflicting with the KARMEN and BNL-E776 experiments, would indicate $m_{ν_e}\approx m_{ν_τ}\approx 1.62\,\eV$ and $m_{ν_μ}\approx1.77\,\eV$. This scheme of C$ν^3$DM maintains, and even may improve, the essential cosmological model implications for large-scale structure, leaving no conflict with SN r-process nucleosynthesis. It may improve the discordance between the SN~1987A neutrino spectra inferred from Kamiokande~II and IMB.