The effect of Coulomb interactions on relic neutrino detection via beta decaying impurities in (semi)metals

TL;DR

This paper tackles the challenge of relic neutrino detection via β-decay impurities in (semi)metals by analyzing how Coulomb interactions with the solid-state environment affect energy resolution. It first uses a classical image-charge approach with a dielectric spacer to map stability regions for integer impurity charges, identifying conditions under which a stable mother/daughter configuration could exist. It then treats the nonzero emitter–environment coupling with a quantum architecture: a disk Anderson impurity embedded in a 2D Weyl fermion bath, bosonized into a Tomonaga–Luttinger liquid, and analyzed to leading order in the hybridization; this yields an X-ray edge singularity in the spectral function, potentially preserving the relic neutrino signal. The results imply that while a dielectric spacer can harm signal visibility, a controlled nonzero hybridization—possibly aided by high-dielectric substrates—could sustain the needed spectral features, guiding experimental design for PTOLEMY-like experiments and highlighting further quantum effects (phonons, Friedel oscillations, disorder) to be explored.

Abstract

Measuring the electron neutrino mass is a long-standing objective and requires a high energy resolution of certain $β$-decay experiments, as well as a visible cosmic neutrino background ($CνB$) spectrum. Many quantum mechanical and chemical effects could potentially impair the required resolution/visibility, e.g., the Coulomb interactions between the electrons in the \b{eta}-decaying impurity and in the solid-state environment. We analyze the effect when hybridization is suppressed completely using a dielectric spacer, and also when hybridization is present up to the lowest nontrivial order in perturbation theory.

Figures (4)

• Figure 1: The spontaneous $\beta$-decay has a continuous spectrum, for the electron's energy is measured and the energy in channel \ref{['First reaction']} can be distributed among the kinetic energy of the electron and the kinetic energy of the electron antineutrino. In channel \ref{['Second reaction']}, however, the $C\space\nu B$ is captured and all energy is transformed into the motion of the electron, making the spectrum peaked around the neutrino masses. To make this plot, we have assumed that $m_{\nu_{e}} = 0.05$$eV$.
• Figure 2: a)There are real charges $-e$ and $q$ on the left side of the graphene layer.The corresponding image charges are on the right side of the graphenelayer. Also the substrate has a mirror image on the right side, whicheffectively makes it twice as thick.b)The charge $-e$ feels the electric field from the other three charges in Fig.\ref{['fig: image charges']}a. Equivalently, we remove these three charges and the substrate, andwe replace them with an infinite number of image charges that generatethe same field InfiniteImageCharges. The charge values are found in the legend, bottomleft of the figure.
• Figure 3: The purple region indicates a stable configuration for both $Tm^{-}$ and $Yb$.
• Figure 4: The green dots form a two-dimensional slice of the stability region for constant thickness $h$.