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Direct Measurement of the $^{39}$Ar Half-life from 3.4 Years of Data with the DEAP-3600 Detector

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Pith's one-line read DEAP-3600 directly observed the $^{39}$Ar decay curve over 3.4 years and measured the half-life as $(302 \pm 8_{\mathrm{stat}} \pm 6_{\mathrm{sys}})$ years, about 12% longer than the accepted 269-year value.

desk verdict First direct 39Ar half-life measurement from a decay curve, but the light-yield correction as written is inverted and could shift the central value past the quoted systematic. read the letter →

arxiv 2501.13196 v3 pith:HUYFEZYV submitted 2025-01-22 nucl-ex physics.ins-det

DEAP Collaboration: P. Adhikari , R. Ajaj , M. Alpízar-Venegas , P.-A. Amaudruz , J. Anstey , D.J. Auty , M. Batygov , B. Beltran
show 108 more authors
M.A. Bigentini C.E. Bina W.M. Bonivento M.G. Boulay J.F. Bueno M. Cadeddu B. Cai M. Cárdenas-Montes S. Cavuoti Y. Chen S. Choudhary B.T. Cleveland R. Crampton S. Daugherty P. DelGobbo P. Di Stefano G. Dolganov L. Doria F.A. Duncan M. Dunford E. Ellingwood A. Erlandson S.S. Farahani N. Fatemighomi G. Fiorillo R.J. Ford D. Gahan D. Gallacher A. Garai P. García Abia S. Garg P. Giampa A. Giménez-Alcázar D. Goeldi V.V. Golovko P. Gorel K. Graham A. Grobov A.L. Hallin M. Hamstra S. Haskins J. Hu J. Hucker T. Hugues A. Ilyasov B. Jigmeddorj C.J. Jillings A. Joy G. Kaur A. Kemp M. Khoshraftar Yazdi M. Kuźniak F. La Zia M. Lai S. Langrock B. Lehnert J. LePage-Bourbonnais N. Levashko M. Lissia L. Luzzi I. Machulin A. Maru J. Mason A.B. McDonald T. McElroy J.B. McLaughlin C. Mielnichuk L. Mirasola A. Moharana J. Monroe A. Murray C. Ng G. Oliviéro M. Olszewski S. Pal D. Papi B. Park M. Perry V. Pesudo T.R. Pollmann F. Rad C. Rethmeier F. Retière I. Rodríguez García L. Roszkowski R. Santorelli F.G. Schuckman II S. Seth V. Shalamova P. Skensved T. Smirnova K. Sobotkiewich T. Sonley J. Sosiak J. Soukup R. Stainforth M. Stringer J. Tang R. Turcotte-Tardif E. Vázquez-Jáuregui S. Viel B. Vyas M. Walczak J. Walding M. Ward S. Westerdale R. Wormington A. Zuñiga-Reyes
This is my paper · ORCID
classification nucl-exphysics.ins-det
keywords argon-39half-lifebetadecayDEAP-3600liquidargondetectorpulse-shapediscriminationradioisotopedatingatmospheric
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports the first direct measurement of the $^{39}$Ar half-life from continuous observation of its decay curve, using 3.4 years of data from the DEAP-3600 liquid-argon detector. The measured value is $T_{1/2}=(302 \pm 8_{\mathrm{stat}} \pm 6_{\mathrm{sys}})$ years, about 12% longer than the widely used $(269 \pm 3_{\mathrm{stat}} \pm 8_{\mathrm{sys}})$-year value from 1965 and the $(268 \pm 8)$-year Nuclear Data Sheets evaluation. A direct decay-curve measurement matters because all previous estimates relied on isotopic-ratio or activity-ratio methods, none of which continuously tracked the decay. If correct, the longer half-life changes the inferred $^{39}$Ar abundance in atmospheric argon and recalibrates dating and radiochemistry applications that use this isotope.

What carries the argument

The machine that carries the argument is the detector's ability to count $^{39}$Ar decays continuously and to model the trigger rate. DEAP-3600's liquid argon target is so rich in $^{39}$Ar that this isotope dominates triggers by two orders of magnitude; pulse-shape discrimination (the ratio of prompt to total charge, $F_{\mathrm{prompt}}$) separates the electron-recoil band from nuclear recoils, and a data-cleaning cut plus livetime calculation converts raw triggers into rates. The rate model explicitly includes Poisson probabilities for uncorrelated pile-up (one, two, or three $^{39}$Ar decays landing in the same 10 $\mu$s trigger window, and $^{39}$Ar plus Cherenkov light), so the exponential decay $R_{^{39}\mathrm{Ar}}(t)=R_{^{39}\mathrm{Ar}}e^{-t/\tau_{^{39}\mathrm{Ar}}}$ can be extracted with the mean lifetime $\tau$ as a free parameter. A light-yield correction, derived from daily calibrations with $^{40}$K, $^{208}$Tl, and the $^{39}$Ar $\beta$ spectrum, is applied to each event's PE value to remove time-dependent detector response changes.

