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

In this paper, we study the implications of the Dark Large Mixing Angle (DLMA) solutions of (Formula presented.) in the context of the IceCube data. We study the consequences in the measurement of the neutrino oscillation parameters, namely the octant of (Formula presented.) and (Formula presented.) in light of both Large Mixing Angle (LMA) and DLMA solutions of (Formula presented.). We find that it will be impossible for IceCube to determine the (Formula presented.) and the true nature of (Formula presented.), 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 (Formula presented.) and two solutions of (Formula presented.) for a fixed value of (Formula presented.). We perform a chi-square fit using three different astrophysical sources, i.e., (Formula presented.) source, (Formula presented.) source, and n source, to find that both (Formula presented.) source and (Formula presented.) source are allowed within (Formula presented.), whereas the n source is excluded at (Formula presented.). It is difficult to make any conclusion regarding the measurement of (Formula presented.), (Formula presented.) for (Formula presented.) source. However, the (Formula presented.) (n) source prefers the higher (lower) octant of (Formula presented.) for both LMA and DLMA solution of (Formula presented.). The best-fit value of (Formula presented.) is around (Formula presented.) ((Formula presented.)) for the LMA (DLMA) solution of (Formula presented.), whereas for the DLMA (LMA) solution of (Formula presented.), the best-fit value is around (Formula presented.) ((Formula presented.)) for the (Formula presented.) (n) source. If we assume the current best-fit values of (Formula presented.) and (Formula presented.) to be true, then the (Formula presented.) and (Formula presented.) sources prefer the LMA solution of (Formula presented.), whereas the n source prefers the DLMA solution of (Formula presented.).