Parameter Degeneracy in Flavor-Dependent Reconstruction of Supernova Neutrino Fluxes

TL;DR

This paper investigates the challenges in reconstructing supernova neutrino fluxes, revealing a continuous degeneracy in parameters due to the inclusion of a width parameter, and discusses potential ways to resolve this issue.

Contribution

It introduces a novel method incorporating a width parameter in flux reconstruction and uncovers a fundamental degeneracy in the parameter space.

Findings

Identified a continuous degeneracy in flux parameter reconstruction.

Demonstrated that the degeneracy persists regardless of the chosen parametrization.

Discussed potential approaches to resolve the degeneracy.

Abstract

We reexamine the possibility of reconstructing the initial fluxes of supernova neutrinos emitted in a future core-collapse galactic supernova explosion and detected in a Megaton-sized water Cherenkov detector. A novel key element in our method is the inclusion, in addition to the total and the average energies of each neutrino species, of a "pinching" parameter characterizing the width of the distribution as a fit parameter. We uncover in this case a continuous degeneracy in the reconstructed parameters of supernova neutrino fluxes at the neutrinosphere. We analyze in detail the features of this degeneracy and show how it occurs irrespective of the parametrization used for the distribution function. Given that this degeneracy is real we briefly comment on possible steps towards resolving it, which necessarily requires going beyond the setting presented here.