What would settle it

Re-fit the trigger-rate curve with the light-yield correction omitted and again with its sign reversed (dividing by $Y_j/Y_0$ instead of multiplying). If either variant shifts the half-life by more than the quoted $\pm 6$-year systematic, the central result is controlled by the correction rather than by the decay; a second, independent check is to fit the two halves of the 3.4-year dataset separately and compare their $T_{1/2}$ values.

Watch

Extended reading notes

Core claim

The central discovery is a half-life value obtained from a direct decay-rate fit. Selecting clean electron-recoil events with pulse-shape discrimination in the 700–1200 PE window, the collaboration measured the $^{39}$Ar trigger rate as a function of time and fit it with a model that includes single decays, double and triple pile-up, $^{39}$Ar–Cherenkov pile-up, and a constant ERB $\gamma$ background. The fit yields $T_{1/2}=(302 \pm 8_{\mathrm{stat}} \pm 6_{\mathrm{sys}})$ years, and the paper reports a $p$-value of 0.008 for consistency with the NDS value, i.e. the two are in tension. When combined with the earlier DEAP specific-activity measurement, this corresponds to a $^{39}$Ar abundance in atmospheric argon of $(8.6 \pm 0.4)\times 10^{-16}$.

Load-bearing premise

The load-bearing assumption is that the PE-scale correction of Section 3.1 completely removes time-dependent light-yield variations, so that the remaining change in trigger rate is purely the $^{39}$Ar decay; if the correction leaves, or introduces, a drift, the measured half-life changes by more than the quoted systematic uncertainty.

Editorial extensions

If this is right

  • If the 302-year value is right, the 269-year standard is about 12% too short, and the NDS evaluation (268 ± 8 years) disagrees at a p-value of 0.008.
  • Combining the new half-life with DEAP's measured specific activity gives an atmospheric $^{39}$Ar abundance of $(8.6 \pm 0.4)\times10^{-16}$, a direct estimate that does not depend on the older half-life.
  • Radiometric dating and tracer methods that use $^{39}$Ar would need to update their decay constants, shifting inferred ages by the corresponding factor.
  • Future dark-matter experiments using atmospheric argon would see a slightly higher $^{39}$Ar background rate per unit mass if the half-life is longer, which affects their background-model inputs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Not stated in the paper, the sign of the light-yield correction in Section 3.1 is worth an independent check: the text says each event's PE value is corrected by multiplying by $Y_j/Y_0$, and if the intended correction was to divide by that ratio, the drift used to extract the half-life would move in the opposite direction and could shift the central value by more than the quoted $\pm 6$-year syst
  • Because the light-yield correction dominates the systematic budget, an external test would be to fit the 700–900 PE and 900–1200 PE sub-regions separately; a significant disagreement between the two inferred half-lives would indicate residual spectral-shape sensitivity.
  • The method of continuously counting a dominant endogenous decay and modeling pile-up statistics could be transplanted to other long-lived isotopes in large liquid detectors, such as $^{85}$Kr in liquid argon or $^{14}$C in organic scintillators, where no direct decay-curve half-life measurement exists.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper reports the first direct measurement of the 39Ar half-life by observing the decay curve with the DEAP-3600 liquid-argon detector over 3.4 years. The authors select electron-recoil events in a 700-1200 PE region of interest, model the ROI trigger rate as a combination of single, double, and triple 39Ar pile-up, 39Ar-Cherenkov pile-up, and a constant gamma background, and fit for the initial 39Ar rate and lifetime. The result is T1/2 = (302 ± 8stat ± 6sys) years, about 12% longer than the NDS value, with a reported p-value of 0.008 for disagreement. The systematic budget is dominated by light yield corrections.

