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

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.

14 pages, 5 figures

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• A study of the relativistic corrections to polarized tritium $\beta$-decay
• Microscopic calculation of the ${\beta }^{-}$ decays of ${}^{151}$Sm, ${}^{171}$Tm, and ${}^{210}$Pb with implications to detection of the cosmic neutrino background
• The Universe at the MeV era: neutrino evolution and cosmological observables
• Individual Neutrino Masses From a Supernova
• Probing Cosmic Neutrino Background through Parametric Fluorescence
• Importance of the X-ray edge singularity for the detection of relic neutrinos in the PTOLEMY project
• Hydrogenated carbon structures as directional sub-GeV dark matter detectors
• Imprints of light dark matter on the evolution of cosmic neutrinos
• Cosmic neutrino background detection in the minimally extended Standard Model
• Numerical treatment of annual modulation of relic neutrinos
• Neutrino Oscillations in the Three Flavor Paradigm