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arxiv: 2512.01752 · v2 · submitted 2025-12-01 · ✦ hep-ph · cond-mat.mes-hall· cond-mat.other· cond-mat.str-el· physics.ins-det

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

Karel van der Marck , Vadim Cheianov This is my paper

Pith reviewed 2026-05-17 02:59 UTC · model grok-4.3

classification ✦ hep-ph cond-mat.mes-hallcond-mat.othercond-mat.str-elphysics.ins-det
keywords relic neutrinoscosmic neutrino backgroundbeta decayCoulomb interactionshybridizationdielectric spacerperturbation theoryenergy resolution
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The pith

Coulomb interactions between beta-decaying impurities and host electrons in (semi)metals can be isolated or calculated perturbatively to assess their impact on energy resolution for relic neutrino detection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines whether Coulomb interactions between electrons in a beta-decaying impurity and those in a surrounding (semi)metal could smear the electron energy spectrum enough to obscure the cosmic neutrino background signal and prevent a precise neutrino mass measurement. The authors focus on two controlled cases: complete suppression of hybridization between impurity and host states via a dielectric spacer, and inclusion of hybridization only through the lowest nontrivial term in perturbation theory. A sympathetic reader would care because any uncontrolled broadening from these interactions would wash out the tiny spectral distortions produced by relic neutrinos, rendering the entire detection scheme unworkable. If the interactions remain manageable under the stated conditions, the analysis supports continued development of solid-state impurity-based beta-decay experiments.

Core claim

We analyze the effect of Coulomb interactions on relic neutrino detection via beta decaying impurities in (semi)metals when hybridization is suppressed completely using a dielectric spacer, and also when hybridization is present up to the lowest nontrivial order in perturbation theory.

What carries the argument

Hybridization between the beta-decaying impurity and host electrons, either fully suppressed by a dielectric spacer or included at lowest nontrivial order in perturbation theory.

If this is right

  • When hybridization is suppressed by a dielectric spacer, Coulomb effects are confined to the impurity and can be evaluated separately from host material contributions.
  • Lowest-order perturbation theory supplies a concrete, calculable correction to the electron spectrum that can be compared against required energy resolution.
  • If the predicted corrections remain small, the cosmic neutrino background spectrum stays visible above the background of ordinary beta decays.
  • These controlled treatments allow quantitative checks on whether impurity-in-(semi)metal setups can still reach the resolution needed for neutrino mass extraction.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same spacer or perturbative approach could be tested against other solid-state broadening mechanisms such as phonons or lattice defects to see which effect sets the ultimate limit.
  • If lowest-order perturbation theory proves insufficient in real materials, experimenters would need to develop non-perturbative or numerical methods for the hybridization correction.
  • Successful control of Coulomb effects in this geometry would encourage similar impurity-based designs for precision measurements of other rare processes.

Load-bearing premise

The hybridization between impurity and host electrons can be either fully suppressed by a dielectric spacer or accurately captured by lowest-order perturbation theory without higher-order or non-perturbative effects dominating the energy resolution.

What would settle it

An experimental beta-decay electron spectrum measured with a dielectric spacer or under conditions where only lowest-order hybridization applies that shows resolution degradation beyond what the Coulomb analysis predicts.

Figures

Figures reproduced from arXiv: 2512.01752 by Karel van der Marck, Vadim Cheianov.

Figure 1
Figure 1. Figure 1: The spontaneous β-decay has a continuous spectrum, for the electron’s energy is measured and the energy in channel 1a can be distributed among the kinetic energy of the electron and the kinetic energy of the electron antineutrino. In channel 1b, however, the CνB is captured and all energy is transformed into the motion of the electron, making the spectrum peaked around the neutrino masses. To make this plo… view at source ↗
Figure 2
Figure 2. 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 graphene layer. Also the substrate has a mirror image on the right side, which effectively makes it twice as thick. b) The charge −e feels the electric field from the other three charges in Fig. 2a. Equivalently, we remove these three charges and the substrate, and we repl… view at source ↗
Figure 3
Figure 3. Figure 3: The purple region indicates a stable configuration for both [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The green dots form a two-dimensional slice of the stability region for [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

Measuring the electron neutrino mass is a long-standing objective and requires a high energy resolution of certain $\beta$-decay experiments, as well as a visible cosmic neutrino background (C$\nu$B) spectrum. Many quantum mechanical and chemical effects could potentially impair the required resolution/visibility, e.g., the Coulomb interactions between the electrons in the $\beta$-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes the impact of Coulomb interactions between beta-decaying impurities and their (semi)metallic host on the energy resolution and visibility of the cosmic neutrino background (CνB) in relic neutrino detection experiments. It treats two regimes: complete suppression of impurity-host hybridization via a dielectric spacer, and hybridization included to lowest nontrivial order in perturbation theory.

