Long, Lunardini & Sabancilar (JCAP 08 (2014) 038) established neutrino capture on tritium as the leading route to directly detect the cosmic neutrino background (CνB) and identified the central obstacle that their work left open for interpreting such a detection: degeneracies among gravitational clustering, primordial lepton asymmetry, neutrino decay, non-standard thermal history, and sterile components, which can enhance or suppress the capture rate in partially compensating ways so that a single rate-plus-peak-energy measurement cannot disentangle them. What any future measurement can infer is also conditioned on the electron energy resolution achieved — the capture peak is displaced by approximately 2mν2m_\nu above the tritium beta endpoint and must be extracted from the beta-decay tail — and the source paper noted energy resolution and background control among the major challenges for such an experiment. The interpretability problem remains open in light of the later literature (PTOLEMY proposals and theory updates, KATRIN relic-overdensity limits, clustering simulations, Dirac/Majorana studies): no direct CνB detection exists, the resolution frontier is actively contested, and no complete quantitative identifiability analysis of the degenerate mechanisms has been published.

Background

The cosmic neutrino background (CνB) is the sea of relic neutrinos that decoupled from primordial matter roughly one second after the Big Bang; standard cosmology predicts a present temperature of about 1.95 K and a total number density of roughly 336 particles per cubic centimeter over all flavors and antiparticles. For neutrino masses above about 0.01 eV the relic neutrinos are non-relativistic today, but their kinetic energies (sub-meV) are far too small to observe through scattering, so the only practical laboratory route is neutrino capture on beta-decaying nuclei. In the process νe+3H→3He+e−\nu_e + {}^3\mathrm{H} \to {}^3\mathrm{He} + e^- the capture is thresholdless: the neutrino's entire rest-mass energy is added to the electron's, so the signal is a monoenergetic electron line displaced above the endpoint of the ordinary tritium beta-decay spectrum (Q≈18.6Q \approx 18.6 keV) by approximately 2mν2m_\nu (about 2×10−22\times10^{-2} eV for the smallest mass eigenstate). PTOLEMY is a proposed experiment designed to exploit this: roughly 100 g of atomic tritium adsorbed on a graphene substrate, with the beta electrons measured by cryogenic microcalorimeters (detectors that convert each absorbed electron's energy into a measurable temperature rise). Long, Lunardini & Sabancilar (2014) computed the expected rates — about 4 events per year for Dirac neutrinos and about 8 per year for Majorana neutrinos per 100 g of tritium in the absence of clustering — and derived the detector requirements: the projected baseline energy resolution is Δ≈0.15\Delta \approx 0.15 eV, aimed at a quasi-degenerate mass spectrum with mν≳0.1m_\nu \gtrsim 0.1 eV; extracting the capture peak from the beta-decay tail requires the resolution to satisfy Δ≲0.7 mν\Delta \lesssim 0.7\,m_\nu; and resolving the individual mass eigenstates, or the mass hierarchy (the ordering of the three neutrino masses), requires Δ\Delta far below the splittings of a few ×10−2\times10^{-2} eV, which the baseline design may not reach. The capture rate is proportional to the local relic number density, which can exceed the cosmic average through gravitational clustering in the Milky Way halo; the enhancement factor fcf_c (the ratio of local to cosmic density) is predicted by halo models to be anywhere from order unity to a few for quasi-degenerate masses, and is negligible for the smallest masses. The paper's central interpretability problem is that several independent mechanisms change the expected rate in partially compensating ways: gravitational clustering (enhances), a primordial lepton asymmetry (an early-universe excess of leptons over antileptons, which changes the relative abundances of neutrinos and antineutrinos and can distort their spectra), neutrino decay, visible or invisible (depopulates or regenerates the background), non-standard entropy injection that alters the neutrino temperature TνT_\nu (the rate scales as nν∝Tν3n_\nu \propto T_\nu^3), and additional sterile mass eigenstates (hypothetical neutrino states beyond the three known active flavors that interact only through mixing; they add capture channels weighted by unknown mixing angles and abundances). Since a direct detection provides only two primary observables — the capture rate and the peak energy/shape — the authors conclude it would be impossible to distinguish the different causes of enhancement or suppression unless the capture data are combined with indirect information from cosmological and other laboratory measurements. This problem asks what it would take to make such a measurement scientifically decisive.

Problem Statement

The problem, as posed by Long, Lunardini & Sabancilar (2014) and left open by a decade of follow-up work, is to make a PTOLEMY-style tritium-capture measurement of the cosmic neutrino background scientifically decisive: to determine, quantitatively, what a direct detection — which supplies essentially two primary observables, the capture rate and the peak energy/line shape — can actually infer about the relic neutrino population, given that gravitational clustering (parameterized by the model-dependent enhancement fcf_c), primordial lepton asymmetry (an early-universe lepton-antilepton imbalance), neutrino decay (visible or invisible), non-standard thermal history (an altered TνT_\nu, with rate ∝Tν3\propto T_\nu^3), additional sterile components (gauge-singlet neutrino states mixing with the active flavors), and the neutrino's Dirac/Majorana nature can all change the expected rate in partially compensating ways.

Because terms such as "identifiable", "broken", and "feasible" are not self-defining, identifiability is assessed against an explicitly stated statistical separability threshold together with the target mass, exposure, background level, and electron energy resolution at which it is evaluated, and the same criterion governs each sub-question below; where no single benchmark is assumed, the conclusions are reported as a function of it.

The analysis must determine:

  1. which combinations of these mechanisms are identifiable from capture observables alone;
  2. which degeneracies can be broken by combining the capture data with complementary measurements such as oscillation data, neutrinoless double-beta decay searches (a lepton-number-violating nuclear decay whose observation would signal Majorana neutrino mass), cosmological constraints on NeffN_{\mathrm{eff}} (the effective number of light relativized species) and Σmν\Sigma m_\nu (the sum of the neutrino masses), and X-ray and short-baseline sterile searches;
  3. how these conclusions depend on the electron energy resolution achieved at the tritium endpoint — sub-eV, down to the ≲0.7 mν\lesssim 0.7\,m_\nu scale needed for signal extraction over the beta tail, and ultimately below the few-×10−2\times10^{-2} eV mass splittings — since the value of any achieved resolution depends on which degeneracies the resulting observables can break;
  4. whether resolving the mass hierarchy or the individual mass eigenstates is feasible at all, and what each inference requires.

References

  1. A. J. Long, C. Lunardini, E. Sabancilar, 'Detecting non-relativistic cosmic neutrinos by capture on tritium: phenomenology and physics potential', JCAP 08 (2014) 038, DOI 10.1088/1475-7516/2014/08/038, arXiv:1405.7654, https://arxiv.org/abs/1405.7654
  2. PTOLEMY Collaboration (E. Baracchini et al.), 'PTOLEMY: A Proposal for Thermal Relic Detection of Massive Neutrinos and Directional Detection of MeV Dark Matter', 2018, arXiv:1808.01892, https://arxiv.org/abs/1808.01892
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