ECHo-1k Experiment: Neutrino Mass Probe

• ECHo-1k experiment is a high-precision calorimetric study aimed at determining the effective electron neutrino mass by analyzing the 163Ho electron capture spectrum.
• It employs state-of-the-art cryogenic metallic magnetic calorimeters with energy resolutions below 10 eV FWHM to generate a high-statistics, low-background dataset.
• The experiment constrains the neutrino mass to below 15 eV/c² and cross-validates the decay energy using Penning-trap mass spectrometry.

The ECHo-1k experiment is a pivotal phase of the Electron Capture in $^{163}$Ho (ECHo) program, designed to determine the effective electron neutrino mass via high-precision calorimetric measurement of the electron capture (EC) spectrum of $^{163}$Ho. ECHo-1k establishes improved limits on the neutrino mass scale, leverages advanced cryogenic microcalorimeter technology, and produces a high-statistics, low-background dataset fundamental for neutrino mass analyses.

1. Scientific Context and Objectives

The central goal of ECHo-1k is the model-independent determination of the effective electron neutrino mass ($m_{\nu_e}$) by precisely measuring the endpoint region of the $^{163}$Ho EC spectrum. The experiment capitalizes on the low $Q$-value of $^{163}$Ho EC (approximately 2.8–2.9 keV) to enhance sensitivity to the spectral endpoint, where phase space suppression due to finite $m_{\nu_e}$ becomes significant. Compared to previous efforts, ECHo-1k seeks to improve limits on $m_{\nu_e}$, aiming for sub-20 eV/c² sensitivity, representing a factor of two improvement over previous calorimetric EC experiments (Adam et al., 3 Sep 2025).

The experiment further aims to achieve a precise determination of the decay energy $Q$ (endpoint energy), independently cross-validated using Penning-trap mass spectrometry.

2. Experimental Apparatus and Detector Technology

ECHo-1k uses arrays of metallic magnetic calorimeters (MMCs) operated at temperatures below 20 mK to achieve energy resolutions better than 10 eV FWHM (Mantegazzini et al., 2021). The detector design features a 72-pixel MMC chip, each pixel consisting of:

• Niobium meander-shaped pick-up coils forming the basis of a two-stage dc-SQUID readout;
• Paramagnetic Ag:Er sensors, thermally coupled via stems to a sandwich-absorber structure;
• An absorber constructed from gold or silver, with a thin, dedicated $^{163}$Ho implantation region (optimized for maximal quantum efficiency and full 4$\pi$ coverage).

The $^{163}$Ho source is embedded at a depth of $\sim$5 nm via 30 keV ion implantation. The per-pixel activity is 0.81 Bq for gold-host and 0.71 Bq for silver-host detectors, with an average energy resolution of 6.07 eV (gold) and 5.55 eV (silver) FWHM, satisfying the experiment's design criteria (Mantegazzini et al., 2021).

Detector Table

Detector Host	Avg. Activity [Bq]	Energy Resolution [eV FWHM]
Gold	0.81 ± 0.30	6.07
Silver	0.71 ± 0.44	5.55

3. Readout Electronics and Multiplexing

Each MMC channel in ECHo-1k is read out by a two-stage dc-SQUID system, with signals digitized at 125 MS/s using synchronized 16-bit ADCs (Adam et al., 3 Sep 2025). Moving forward, the ECHo program has developed large-scale microwave SQUID multiplexers (μMUX) and software-defined radio readout electronics. These systems utilize broadband frequency combs (4–8 GHz), IQ mixers, and FPGAs (e.g., Xilinx Zynq Ultrascale+ MPSoCs) for efficient event multiplexing and real-time online data reduction (Sander et al., 2018, Muscheid et al., 3 Apr 2024). While full μMUX deployment applies to later ECHo phases, the modular, scalable readout architecture demonstrated in ECHo-1k informs the design of larger arrays.

Notable features include:

• Digital channelization and demodulation using polyphase filter banks, yielding >55 dB crosstalk suppression;
• Power-equalized, IQ-imbalance-corrected frequency comb generation with >40 dB image rejection;
• System linearity of 194 μA/$\Phi_0$, essential for precise energy recovery per event (Muscheid et al., 3 Apr 2024).

