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 (v(1), v(2)) "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 U-e4-encoding the admixture of the electron neutrino with a new mass eigenstate-which is comparable to that achieved on the standard matrix element U-e3. In addition, and more importantly, our analysis evidences that, in a 4-flavor framework, the current preference for |U-e3| not equal 0 is indistinguishable from that for |Ue4| not equal 0, having both a similar statistical significance (which is similar to 1.3 sigma adopting the old reactor fluxes determinations, and similar to 1.8 sigma 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.