arxiv: 2511.11149 · v2 · submitted 2025-11-14 · ⚛️ physics.data-an · hep-ex

The High W Challenge: Robust Neutrino Energy Estimators for LArTPCs

Christopher Thorpe , Elena Gramellini This is my paper

Pith reviewed 2026-05-17 22:39 UTC · model grok-4.3

classification ⚛️ physics.data-an hep-ex

keywords neutrino energy estimationLArTPChadronic invariant massoscillation analysisenergy estimatorfinal state interactionsdeep inelastic scattering

0 comments p. Extension

The pith

A new W²-based neutrino energy estimator using hadronic invariant mass shows the smallest bias and greatest stability against mismodelling in LArTPCs.

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

The paper introduces the W²-based estimator for neutrino energy, calculated from the final-state hadronic invariant mass, for use in liquid argon time-projection chambers with broadband beams. This targets the transition region between shallow and deep inelastic scattering where energy reconstruction is difficult. The new method is compared to four standard estimators through a toy long-baseline oscillation analysis that extracts δ_CP and Δm²_23. It exhibits the smallest bias versus true neutrino energy and remains stable when models of lepton angle, momentum, missing energy, hadronic mass or final-state interactions are imperfect. The approach is inclusive, applying to events with at least one proton and any number of pions, and is positioned to complement more exclusive high-resolution techniques.

Core claim

The W²-based estimator shows the smallest bias as a function of true neutrino energy and is particularly stable against the mismodelling of lepton scattering angle and momentum, missing energy, hadronic invariant mass and final state interactions, though this comes with somewhat worse energy resolution when perfect modeling is assumed.

What carries the argument

The W²-based estimator, which reconstructs neutrino energy from the measured final-state hadronic invariant mass for inclusive events containing at least one proton and any number of pions.

If this is right

Choice of energy estimator directly affects the extracted values of δ_CP and Δm²_23 in long-baseline oscillation measurements.
An inclusive estimator valid for events with protons and pions can be combined with exclusive methods to cover different event classes.
Detailed comparison of bias and resolution across estimators informs which to use or combine in future LArTPC analyses.

Where Pith is reading between the lines

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

Pairing the W² estimator with high-resolution exclusive techniques could improve both bias control and overall precision in a single analysis.
Application to actual detector data with varied beam conditions would test stability beyond the toy mismodelling scenarios used here.
The invariant-mass approach may extend to other neutrino detectors operating in similar energy ranges where model uncertainties dominate.

Load-bearing premise

The toy long-baseline oscillation analysis and the assumed mismodelling scenarios sufficiently capture the dominant uncertainties present in real LArTPC data taking and reconstruction.

What would settle it

A test that applies all five estimators to real LArTPC data from a neutrino beam where true energy can be inferred independently, such as from a near detector with known flux, and checks whether the W² estimator retains the smallest bias.

Figures

Figures reproduced from arXiv: 2511.11149 by Christopher Thorpe, Elena Gramellini.

**Figure 2.** Figure 2: FIG. 2. Confusion matrices describing the smearing from true neutrino energy to estimated neutrino energy using each energy [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. The distribution of fractional error in neutrino en [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Fractional bias and variance as a function of true neu [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Comparison of the biases in neutrino energy when calculated using different event generators, for each method of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Fractional bias as a function of true neutrino energy, calculated before and after simulating final state interactions. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Fractional change in the estimated neutrino energy due to FSI for each estimation method. The CCQE-like method is [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Fractional bias and variance as a function of visible hadronic invariant mass. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Fractional bias and variance as a function of missing hadronic energy. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Fractional bias and variance as a function of the lepton scattering angle. [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Relative exclusion power of different estimators, expressed as the ratio of [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Bias in extracted ∆ [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Dependence of energy bias on visible hadronic in [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. Oscillation fits when events are selected by visible [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15. Change in reconstructed energy bias as a func [PITH_FULL_IMAGE:figures/full_fig_p016_15.png] view at source ↗

**Figure 16.** Figure 16: FIG. 16. Oscillation fits under restrictions on missing [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗

**Figure 17.** Figure 17: FIG. 17. Change in average bias as a function of a cut on [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗

**Figure 18.** Figure 18: FIG. 18. Extracted oscillation parameters when restricting [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗

read the original abstract

Accurate determination of the neutrino energy is central to precision oscillation measurements. In this work, we introduce the W$^2$-based estimator, a new neutrino energy estimator based on the measurement of the final-state hadronic invariant mass. This estimator is particularly designed to be employed in liquid-argon time-projection chambers exposed to broadband beams that span the challenging transition region between shallow inelastic scattering and deep inelastic scattering. The performance of the W$^2$-based estimator is compared to four other commonly used estimators. The impact of the estimator choice is evaluated by performing measurements of $\delta_{CP}$ and $\Delta m^2_{23}$ in a toy long-baseline oscillation analysis. We find that the W$^2$-based estimator shows the smallest bias as a function of true neutrino energy and it is particularly stable against the mismodelling of lepton scattering angle and momentum, missing energy, hadronic invariant mass and final state interactions. However, studies of the resolution of each estimator as a function of true neutrino energy show this is somewhat offset by worse energy resolution when perfect modeling of these quantities is assumed. This estimator is valid for events with at least one proton and any number of pions; an inclusive channel that complements the strength of more exclusive methods that optimize the energy resolution. By providing a detailed analysis of the strengths, weaknesses and domain of applicability of each estimator, this work informs the combined use of energy estimators in any future LArTPC-based oscillation analysis.