4. Data Acquisition and Reduction Scheme

Over 200 million $^{163}$Ho EC events were collected corresponding to an effective exposure of ~4000 pixel-days (Adam et al., 3 Sep 2025). The data reduction follows a rigorously characterized, two-stage filtering method (Hammann et al., 2021):

1. Time-Info-Filter (TIF): Applies four time-based subfilters (holdoff, burst, coincidence, GSM) to reject events caused by pile-up, noise bursts, coincident backgrounds, and electromagnetic interference. Each filter operates on event time-stamps and is largely energy-independent.
   • Holdoff filter: $\Delta t < t_\mathrm{hold}$ (e.g., $t_\mathrm{hold}=15$ ms) for pile-up rejection.
   • Coincidence filter: $\Delta t < t_\mathrm{coinc}$ (e.g., $t_\mathrm{coinc}=8$ μs) to suppress coincident backgrounds.
2. Pulse Shape Analysis (PSA): Uses a template-matching $\chi^2_\mathrm{red}$ fit to reject events with non-ideal pulse shapes (unresolved pile-up or spurious signals). The selection retains >99.8% of genuine $^{163}$Ho events with <0.7% loss.

Calibration uses distinct EC resonances (e.g., MI, MII, NI), with quadratic fits determining the energy scale. The calibrated spectrum forms the basis of endpoint analysis.

5. Spectral Analysis and Endpoint Measurement

The observed calorimetric spectrum is modeled as a sum of atomic shell resonances, with the endpoint region parameterized by the convolution:

$$\frac{dN}{dE} = C [A(E) \cdot F_\mathrm{PS}(E, Q)] \otimes g(E, \sigma) + b(E)$$

where $$F_\mathrm{PS}(E, Q) = (Q - E) \sqrt{(Q - E)^2 - m_{\nu_e}^2}$$ is the phase-space factor, $g(E,\sigma)$ is the detector response (Gaussian, $\sigma$ from high-statistics MI Iine), and $b(E)$ models the residual background and unresolved pile-up ($f_\mathrm{pu}=0.8(5)\times 10^{-6}$). Analytical methods ("A$_1$", "A$_2$") are used to probe the endpoint and determine $Q$ and $m_{\nu_e}$ (Adam et al., 3 Sep 2025).

The measured endpoint is $Q = 2862(4)$ eV, in close agreement with $Q=2863.2(6)$ eV from Penning-trap mass spectrometry, validating both the calorimetric and mass-based approaches. The EC background rate is exceptionally low, $B=9.1(1.3)\times10^{-6}$ counts/eV/pixel/day, which is critical for robust endpoint analysis.

6. Results and Neutrino Mass Limit

The endpoint analysis using Hamiltonian Monte Carlo Bayesian inference constrains the effective electron neutrino mass to $m_{\nu_e} < 15$ eV/c² (90% credible interval) (Adam et al., 3 Sep 2025). This constitutes a nearly twofold improvement over prior $^{163}$Ho EC calorimetric measurements. Systematic uncertainties are minimized by the rigorous data cleaning protocol, validated event classification, and the comparable $Q$-value measurements from independent techniques.

7. Significance, Implications, and Future Directions

ECHo-1k demonstrates the reliability of calorimetric $^{163}$Ho EC for neutrino mass determination, with critical achievements in background suppression, energy resolution, source integration, and data processing. The approach offers a complementary, model-independent measurement to tritium β-decay endpoint studies (e.g., KATRIN).

The technological advances in MMC arrays, multiplexed readout, and ion-implanted source production are directly translatable to future ECHo phases (such as ECHo-100k), anticipated to reach sub-eV sensitivity by scaling up to thousands of pixels and higher per-pixel activities (Mantegazzini et al., 2023, Muscheid et al., 3 Apr 2024). The convergence of calorimetric and Penning-trap $Q$-value measurements reinforces the robustness of the approach. Ongoing and future upgrades focus on further background reduction, improved pile-up handling, higher pixel densities, and more sophisticated theoretical and statistical endpoint analyses.

These developments position the ECHo program as a leading avenue for probing absolute neutrino mass, testing fundamental symmetries, and potentially revealing new physics beyond the Standard Model.