$\Delta m^2$ Limits from $R(E_{\nu })$

Abstract

A lower bound on $\Delta m^2$ for atmospheric neutrino oscillations can be obtained from the global value of $R$ at a given energy. This bound may be more reliable than one based on the observed isotropy. Some global values of $R$ imply an anisotropy in the neutrino flux that may, or may not be manifest in the observed neutrino interactions. A limit of $\Delta m^2>0.0077$ eV${}^2$ is easily obtained. Much higher mass scales are implied by the reported energy independence and magnitude of $R$

Comments: 5 pages, 2 figures. The revisions include a full fit to R(E) and a discussion of geomagnetic effects