Significance. If the result is correct, it is a valuable first direct decay-curve measurement of the 39Ar half-life, with implications for geochronology, radiochemistry, and argon-based dark matter detectors. The paper's strengths include a clean derivation of the fit model from Poisson statistics, a free-floating half-life (so no circularity in the central fit), very high statistics, explicit Monte Carlo and data cross-checks, and a reasonably complete systematic inventory. The main weakness is the light yield correction described in Section 3.1: as written, the direction of the correction appears inverted, and the dominant systematic is evaluated by perturbing that same factor. Because the expected decay signal over 3.4 years is only about 0.8% in rate, an error in this correction could change the central value well beyond the quoted uncertainties. The result is therefore conditional on resolving this point.

major comments (2)
  1. [Sec. 3.1 and Sec. 6.1] The stated correction factor appears inverted. Section 3.1 says 'The PE value of each event in a run is then corrected by a factor of Yj/Y0,' where Y is the light yield in PE/keVee. For a standard light yield definition, an event with a given energy has PE_j = Y_j * E, so the mapping to the reference run is PE_0 = (Y_0 / Y_j) * PE_j. The paper's formula multiplies by Y_j / Y_0, which would amplify, not remove, run-to-run light yield drift; Section 6.1 repeats this form as 'Yj/Y0 + ΔY'. Since the ROI is fixed in PE, an inverted correction changes the fraction of the 39Ar spectrum inside the ROI as a function of time, potentially mimicking a change in the decay rate. The quoted differential systematic (5.1 years) is obtained by perturbing this factor in magnitude, not by checking its sign, so it does not cover an inversion. The authors must clarify whether a non-standard definition of Y is being used, correct the formula if it is a typo, and show with a closure test (e.g., Monte Carlo injection of a known lifetime or a residual-rate versus light-yield check) that the implemented correction is in the direction that removes drift.
  2. [Sec. 6.1 and Fig. 6] The differential drift systematic is evaluated by adding a linear ramp of amplitude ΔY = 0.00076 to the correction factor and refitting. However, the calibration source light yields plotted in Fig. 6 show substantially larger, non-linear time variations (of order 0.1 PE/keVee over the dataset). While the nominal run-by-run correction may remove these variations if the calibration measurements perfectly track the detector response relevant to the ROI, the paper does not provide a direct closure check demonstrating that the corrected rates are insensitive to the observed non-linear light yield structure. Given that the physics signal is only about 0.8% in rate over the full dataset, a non-linear residual drift at the level visible in Fig. 6 could be comparable to the signal. The revision should include an explicit validation that the applied correction removes the observed time-dependent light yield changes, beyond the linear-ramp perturbation used for the systematic.
minor comments (3)
  1. [Title/header] The manuscript header contains '3.4 Y ears of Data'; the word 'Years' should be restored.
  2. [Sec. 3] The text 'Individual runtimes Trun vary in the range of [ O(1minute ), ∼2 days]' has spacing and notation issues; it should read 'O(1 minute)' or a conventional notation for order-of-magnitude ranges.
  3. [Table 2] In the 'Constraints' column, entries such as 'Run-dependent N/A' are unclear: the table should specify that the light yield correction factors are run-dependent parameters whose uncertainties are evaluated as described in Section 6.1, and what 'N/A' refers to.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 39Ar half-life is a free fit parameter and no load-bearing step reduces to an input.

full rationale

The central claim is derived by fitting the observed time-dependent trigger rate with Eq. 13, where R39Ar(t) = R39Ar exp(-t/tau39Ar) and tau39Ar is explicitly a free-floating parameter. The auxiliary inputs are determined independently of the target half-life: RChv is measured from low-threshold data and matched by MC (Sec. 5.1); Rbg is obtained by subtracting the MC 39Ar spectrum from the total MC ERB sum (Sec. 5.3); the ROI fractions fi come from a toy MC based on the external beta-spectrum model of Ref. [28] and a detector response model; the efficiencies eps_i come from MC and data-side selection studies without reference to the decay rate change. Thus the half-life is not an input to the fit, and no equation in the paper defines the result in terms of itself. The self-citations (prior DEAP specific-activity measurement [7] and PSD analysis [25]) are not load-bearing for the half-life: [7] is used only in the conclusion to convert the measured half-life into an abundance, and [25] supports the established pulse-shape discrimination technique. There is no imported uniqueness theorem, no ansatz smuggled in via citation, and no renaming of a known empirical pattern. The reader-identified concern about the direction of the light-yield correction factor (Sec. 3.1) is a potential implementation/correctness issue, not a circularity: even if the factor were inverted, that would bias the fitted rate trend, but it would not make the half-life equivalent to an input by construction. The paper also honestly reports the light-yield correction as the dominant systematic (5.1 years), so no fitted parameter is being relabeled as a prediction. Overall, the derivation chain is self-contained against the measured decay curve, and no step reduces to its own inputs.

