Neutrino flavor ratios as diagnostic of solar WIMP annihilation

We consider the neutrino (and antineutrino) flavors arriving at the Earth for neutrinos produced in the annihilation of weakly interacting massive particles (WIMPs) in the sun’s core. Solar-matter effects on the flavor propagation of the resulting $\gtrsim \mathrm{GeV}$ neutrinos are studied analytically within a density-matrix formalism. Matter effects, including mass-state level crossings, influence the flavor fluxes considerably. The exposition herein is somewhat pedagogical, in that it starts with adiabatic evolution of single flavors from the sun’s center, with ${\theta }_{13}$ set to zero, and progresses to fully realistic processing of the flavor ratios expected in WIMP decay, from the sun’s core to the Earth. In the fully realistic calculation, nonadiabatic level crossing is included, as are possible nonzero values for ${\theta }_{13}$ and the CP-violating phase $\delta$. Because of resonance enhancement in matter, nonzero values of ${\theta }_{13}$ even smaller than a degree can noticeably affect flavor propagation. Both normal and inverted neutrino-mass hierarchies are considered. Our main conclusion is that measuring flavor ratios (in addition to energy spectra) of $\gtrsim \mathrm{GeV}$ solar neutrinos can provide discrimination between WIMP models. In particular, we demonstrate the flavor differences at the Earth for neutrinos from the two main classes of WIMP final states, namely $W^{+}{W}^{-}$ and $95\%b\overline{b}+5\%{\tau }^{+}{\tau }^{-}$. Conversely, if WIMP properties were to be learned from production in future accelerators, then the flavor ratios of $\gtrsim \mathrm{GeV}$ solar neutrinos might be useful for inferring ${\theta }_{13}$ and the mass hierarchy. From the full calculations, we find (and prove) some general features: a flavor-democratic flux produced at the sun’s core arrives at the Earth still flavor democratic; for maximal ${\theta }_{32}$ but arbitrary ${\theta }_{21}$ and ${\theta }_{13}$, the replacement $\delta \to \pi -\delta$ leaves the ${\nu }_e$ flavor spectra unaltered but interchanges ${\nu }_{\mu }$ and ${\nu }_{\tau }$ spectra at the Earth; and, only for neutrinos in the inverted hierarchy and antineutrinos in the normal hierarchy is the dependence on the mixing phase $\delta$ not suppressed to order $\delta m_{21}^2/\delta m_{32}^2$.