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arxiv: 2606.17948 · v1 · pith:SGCL4HXQnew · submitted 2026-06-16 · ⚛️ physics.ins-det · hep-ex· nucl-ex

Optimized filtering for pulse-shape based pile-up rejection applied to 0νββ search with ¹⁰⁰Mo

V. Berest , M. Buchynska , P. Carniti , A. Giuliani , C. Gotti , H. Khalife , P. Loaiza , P. de Marcillac
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C. Nones M. Pageot E. Olivieri G. Pessina D. V. Poda J. A. Scarpaci B. Schmidt A. S. Zolotarova
This is my paper

Pith reviewed 2026-06-26 21:56 UTC · model grok-4.3

classification ⚛️ physics.ins-det hep-exnucl-ex
keywords pile-up rejectiondigital filterneutrinoless double beta decaycryogenic detectorspulse shape discriminationLi2MoO4background reduction0νββ search
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The pith

An optimized digital filter reduces pile-up background by 31% at 90% efficiency in neutrinoless double beta decay searches with 100Mo detectors.

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

The paper develops an algorithm to derive a digital filter that discriminates pile-up events, where multiple detector signals overlap in time and can mimic rare processes. It assumes the detector signal shape is known and the noise power spectral density remains stationary. Applied to cryogenic Li2 100MoO4 detectors for 0νββ searches, where 2νββ pile-up is the leading background, the filter improves rejection compared to a prior method. This matters because better pile-up identification preserves energy resolution and lowers backgrounds that could obscure the signal of interest. The approach is presented as generalizable to other detectors with similar signal and noise properties.

Core claim

The paper presents an algorithm to obtain an optimized digital filter for the discrimination of pile-up events for detectors with known signal response and stationary noise power spectral density. When applied to the search for neutrinoless double beta decay with cryogenic Li₂¹⁰⁰MoO₄ detectors, the new filter discriminant reduces the pile-up induced background by 31% at 90% efficiency compared to a reference method.

What carries the argument

The optimized digital filter discriminant, built from the known signal response and stationary noise power spectral density to separate single pulses from overlapping pile-up events.

If this is right

  • The filter can be deployed in the CUPID experiment to suppress the dominant 100Mo 2νββ pile-up background.
  • Energy resolution and event reconstruction accuracy improve when pile-up is correctly identified and rejected.
  • The same construction method applies to other cryogenic calorimeters that satisfy the known-response and stationary-noise conditions.
  • Higher signal efficiency becomes feasible without increasing the accepted background rate.

Where Pith is reading between the lines

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

  • The method could be tested on non-cryogenic detectors such as high-purity germanium or liquid scintillators if their pulse shapes and noise spectra can be characterized.
  • If noise stationarity breaks down over long runs, periodic recalibration of the filter coefficients would be needed to maintain performance.
  • Integration with machine-learning pulse classifiers might produce a hybrid discriminant with further gains in separation power.

Load-bearing premise

The detector signal response must be known in advance and the noise power spectral density must remain stationary.

What would settle it

Measure the background reduction factor in real or simulated data from Li2 100MoO4 detectors at 90% signal efficiency and check whether it equals or exceeds the claimed 31% improvement over the reference method.

Figures

Figures reproduced from arXiv: 2606.17948 by A. Giuliani, A. S. Zolotarova, B. Schmidt, C. Gotti, C. Nones, D. V. Poda, E. Olivieri, G. Pessina, H. Khalife, J. A. Scarpaci, M. Buchynska, M. Pageot, P. Carniti, P. de Marcillac, P. Loaiza, V. Berest.