Assumptions & free parameters 9 free parameters · 6 assumptions · 0 invented entities

The fit model in Eq. 13 has two free parameters, the initial 39Ar trigger rate R39Ar and the mean lifetime τ, which are the measured quantities. The central claim also depends on fixed auxiliary parameters estimated from data or MC: the background rate Rbg, the Cherenkov rate RChv, the spectral fractions f_i, selection efficiencies ε_i, and the run-by-run light yield ratio. Uncertainties on these are propagated as systematics. No novel entities are introduced.

free parameters (9)
  • Rbg (ERB gamma background rate) = 1.65 ± 0.31 Hz
    Determined by subtracting the MC 39Ar spectrum from the total ERB spectrum in the ROI; fixed in the half-life fit, uncertainty propagated as a 0.15-year systematic.
  • RChv (Cherenkov trigger rate) = 538 ± 4 Hz
    Measured from low-threshold data and normalized to the nominal threshold; fixed in the fit, treated as constant with weekly variations included as a systematic.
  • f1 (single 39Ar spectrum fraction in ROI) = 0.21 ± 0.05
    Estimated from toy MC using a beta spectrum model and detector response; varied by ±0.05 as a conservative systematic.
  • f2 (double 39Ar pile-up spectrum fraction in ROI) = 0.20 ± 0.05
    Estimated from toy MC pile-up spectra; varied by ±0.05 as a conservative systematic.
  • f3 (triple 39Ar pile-up spectrum fraction in ROI) = 0.19 ± 0.05
    Estimated from toy MC pile-up spectra; varied by ±0.05 as a conservative systematic.
  • f4 (39Ar-Cherenkov pile-up spectrum fraction in ROI) = 0.21 ± 0.05
    Estimated from toy MC of 39Ar with low-energy Cherenkov light; varied by ±0.05 as a conservative systematic.
  • ε2 (double 39Ar pile-up selection efficiency) = 0.9099 ± 0.0033
    Corrected efficiency from data and MC with a sub-event count cut; uncertainty propagated as a 1.8-year systematic.
  • ε3 (triple 39Ar pile-up selection efficiency) = 0.860 ± 0.039
    Corrected efficiency for triple pile-up events; uncertainty propagated as a 0.19-year systematic.
  • Light yield ratio Yj/Y0 = Run-dependent, average ΔY = 0.00076
    Used to correct PE values for time-varying light yield; dominant systematic, assessed by constant offset and differential drift models.
assumptions (6)
  • standard math Poisson statistics for the occurrence of 39Ar decays in the 10 µs trigger window (Eqs. 5-12)
    Used to derive single, double, triple, and Cherenkov pile-up trigger rates.
  • domain assumption The 39Ar beta spectrum shape from Kostensalo, Suhonen, and Zuber (Ref. [28])
    Used in toy MC to compute the fraction f_i of each event type's spectrum inside the ROI.
  • domain assumption Detector response is a Gaussian smearing with mean <NDN> + Y*E (Eq. 14)
    Used to generate toy MC spectra and to compute ROI fractions.
  • domain assumption The ERB gamma background rate Rbg is constant across the dataset
    Assumed in Eq. 4; cross-check with 232Th and 238U chains gives at most 0.15 years shift.
  • domain assumption The Cherenkov trigger rate RChv is constant in time
    Weekly averages are stable; small variations included as a systematic.
  • domain assumption The data-cleaning cut and livetime calculation in Eq. 2 correctly account for deadtime
    The livetime Tlive is used to convert event counts to rates; errors here would scale all rates.

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Cite this review

Pith. "Pith review of Direct Measurement of the $^{39}$Ar Half-life from 3.4 Years of Data with the DEAP-3600 Detector." pith.science (2026). https://pith.science/paper/HUYFEZYV

@misc{pith2026250113196,
  author       = {Pith},
  title        = {Pith review of: Direct Measurement of the $^39$Ar Half-life from 3.4 Years of Data with the DEAP-3600 Detector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HUYFEZYV}},
  note         = {Machine review of arXiv:2501.13196}
}
abstract

The half-life of $^{39}$Ar is measured using the DEAP-3600 detector located 2 km underground at SNOLAB. Between 2016 and 2020, DEAP-3600 used a target mass of (3269 $\pm$ 24) kg of liquid argon distilled from the atmosphere in a direct-detection dark matter search. Such an argon mass also enables direct measurements of argon isotope properties. The decay of $^{39}$Ar in DEAP-3600 is the dominant source of triggers by two orders of magnitude, ensuring high statistics and making DEAP-3600 well-suited for measuring this isotope's half-life. Use of the pulse-shape discrimination technique in DEAP-3600 allows powerful discrimination between nuclear recoils and electron recoils, resulting in the selection of a clean sample of $^{39}$Ar decays. Observing over a period of 3.4 years, the $^{39}$Ar half-life is measured to be $(302 \pm 8_{\rm stat} \pm 6_{\rm sys})$ years. This new direct measurement suggests that the half-life of $^{39}$Ar is significantly longer than the accepted value, with potential implications for measurements using this isotope's half-life as input.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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