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.