Updated parameters of the LArQL model

F. Cavanna; F. Marinho; L. Paulucci; V. Vale

REVIEW 5 major objections 4 minor 11 references

Updated parameters of the LArQL model

T0 review · 5 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A global re-fit of the LArQL model's parameters lowers residuals for every tested liquid-argon charge and light dataset and improves the match to MicroBooNE dQ/dx over Birks alone.

desk verdict A transparent, incremental re-fit of LArQL parameters; the modest improvement is plausible but in-sample, and the external MicroBooNE check needs quantification. read the letter →

arxiv 2504.17866 v1 pith:AYF5VFHB submitted 2025-04-24 hep-ex

L. Paulucci , F. Cavanna , V. Vale , F. Marinho This is my paper · ORCID

classification hep-ex

keywords liquidargontimeprojectionchamberLArQLmodelionizationchargeyieldscintillationlightrecombinationfactorescapingelectronscharge-lightanti-correlationglobalparameterfit

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

LArQL is a phenomenological model that describes, from one master equation, how energy deposited in liquid argon splits into ionization charge and scintillation light, including electrons that escape recombination even at zero field. This paper re-fits the model's six phenomenological parameters plus the two Birks parameters, within their known uncertainties, to published ICARUS charge data and ARIS scintillation data in a single weighted global fit. The result is a parameter table that reduces the sum of squared residuals for every dataset compared with the original LArQL parameters, with relative reductions all under ten percent, and that agrees visually with MicroBooNE charge-per-length data better than the Birks model alone. The goal is a single internally consistent charge-and-light description for LArTPCs over $\mathcal{E}$ from 0 to 0.75 kV/cm and $dE/dx$ from 2 to 40 MeV/cm, which matters for energy reconstruction in neutrino detectors.

What carries the argument

The load-bearing object is the LArQL charge-light master equation $Q + L = N_i + N_{ex}$ together with the modified Birks formula of Eq. (2.3): $Q = \frac{A_B/W_{ion}}{1 + \frac{k_B}{\rho_{LAr}}\frac{1}{\mathcal{E}}\frac{dE}{dx}} + \chi_0(dE/dx)\, f_{corr}(\mathcal{E},dE/dx)\, Q_\infty$. The first term is standard Birks recombination; the second adds escaping electrons, with $\chi_0$ the fraction of electrons that escape recombination at zero field and $f_{corr}$ the empirical field dependence, both defined in Eq. (2.4) as $f_{corr} = e^{-\mathcal{E}/(\alpha \ln(dE/dx)+\beta)}$ and $\chi_0 = A/[B+e^{C+D\,dE/dx}]$. The argument is carried by the weighted residual objective of Eq. (3.1), which forces a single parameter set to account for charge and light together, and by the correlation structure among the fitted parameters, especially the strong $A_B$--$k_B$ correlation and the coupling of $\alpha$ to both.

What would settle it

Measure the recombination factor $R$ and the scintillation ratio $S/S_0$ in liquid argon at field values not well covered by the training data, such as $\mathcal{E} = 0.1$ kV/cm at $dE/dx = 30$ MeV/cm, with percent-level uncertainties; if the updated LArQL parameters do not reproduce the measured points within the residuals quoted for the original datasets, the functional forms are the limiting assumption. Alternatively, re-fit the same data with different two-parameter forms for $\chi_0$ and $f_{corr}$; a meaningfully lower $WSSR$ would show the claimed improvement depends on the chosen parametrization.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that all the charge and light datasets used can be described simultaneously with a single LArQL parameter set, and that this set beats the original one on every dataset. Using a weighted sum of squared residuals ($WSSR$) and random sampling of parameter space around the original values, the fit gives $A_B = 0.808(2)$, $k_B = 49.7(4)\ \mathrm{g\,V\,MeV^{-1}\,cm^{-3}}$, $\alpha = 0.0387(8)\ \mathrm{cm/kV}$, $\beta = 0.0128(6)\ \mathrm{cm/kV}$, $A = 3.61(5)\times 10^{-3}$, $B = -5.7(1)$, $C = 1.74(2)$, and $D = 2.01(3)\times 10^{-4}\ \mathrm{cm/MeV}$. Every dataset's $SSR_i$ is lower than with the original parameters and satisfies $|1 - SSR_i^\mathrm{fit}/SSR_i^\mathrm{original}| < 10\%$. The paper is explicit that the fitted $A_B$ and $k_B$ are not standalone Birks values; they are only meaningful inside the full LArQL expression. In the MicroBooNE $dQ/dx$ comparison, both LArQL versions track the data while the Birks model alone slightly underestimates $dQ/dx$ at higher $dE/dx$.

