Heisenberg's uncertainty principle in the PTOLEMY project: a theory update

TL;DR

This paper examines how quantum uncertainty affects the electron energy spectrum in the PTOLEMY experiment, providing detailed calculations and proposing methods to mitigate these effects to improve neutrino detection accuracy.

Contribution

It offers a quantitative analysis of quantum uncertainty impacts on electron spectra in the PTOLEMY project and suggests strategies to reduce these effects.

Findings

Quantitative assessment of quantum uncertainty on electron spectra.

Calculations of tritium-graphene potentials for various configurations.

Proposed mitigation strategies for quantum uncertainty effects.

Abstract

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $\beta$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised in [Cheipesh et al., Phys. Rev. D 104, 116004 (2021)], and discuss the relevant time scales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty.