Implications of the DLMA Solution of θ12 for IceCube Data Using Different Astrophysical Sources

Abstract

In this paper, we study the implications of the Dark Large Mixing Angle (DLMA) solutions of θ12 in the context of the IceCube data. We study the consequences in the measurement of the neutrino oscillation parameters, namely the octant of θ23 and δCP in light of both Large Mixing Angle (LMA) and DLMA solutions of θ12. We find that it will be impossible for IceCube to determine the δCP and the true nature of θ12, i.e., LMA or DLMA, at the same time. This is because of the existence of an intrinsic degeneracy at the Hamiltonian level between these parameters. Apart from that, we also identify a new degeneracy between θ23 and two solutions of θ12 for a fixed value of δCP. We perform a chi-square fit using three different astrophysical sources, i.e., μ source, π source, and n source, to find that both μ source and π source are allowed within 1σ, whereas the n source is excluded at 2σ. It is difficult to make any conclusion regarding the measurement of θ23, δCP for μ source. However, the π (n) source prefers the higher (lower) octant of θ23 for both LMA and DLMA solution of θ12. The best-fit value of δCP is around 180∘ (0∘/360∘) for the LMA (DLMA) solution of θ12, whereas for the DLMA (LMA) solution of θ12, the best-fit value is around 0∘/360∘ (180∘) for the π (n) source. If we assume the current best-fit values of θ23 and δCP to be true, then the μ and π sources prefer the LMA solution of θ12, whereas the n source prefers the DLMA solution of θ12.