Load-bearing premise

The load-bearing premise is that the two chosen formulas—an exponential field correction and a logistic-type escape fraction—are the correct shapes for the whole 0–0.75 kV/cm and 2–40 MeV/cm range; if real physics takes different forms, the new parameter table only re-fits a wrong model.

Editorial extensions

If this is right

LArTPC simulations that adopt the updated table describe the anti-correlated charge and light channels with one parameter set instead of separate charge and light fits.
Because every individual $SSR_i$ decreased, the global fit did not improve the overall picture by sacrificing one dataset for another.
The strong $A_B$--$k_B$ correlation means the parameters should be used as a block; varying one alone damages the model's electric-field behavior.
The fitted $A_B$ and $k_B$ cannot be transplanted into standalone Birks recombination calculations; the paper restricts them to use within LArQL.
The same functional forms can be re-fitted as new charge and light datasets become available, which is the paper's stated next step.

Reading between the lines

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

A sharper test of the model would be to check whether the same two functional forms also fit liquid-xenon charge and light data; if they do, the phenomenological core generalizes beyond argon, and if they do not, the forms are argon-specific.
The reported residual reductions are all below ten percent, so the practical payoff may lie more in the MicroBooNE $dQ/dx$ comparison, a dataset outside the fit; the shape agreement there is the stronger evidence of genuine improvement.
Because the optimizer was a random sampling rather than a more systematic minimizer, a repeat fit with a gradient-based or Bayesian sampler on the same objective could confirm that the reported 'most probable' parameters are a true minimum and not just the best point found.
Computing energy resolution from the fitted parameters versus the original set would make the impact concrete: if the charge-light anti-correlation is sharper, the benefit for neutrino oscillation analyses becomes quantitative.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The short version: this paper re-fits the parameters of the LArQL phenomenological model for charge and light in liquid argon, using the same functional forms and mostly the same data as the original. It gives a new parameter table with uncertainties and claims a modest (<10%) reduction in summed squared residuals across all datasets. That claim is likely true as an in-sample statement, but it is not yet supported as a robust update.

What's actually new is the parameter set and the correlations. The authors are honest: they say the search was restricted around the original values, and the weights in Eq. (3.1) come from intermediate individual fits of the same model to the same datasets. So the 'global' fit is a local refinement, and the reported SSR reduction is exactly what you'd expect from fitting nine parameters to data that already informed the original choice. The MicroBooNE dQ/dx comparison is external and not used in the fit, which is good, but it's only shown visually with no quantified metric. That's the soft spot, and it's the main one.

The paper does push in the right direction: it makes the fit procedure explicit, gives uncertainties for all parameters, notes the strong AB–kB correlation, and flags that the AB/kB values should not be interpreted as Birks parameters in isolation. That restraint is creditable.

The bigger question — whether the chosen functional forms for f_corr and chi0 are adequate over the full 0–0.75 kV/cm and 2–40 MeV/cm range — is not addressed, but that's a limitation stated in the model's foundations, not a new flaw introduced here. The paper is a calibration update, not a claim about the correct parametric form.

Bottom line: if you're working with LArQL in LArSoft and need current parameter values with tolerances, this is useful and worth knowing about. As a standalone physics paper it's minor but legitimate. I'd send it to a competent referee for the instrumentation community, mainly because the parameters are embedded in simulation software and independent verification of the fit weights and uncertainties matters. I would not require new data for acceptance, but I would ask the authors to state clearly that the SSR reduction is in-sample and to quantify the MicroBooNE comparison, even with a simple chi2 or residual plot.

Referee Report

5 major / 4 minor

Summary. This manuscript reports a re-fit of the parameters of the LArQL phenomenological model, which describes ionization charge and scintillation light in liquid argon as a function of electric field and dE/dx. The authors minimize a weighted sum of squared residuals (Eq. 3.1) over the Birks parameters (A_B, k_B) and the four parameters of the escape-electron correction (alpha, beta, A, B, C, D) using ICARUS charge data [7] and ARIS/scintillation data [5,8]. They obtain a new parameter set (Table 1) and report that the sum of squared residuals for each individual dataset is reduced by less than 10% relative to the original LArQL parameters. They also show a qualitative comparison with MicroBooNE dQ/dx data, where the updated LArQL curve lies closer to the data than the Birks model alone.