Significance. If the perturbative analysis and spacer model are shown to be controlled at the sub-eV level, the work would provide useful guidance for mitigating solid-state systematics in proposed beta-decay searches for the electron neutrino mass and CνB. The forward, parameter-free character of the calculation is a strength.

major comments (2)
  1. [perturbative hybridization analysis] The central claim for the hybridization-present case rests on the validity of lowest-order perturbation theory. The manuscript does not derive or numerically bound the size of next-order virtual processes or possible non-perturbative renormalization of the impurity level relative to the Coulomb shift and the sub-eV neutrino-mass scale (see the section describing the perturbative treatment and the discussion of energy resolution).
  2. [dielectric spacer regime] For the dielectric-spacer case, the model must demonstrate that the spacer fully suppresses hybridization while preserving the Coulomb interaction at the relevant energies; an explicit estimate or reference to the spacer thickness and dielectric constant relative to the beta-decay Q-value is needed to support the claimed complete suppression.
minor comments (2)
  1. Notation for the hybridization matrix element and the Coulomb shift should be defined consistently across equations and text.
  2. A brief comparison to existing literature on impurity levels in metals would help place the perturbative treatment in context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the parameter-free character of the calculation and its potential utility for mitigating systematics in relic neutrino searches. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [perturbative hybridization analysis] The central claim for the hybridization-present case rests on the validity of lowest-order perturbation theory. The manuscript does not derive or numerically bound the size of next-order virtual processes or possible non-perturbative renormalization of the impurity level relative to the Coulomb shift and the sub-eV neutrino-mass scale (see the section describing the perturbative treatment and the discussion of energy resolution).

    Authors: We agree that an explicit bound on higher-order corrections would strengthen the perturbative analysis. The current manuscript focuses on the leading nontrivial order without deriving numerical bounds on next-order terms. In the revised version we will add a dedicated paragraph in the perturbative treatment section that estimates the magnitude of second-order virtual processes by computing the ratio of the O(V^2) correction to the leading Coulomb shift, using the hybridization amplitude V as the expansion parameter. We will show that for the impurity densities and energy scales considered, this ratio is O(0.1) or smaller near the sub-eV regime. We will also add a short discussion noting that the impurity level renormalization induced by hybridization is itself higher order in V and does not alter the leading Coulomb-induced shift that sets the energy resolution scale. revision: yes

  2. Referee: [dielectric spacer regime] For the dielectric-spacer case, the model must demonstrate that the spacer fully suppresses hybridization while preserving the Coulomb interaction at the relevant energies; an explicit estimate or reference to the spacer thickness and dielectric constant relative to the beta-decay Q-value is needed to support the claimed complete suppression.

    Authors: We acknowledge that the manuscript presently assumes complete hybridization suppression without quantitative justification. In the revision we will insert an explicit estimate in the dielectric-spacer section. Using representative values (spacer thickness d ≈ 2–5 nm and dielectric constant ε_r ≈ 4 for SiO2 or Al2O3), we will show that the tunneling amplitude is exponentially suppressed as exp(−κd) with κ determined by the barrier height relative to the beta-decay Q-value, rendering hybridization negligible compared with the sub-eV scale. Because the Coulomb interaction is long-range and only weakly screened by the thin dielectric layer, its strength at the relevant energies remains essentially unchanged. We will cite standard references on dielectric barriers in solid-state beta-decay and tunneling experiments to support these estimates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward calculation of Coulomb effects in two regimes

full rationale

The manuscript performs a direct theoretical analysis of Coulomb interactions between beta-decaying impurities and the host electrons, considering two explicit regimes (full suppression by dielectric spacer, and hybridization to lowest nontrivial order in perturbation theory). No load-bearing step reduces by construction to a fitted parameter renamed as a prediction, a self-citation chain, or a self-definitional loop; the derivation chain consists of standard perturbative expansions and electrostatic modeling whose outputs are not forced by the inputs. External benchmarks such as the beta-decay Q-value and neutrino-mass scale remain independent of the present calculation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard quantum-mechanical assumptions about electron hybridization and the applicability of perturbation theory in solids; no free parameters or new entities are mentioned in the abstract.

axioms (2)
  • domain assumption Lowest-order perturbation theory suffices to capture hybridization effects on energy resolution
    Explicitly invoked for the case with hybridization present.
  • domain assumption A dielectric spacer can completely suppress hybridization without introducing other dominant broadening mechanisms
    Stated for the suppressed-hybridization case.

pith-pipeline@v0.9.0 · 5403 in / 1195 out tokens · 47682 ms · 2026-05-17T02:59:57.841852+00:00 · methodology

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Works this paper leans on

3 extracted references · 3 canonical work pages

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    Publishing, ISBN 978-3-031-16305-0, doi:10.1007/978-3-031-16305-0_6 (2022). 18

    work page doi:10.1007/978-3-031-16305-0_6 2022