Can a mass inversion save solar neutrino oscillations from the Los Alamos neutrino?

Abstract

In the light of the ${\nu }_{\mu }\to {\nu }_e$ 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 ${\nu }_e$ and ${\nu }_{\tau }$. The favored LSND value $\Delta m^2=6{\text{eV}}^2$ leads to $m_{{\nu }_e}\approx m_{{\nu }_{\tau }}\approx 2.5\text{eV}$ and $m_{{\nu }_{\mu }}\approx 0$ so that cosmology can benefit from a recently proposed ``cold plus hot dark matter'' structure formation scenario with two equal mass light neutrinos (C${\nu }^2$DM). Solar neutrino oscillations (${\nu }_e\to {\nu }_{\tau }$) can occur with one of the large mixing angle solutions so that a serious conflict with $\beta \beta$ decay Majorana mass limits is avoided without invoking Dirac masses. However, there is a problem with the SN~1987A signal because of resonant $\text{anti}{\nu }_e\leftrightarrow \text{anti}{\nu }_{\mu }$ oscillations which are expected to cause far higher $\text{anti}{\nu }_e$ energies at the IMB and Kamiokande~II detectors than have been observed. A small value $\Delta m^2=0.5{\text{eV}}^2$ at LSND, which allows for a relatively large ${\nu }_e$-${\nu }_{\mu }$ mixing angle without conflicting with the KARMEN and BNL-E776 experiments, would indicate $m_{{\nu }_e}\approx m_{{\nu }_{\tau }}\approx 1.62\text{eV}$ and $m_{{\nu }_{\mu }}\approx 1.77\text{eV}$. This scheme of C${\nu }^3$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.

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