Significance. If the updated parameters are robust, they provide a practical improvement for LArTPC simulations, especially because LArQL is already used in the LArSoft framework. The paper is transparent that the parameters are fitted to data, and the MicroBooNE comparison is an external check that was not part of the fit, which strengthens the empirical relevance. The main limitation is that the reported improvement is evaluated on the same data used to set the weights and to narrow the parameter ranges, so the central claim of a better description is currently supported only in-sample.

major comments (5)

[Sec. 3, Eq. (3.1)] The weights in Eq. (3.1) are derived from RMS_i^best obtained from an intermediate fit of the same LArQL model to each individual dataset, and the parameter ranges were narrowed using the same datasets. Consequently, the reported reductions in SSR_i^fit relative to SSR_i^original are in-sample quantities and do not by themselves demonstrate that the updated parameters generalize better. I request a cross-validation or holdout analysis, or at minimum bootstrap confidence intervals on the SSR ratios, to support the claim that the new parameters are a robust improvement rather than an artifact of fitting the calibration data.
[Sec. 3, Eq. (3.1) and Table 1] The text states that the global fit considers all datasets 'with same weight,' but Eq. (3.1) assigns per-dataset weights 1/[n_i (RMS_i^best)^2], which depend on the dataset and on an intermediate fit. If the intended meaning is that all measurements receive equal weight, the formula should be clarified; if the intended meaning is per-dataset weighting, the wording is misleading. This distinction matters for interpreting the relative importance of the charge and light datasets in the fit.
[Sec. 3, Table 1] No global goodness-of-fit statistic, per-dataset chi^2, p-value, or number of data points per dataset is reported. For a nine-parameter fit with model-tuned weights, the statement that minimization provides a 'satisfactory estimate' is unsupported without a quantitative check of fit quality. Please report the actual SSR_i values, the number of measurements n_i, and a global chi^2 or equivalent statistic, together with the parameter covariance matrix.
[Sec. 2, Eq. (2.4)] The claimed improvement is conditional on the assumed functional forms f_corr = exp(-E/(alpha ln(dE/dx)+beta)) and chi0 = A/[B + exp(C + D dE/dx)]. The manuscript does not test alternative forms or examine residual structure as a function of E and dE/dx. If these phenomenological forms are inadequate in some region of the stated validity range, the re-fitted parameters are still an improvement only within the chosen ansatz. Showing residual plots for all datasets at all fields, or a brief comparison with a simple alternative form, would substantially strengthen the conclusion.
[Sec. 3, Fig. 2] The MicroBooNE comparison is presented as a visible improvement, but no quantitative metric is given for the agreement between the updated LArQL curve and the MicroBooNE data. Since this is the only external validation in the paper, I ask for a numerical measure (e.g., chi^2, RMS, or mean absolute difference over the plotted points) and a statement of whether the displayed data were used in any stage of the fit.

minor comments (4)

[Sec. 3] There is a typo: 'stablish' should be 'establish'.
[Fig. 1 caption] The right panel is described as 'S1/S10' in the text but the caption uses 'S'; please define the ratio and its normalization consistently.
[Sec. 1 and Sec. 2] The stated validity range is 0-0.75 kV/cm and 2-40 MeV/cm, but the manuscript does not list the electric-field values and dE/dx ranges actually covered by the fitted datasets. A table of datasets with their field configurations and point counts would help readers assess coverage and the possibility of extrapolation.
[Table 1] In the caption, it would be helpful to state explicitly that the original A, B, C, D values had no uncertainties, whereas the original A_B and k_B uncertainties are from [7]; the current wording is ambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is an openly calibrated re-fit of a phenomenological model, not a derivation that assumes its conclusion.

full rationale

The paper's central claim is that a global weighted fit of the LArQL parameters to published ICARUS charge data and ARIS light data reduces the sum of squared residuals relative to the original LArQL parameter set. This is explicitly a fit, not a prediction: Section 2 states that 'Both χ0 and fcorr are phenomenological, fitted to data,' and Section 3 describes minimizing the weighted sum of squared residuals. The SSR reductions are in-sample comparisons of two parameter sets on the same data, which is a calibration statement, not a circular derivation. The functional forms in Eq. (2.4) are assumed, but assuming a parametric form is a modeling choice rather than a definitional reduction. The weighting by RMS_i_best from intermediate fits does use the data twice, but that affects statistical robustness, not the logical dependence of the result on its inputs. The MicroBooNE dQ/dx comparison (Fig. 2) uses data not included in the fit, providing an external check even though it is only visual. Citations to the authors' earlier LArQL paper [6] are used only to define the baseline parameter values and search ranges; they are not invoked as evidence that the new fit is correct. No equation is asserted to derive a quantity from another quantity that was defined in terms of it, and no fitted parameter is renamed as a prediction. Therefore no circular step can be identified under the required standard.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The LArQL parameter update rests on the chosen phenomenological forms, the assumption that published datasets are mutually consistent, and a weighted least-squares framework whose weights are estimated from intermediate fits to the same data. All parameters in Table 1 are free parameters fitted to data.

free parameters (9)

A_B = 0.808(2)
Birks charge yield constant, fitted here within 3 sigma of the ICARUS value from [7]; strongly correlated with k_B as shown in Fig. 2.
k_B = 49.7(4) gV/(MeV cm3)
Birks recombination constant, fitted within 3 sigma of [7]; pairs with A_B in the first term of Eq. (2.3).
alpha = 0.0387(8) cm/kV
Field-dependence parameter of the escape-electron correction f_corr in Eq. (2.4).
beta = 0.0128(6) cm/kV
Second field-dependence parameter of f_corr in Eq. (2.4).
A = 3.61(5)e-3
Shape parameter of chi0, the zero-field escaping-electron fraction in Eq. (2.4).
B = -5.7(1)
Shape parameter of chi0 in Eq. (2.4).
C = 1.74(2)
Shape parameter of chi0 in Eq. (2.4).
D = 2.01(3)e-4 cm/MeV
dE/dx dependence parameter of chi0 in Eq. (2.4).
Per-dataset weights = not reported; obtained from intermediate fits
Weights 1/(n_i RMS_i^2) are estimated from fits of the same LArQL model to the same datasets used in the global fit, so they are not independent of the final result.

assumptions (5)

domain assumption Residuals of all data groups are normally distributed
Explicitly assumed in Section 3 before defining WSSR in Eq. (3.1); if false, the weighted least-squares parameter estimates and uncertainties are not well grounded.
domain assumption Birks charge recombination formula with A_B and k_B is a valid base model in the stated field and dE/dx ranges
LArQL Eq. (2.3) starts from the Birks formula with parameters from ICARUS [7]; this is the accepted empirical base for the charge term.
ad hoc to paper The f_corr and chi0 functional forms in Eq. (2.4) capture the escape-electron physics
These forms are phenomenological and fitted; no first-principles derivation is given, so the functional form is a load-bearing assumption.
domain assumption Published charge and light datasets from [5,7,8] are mutually consistent and their systematic uncertainties are negligible or properly encoded in weights
The global fit pools data from different experiments without modeling their systematic offsets; any inconsistency is absorbed by the weights.
ad hoc to paper The search region around the original LArQL parameter values contains the true global optimum
The optimization restricted ranges to values around [6] and rejected large variations that degraded some datasets, so the existence of a better minimum outside that region is not demonstrated.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Updated parameters of the LArQL model." pith.science (2026). https://pith.science/paper/AYF5VFHB

@misc{pith2026250417866,
  author       = {Pith},
  title        = {Pith review of: Updated parameters of the LArQL model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AYF5VFHB}},
  note         = {Machine review of arXiv:2504.17866}
}

read the original abstract

The need for a microscopic description of scintillation light generation in liquid argon becomes increasingly desirable with the upcoming operation of large scale LArTPCs in the next decade. While a detailed mathematical account of the process is still to be achieved, a phenomenological model for simultaneously treating ionization and scintillation, LArQL, has been successfully employed to describe the range of electric fields from 0 to 0.75 kV/cm and dE/dx from 2 to 40 MeV/cm providing the anti-correlation between the free ionization charge and scintillation light. A reanalysis of the original model parameter values has been performed within a global fit procedure and is presented.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

11 extracted references · 6 canonical work pages

[7]

Marinho, L

F. Marinho, L. Paulucci, D. Totani and F. Cavanna, LArQL: a phenomenological model for treating light and charge generation in liquid argon , https://doi.org/DOI JINST 17 (2022) C07009

work page 2022
[1]

write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...
[2]

Conti et al., Correlated fluctuations between luminescence and ionization in liquid xenon , https://doi.org/10.1103/PhysRevB.68.054201 Phys

E. Conti et al., Correlated fluctuations between luminescence and ionization in liquid xenon , https://doi.org/10.1103/PhysRevB.68.054201 Phys. Rev. B 68 (2003) 054201 [ https://arxiv.org/abs/hep-ex/0303008 hep-ex/0303008 ]

arXiv 2003
[3]

Kubota et al., Recombination luminescence in liquid argon and in liquid xenon, Phys

S. Kubota et al., Recombination luminescence in liquid argon and in liquid xenon, Phys. Rev. B 17 (1978) 2762

work page 1978
[4]

Doke, Fundamental properties of liquid argon, krypton and xenon as radiation detector media, Portugal Phys

