Spread Complexity of High Energy Neutrino Propagation over Astrophysical Distances

TL;DR

This paper introduces a novel complexity-based measure for high-energy astrophysical neutrino flavor ratios, which could improve flavor discrimination and show sensitivity to neutrino mass ordering.

Contribution

It proposes a new flavor ratio based on spread complexity and explores its potential advantages over traditional ratios in neutrino astrophysics.

Findings

Complexity-based flavor ratios may favor an initial flux ratio of 1:0:0.

The new measure could distinguish neutrino flavors with higher sensitivity.

Complexity ratios show slight sensitivity to neutrino mass ordering.

Abstract

Spread complexity measures the minimized spread of quantum states over all choices of basis. It generalizes Krylov operator complexity to quantum states under continuous Hamiltonian evolution. In this paper, we study spread complexity in the context of high-energy astrophysical neutrinos and propose a new flavor ratio based on complexity. Our findings indicate that our proposal might favor an initial ratio of fluxes as $\phi_{\nu_e}^0: \phi_{\nu_\mu}^0: \phi_{\nu_\tau}^0 = 1:0:0$ over a more generally expected ratio of $1:2:0$, when the IceCube neutrino observatory achieves its projected sensitivity to discriminate between flavors. Additionally, complexity-based definitions of flavor ratios exhibit a slight but nonzero sensitivity to the neutrino mass ordering, which traditional flavor ratios cannot capture.