SUSY radiative corrections on mu-tau neutrino refraction including possible R-parity breaking interactions

23 pages, 15 figures; v2: typos and 5 figures correctedInternational audienceIn this paper we investigate the one-loop radiative corrections to the neutrino indices of refraction from supersymmetric models. We consider the Next-to Minimal Supersymmetric extension of the Standard Model (NMSSM) which happens to be a better supersymmetric candidate than the MSSM for both theoretical and experimental reasons. We scan the relevant SUSY parameters and identify regions in the parameter space which yield interesting values for V_{mu tau}. If R-parity is broken there are significant differences between MSSM and NMSSM contributions contrary to the R-parity conserved case. Finally, for a non-zero CP-violating phase, we show analytically that the presence of V_{mu tau} will explicitly imply CP-violation effects on the supernova electron (anti-) neutrino fluxes