T. Doke, Fundamental properties of liquid argon, krypton and xenon as radiation detector media, Portugal Phys. 12 (1981) 9

work page 1981
[5]

Doke et al., Let dependence of scintillation yields in liquid argon, Nucl

T. Doke et al., Let dependence of scintillation yields in liquid argon, Nucl. Instrum. Meth. A 269 (1988) 291

work page 1988
[6]

T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, H. Okada and E. Shibamura, Absolute scintillation yields in liquid argon and xenon for various particles , https://doi.org/DOI Jpn. J. Appl. Phys. 41 (2002) 1538

work page 2002
[8]

Amoruso et al., Study of electron recombination in liquid argon with the ICARUS TPC , https://doi.org/DOI Nucl

S. Amoruso et al., Study of electron recombination in liquid argon with the ICARUS TPC , https://doi.org/DOI Nucl. Instrum. & Methods A 523 (2004) 275

work page 2004

Show all 11 references

[9]

Agnes et al., Measurement of the liquid argon energy response to nuclear and electronic recoils , https://doi.org/10.48550/arXiv.1801.06653 Phys

P. Agnes et al., Measurement of the liquid argon energy response to nuclear and electronic recoils , https://doi.org/10.48550/arXiv.1801.06653 Phys. Rev. D 97 (2018) 112005 [ https://arxiv.org/abs/1801.06653 1801.06653 ]

2018 doi arXiv
[10]

C. Adams et al., Calibration of the charge and energy loss per unit length of the MicroBooNE liquid argon time projection chamber using muons and protons , https://doi.org/10.48550/arXiv.1907.11736 JINST 15 (2020) P03022 [ https://arxiv.org/abs/1907.11736 1907.11736 ]

2020 doi arXiv
[11]

Church, ``Larsoft: A software package for liquid argon time projection drift chambers.'' arXiv:1311.6774 [physics.ins-det], https://larsoft.org/

E.D. Church, ``Larsoft: A software package for liquid argon time projection drift chambers.'' arXiv:1311.6774 [physics.ins-det], https://larsoft.org/

arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [7]

Marinho, L

F. Marinho, L. Paulucci, D. Totani and F. Cavanna, LArQL: a phenomenological model for treating light and charge generation in liquid argon , https://doi.org/DOI JINST 17 (2022) C07009

work page 2022

[2] [1]

write newline

" write newline "" before.all 'output.state := FUNCTION blank.sep after.quote 'output.state := FUNCTION fin.entry output.state after.quoted.block = 'skip 'add.period if write newline FUNCTION new.block output.state before.all = 'skip output.state after.quote = after.quoted.block 'output.state := after.block 'output.state := if if FUNCTION new.sentence out...

[3] [2]

Conti et al., Correlated fluctuations between luminescence and ionization in liquid xenon , https://doi.org/10.1103/PhysRevB.68.054201 Phys

E. Conti et al., Correlated fluctuations between luminescence and ionization in liquid xenon , https://doi.org/10.1103/PhysRevB.68.054201 Phys. Rev. B 68 (2003) 054201 [ https://arxiv.org/abs/hep-ex/0303008 hep-ex/0303008 ]

arXiv 2003

[4] [3]

Kubota et al., Recombination luminescence in liquid argon and in liquid xenon, Phys

S. Kubota et al., Recombination luminescence in liquid argon and in liquid xenon, Phys. Rev. B 17 (1978) 2762

work page 1978

[5] [4]

Doke, Fundamental properties of liquid argon, krypton and xenon as radiation detector media, Portugal Phys

T. Doke, Fundamental properties of liquid argon, krypton and xenon as radiation detector media, Portugal Phys. 12 (1981) 9

work page 1981

[6] [5]

Doke et al., Let dependence of scintillation yields in liquid argon, Nucl

T. Doke et al., Let dependence of scintillation yields in liquid argon, Nucl. Instrum. Meth. A 269 (1988) 291

work page 1988

[7] [6]

T. Doke, A. Hitachi, J. Kikuchi, K. Masuda, H. Okada and E. Shibamura, Absolute scintillation yields in liquid argon and xenon for various particles , https://doi.org/DOI Jpn. J. Appl. Phys. 41 (2002) 1538

work page 2002

[8] [8]

Amoruso et al., Study of electron recombination in liquid argon with the ICARUS TPC , https://doi.org/DOI Nucl

S. Amoruso et al., Study of electron recombination in liquid argon with the ICARUS TPC , https://doi.org/DOI Nucl. Instrum. & Methods A 523 (2004) 275

work page 2004