Best-case scenarios for neutrino capture experiments

TL;DR

This paper explores the plausibility of detecting the cosmic neutrino background through capture experiments, analyzing potential local neutrino overdensities and their impact on experimental signatures, with implications for future detection strategies.

Contribution

It provides a model-independent analysis of maximum achievable local neutrino overdensities and their effects on detection signatures, considering both cosmic and local sources.

Findings

Cosmic origin of overdensity η > 10^4 is unlikely without new physics.

Local sources could produce η up to 10^11, affecting detection signatures.

Detection sensitivity of η ~ 10^4 requires 10 meV energy resolution.

Abstract

A direct discovery of the cosmic neutrino background would bring to a closure the searches for relic left-over radiation predicted by the Hot Big Bang cosmology. Recently, the KATRIN experiment put a limit on the local relic neutrino overdensity with respect to the cosmological predicted average value at $\eta \lesssim 10^{11}$ [Phys. Rev. Lett. 129, 011806 (2022)]. In this work, we first examine to what extent such values of $\eta$ are conceivable. We show that even under cavalier assumptions, a cosmic origin of $\eta \gtrsim 10^4$ seems out of reach (with the caveat of forming bound objects under a new force,) but find that a hypothetical local source of low-energy neutrinos could achieve $\eta \sim 10^{11}$. Second, when such values are considered, we point out that the experimental signature in KATRIN and other neutrino-capture experiments changes, contrary to what has hitherto been assumed. Our results are model-independent and maximally accommodating as they only assume the Pauli exclusion principle. As intermittent physics target in the quest for C$\nu$B detection, we identify an experimental sensitivity to $\eta \sim 10^4$ for which conceivable sources exist; to resolve the effect of a degenerate Fermi gas for such overdensity an energy resolution of 10 meV is required.