Figure 1
Figure 1. Figure 1: Example of the pulse impulse response s(t) used in this study, together with the range of pile-up time separa￾tions investigated. 2.1 Pile-up model A pile-up event arises from the temporal overlap of two pulses, which we parametrize as: x(t) = (1−r)As(t) +rAs(t +∆t) +n(t), (2) where r denotes the relative amplitude and ∆t the time sep￾aration between the pulses. In the example case of a 0νβ β search with 1… view at source ↗
Figure 2
Figure 2. Figure 2: (top) Approximation of the 2νβ β energy spectrum of 100Mo [29]: E ·(3.034 − E) 5 ·(E 4 + 10E 3 + 40E 2 + 60E + 30), where E is the energy in keV. (bottom) Distribution of the relative amplitude fR(r) for event pairs with total en￾ergy Qβ β = 3.034 MeV. This figure illustrates the 2νβ β decay spectrum and the resulting distribution of relative am￾plitudes r for pile-up events. which maximizes the SNR. The n… view at source ↗
Figure 3
Figure 3. Figure 3: shows the evolution of the cost function ⟨M⟩[m1,m2] during iterative gradient descent for the different detectors. The optimization process shows stable convergence across all detectors, with the cost function decreasing rapidly in the initial iterations before reaching a plateau, confirming the robustness of the gradient-descent approach in detector￾specific conditions. The training time required for a si… view at source ↗
Figure 4
Figure 4. Figure 4: Optimized filter shapes m1(ω) and m2(ω) for the studied detectors at 90% efficiency, along with the median shape computed across all detectors. The performance achieved for each detector is summa￾rized in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of BI obtained from simulated pile-up [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Impact of the time separation ∆t and amplitude ratio r grid size on the BI obtained from simulated pile-up events and from the analytical model prediction. The grid size N is defined as the number of steps in each dimension for ∆t ∈ [0,8×10−4 ] s and r ∈ [0,0.5] [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Impact of different working points of the NTD [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

Pile-up events, arising from the partial or complete temporal overlap of distinct signals, represent a major challenge in many areas of experimental physics where rare or low-rate processes are targeted. If not properly identified, pile-up can distort reconstructed observables, degrade energy resolution, and generate backgrounds that mimic genuine events of interest. This work presents an algorithm to obtain an optimized digital filter for the discrimination of pile-up events for detectors with known signal response and stationary noise power spectral density. It is developed in the context of the search for neutrinoless double beta decay with cryogenic Li$_{2}$$^{100}$MoO$_4$ detectors like CUPID, where pile-up induced background from $^{100}$Mo $2\nu\beta\beta$ is expected to be the leading background contribution. For this application, the new filter discriminant reduces the pile-up induced background (at 90% efficiency) by 31%, compared to an analysis with a reference method previously presented in Eur. Phys. J. C 83(5), 373 (2023). While the discussion is grounded in cryogenic calorimetric detectors, the concepts and methods described are broadly applicable to a wide class of detector technologies and experimental contexts.

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

0 major / 2 minor

Summary. The manuscript presents an algorithm to derive an optimized digital filter for discriminating pile-up events, assuming known detector signal response and stationary noise power spectral density. Developed for cryogenic Li2^100MoO4 detectors in the CUPID 0νββ search, the filter reduces pile-up-induced background by 31% at 90% efficiency relative to the reference method of Eur. Phys. J. C 83(5), 373 (2023). The approach is positioned as applicable to a broader class of detectors.

Significance. If the performance holds, the work offers a targeted improvement in pile-up rejection for low-background rare-event searches, directly addressing the leading 2νββ pile-up background in 100Mo 0νββ experiments. The explicit quantitative comparison to an independently published reference method provides a concrete benchmark, and the method's grounding in known signal and noise properties supports its potential transferability.

minor comments (2)
  1. The abstract states the 31% reduction; the main text should include the corresponding efficiency-versus-rejection curves (with uncertainties) and a clear statement of the dataset or simulation used to obtain this number.
  2. Clarify in the methods section how the optimized filter discriminant is constructed from the signal template and noise PSD, including any matrix inversions or frequency-domain operations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript, the recognition of its potential impact on pile-up rejection in 0νββ searches, and the recommendation for minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmark

full rationale

The paper states its premises explicitly (known signal response and stationary noise PSD) as the basis for deriving the optimized filter, then reports a quantitative performance gain relative to an independently published 2023 reference method. No equation or step reduces by construction to a fitted parameter defined inside the paper, no uniqueness theorem is imported via self-citation, and the comparison is to an external result rather than an internal fit renamed as prediction. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions that are not independently evidenced in the provided abstract: known signal response and stationary noise PSD. No free parameters or invented entities are mentioned.

axioms (2)
  • domain assumption Detector signal response is known
    Explicitly required by the algorithm description in the abstract.
  • domain assumption Noise power spectral density is stationary
    Stated in the abstract as a prerequisite for the filter construction.

pith-pipeline@v0.9.1-grok · 5835 in / 1246 out tokens · 21855 ms · 2026-06-26T21:56:39.145454+00:00 · methodology

discussion (0)

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