Signatures of Quantum Gravity with Lorentz-violating Neutrinos from Extragalactic Sources

The nature and origin of high-energy particles, and more specifically astrophysical neutrinos observed by the IceCube Neutrino Observatory, provide exciting opportunities to probe our current understanding of particle physics. In particular, the observation of these neutrino emissions at high energy levels on the TeV scale points to the probability of these neutrinos originating from extragalactic sources. By studying potential extragalactic sources for these neutrino emissions--with our main focus being the nearby galaxy of NGC-1068--we study a scenario motivated by quantum gravity, where spontaneous Lorentz symmetry breaking is at place at low-energies leading to an effective field theory known as the Standard Model Extension (SME). We further present greater analysis on this by assessing the Lorentz-violating effects of these neutrino emissions in both the three-flavor and two-flavor approximations for neutrino states, and by detailing the interactions between the PMNS mass-mixing matrix in the standard νSM model and the Lorentz-violating Hamiltonian stemming from this theoretical model. We test the SME hypothesis for different effective operator dimensions by looking for a novel, resonant-like SME signature that has never been studied before. The existence of this signature makes astrophysical tests of SME possible where traditional oscillation techniques break down. We present IceCube's sensitivity to this new signature using neutrinos from NGC-1068.