Testing the very-short-baseline neutrino anomalies at the solar sector

Motivated by the accumulating hints of new sterile neutrino species at the eV scale, we explore the consequences of such an hypothesis on the solar sector phenomenology. After introducing the theoretical formalism needed to describe the Mikheyev-Smirnov-Wolfenstein conversion of solar neutrinos in the presence of one (or more) sterile neutrino state(s) located ``far'' from the (ν₁, ν₂) ``doublet'', we perform a quantitative analysis of the available experimental results, focusing on the electron neutrino mixing. We find that the present data posses a sensitivity to the amplitude of the lepton mixing matrix element Uₑ₄---encoding the admixture of the electron neutrino with a new mass eigenstate---which is comparable to that achieved on the standard matrix element Uₑ₃. In addition, and more importantly, our analysis evidences that, in a 4-flavor framework, the current preference for |Uₑ₃|≠0 is indistinguishable from that for |Uₑ₄|≠0, having both a similar statistical significance (which is ~1.3σ adopting the old reactor fluxes determinations, and ~1.8σ using their new estimates.) We also point out that, differently from the standard 3-flavor case, in a $3+1$ scheme the Dirac $CP$-violating phases cannot be eliminated from the description of solar neutrino conversions.