Theoretical Constraints on the Vacuum Oscillation Solution to the Solar Neutrino Problem

TL;DR

This paper investigates the stability of the vacuum oscillation solution to the solar neutrino problem under radiative corrections, highlighting that a hierarchical neutrino mass spectrum is most compatible with this solution.

Contribution

It provides a theoretical analysis of how radiative corrections affect neutrino mass splittings and mixing angles, identifying conditions under which the VO solution remains viable.

Findings

Hierarchical neutrino spectrum supports VO stability.

Radiative corrections induce large mass splittings in degenerate spectra.

Small-angle MSW scenario may be compatible with certain conditions.

Abstract

The vacuum oscillation (VO) solution to the solar anomaly requires an extremely small neutrino mass splitting, Delta m^2_{sol}\leq 10^{-10} eV^2. We study under which circumstances this small splitting (whatever its origin) is or is not spoiled by radiative corrections. The results depend dramatically on the type of neutrino spectrum. If m_1^2 \sim m_2^2 \geq m_3^2, radiative corrections always induce too large mass splittings. Moreover, if m_1 and m_2 have equal signs, the solar mixing angle is driven by the renormalization group evolution to very small values, incompatible with the VO scenario (however, the results could be consistent with the small-angle MSW scenario). If m_1 and m_2 have opposite signs, the results are analogous, except for some small (though interesting) windows in which the VO solution may be natural with moderate fine-tuning. Finally, for a hierarchical spectrum of neutrinos, m_1^2 << m_2^2 << m_3^2, radiative corrections are not dangerous, and therefore this scenario is the only plausible one for the VO solution.