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.

Desk Editor's Note private letter to a colleague

The W² estimator is a solid incremental step for robustness in high-W neutrino energy reconstruction, but the toy mismodelling leaves its real stability open to question.

read the letter

The key takeaway is that this paper introduces a W²-based neutrino energy estimator using hadronic invariant mass, tailored for the high-W transition in broadband beams, and shows it has the smallest bias versus true energy plus better stability than four other estimators under specific mismodelling in a toy oscillation analysis. It targets inclusive events with at least one proton and any number of pions, which fills a gap alongside exclusive methods that prioritize resolution. The comparison and the reported trade-off in resolution when modeling is perfect are useful practical details for LArTPC work. The toy study on delta_CP and Delta m^2_23 gives a sense of downstream impact. The stress-test concern holds up: the mismodelling appears to use independent parameter shifts rather than the correlated detector effects common in real LArTPCs, such as recombination or space charge linking lepton and hadronic observables. That makes the stability claim plausible within the toy but not yet general. The abstract and methods outline are clear enough on the estimator definition and domain, with no obvious circularity since performance is checked on independent toy data. This is aimed at neutrino oscillation groups running or planning LArTPC analyses who need to weigh estimator choices. A reader focused on energy reconstruction or systematic robustness would find concrete comparisons here. It deserves peer review; the physics grounding is straightforward and the topic matters for precision measurements, even with the toy limitations that referees could address.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces the W²-based neutrino energy estimator, derived from the final-state hadronic invariant mass, for use in LArTPCs with broadband beams spanning the shallow-to-deep inelastic scattering transition. It compares performance against four other common estimators in terms of bias versus true neutrino energy, resolution, and stability under mismodelling of lepton kinematics, missing energy, hadronic invariant mass, and final state interactions. These properties are assessed via their impact on δ_CP and Δm²_23 extraction in a toy long-baseline oscillation analysis; the W² estimator is reported to exhibit the smallest bias and greatest stability, at the cost of somewhat worse resolution, for an inclusive selection requiring at least one proton and any number of pions.

Significance. If the reported robustness to mismodelling holds under more realistic conditions, the W² estimator would provide a useful inclusive complement to exclusive methods that optimize resolution, informing combined-estimator strategies for precision oscillation analyses in experiments such as DUNE. The explicit trade-off analysis between bias stability and resolution is a constructive contribution to the field.

major comments (1)

[Toy oscillation analysis and mismodelling description] Toy long-baseline oscillation analysis and mismodelling implementation: the stability claims rest on independent parameter variations for lepton scattering angle/momentum, missing energy, hadronic invariant mass, and FSI. This does not incorporate realistic correlations (e.g., between hadronic energy scale and lepton kinematics arising from recombination, space charge, or PID inefficiencies in LArTPCs). Because the central robustness result is demonstrated only within this toy framework, the generalizability of the smallest-bias and stability conclusions requires either additional correlated-mismodelling tests or explicit justification that the independent variations suffice.

minor comments (2)

[Abstract] The abstract refers to 'four other commonly used estimators' without naming them; listing the specific alternatives (e.g., calorimetric, kinematic, etc.) would improve immediate clarity for readers.
[Results figures] Ensure that all plots of bias and resolution versus true neutrino energy include explicit statements of the event selection and the exact definition of the W² estimator (including any cuts on hadronic invariant mass) in the figure captions or accompanying text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We appreciate the referee's thoughtful review and positive comments on the significance of our manuscript. We address the major comment regarding the toy oscillation analysis and mismodelling implementation below.

read point-by-point responses

Referee: Toy long-baseline oscillation analysis and mismodelling implementation: the stability claims rest on independent parameter variations for lepton scattering angle/momentum, missing energy, hadronic invariant mass, and FSI. This does not incorporate realistic correlations (e.g., between hadronic energy scale and lepton kinematics arising from recombination, space charge, or PID inefficiencies in LArTPCs). Because the central robustness result is demonstrated only within this toy framework, the generalizability of the smallest-bias and stability conclusions requires either additional correlated-mismodelling tests or explicit justification that the independent variations suffice.

Authors: We thank the referee for highlighting this important aspect of our analysis. Our toy long-baseline oscillation study indeed relies on independent variations of the mismodelling parameters to assess the stability of the estimators. This methodology enables us to evaluate the effect of each mismodelling source in isolation, providing clear insights into which aspects the W²-based estimator is particularly robust against. We acknowledge that realistic correlations between these parameters, arising from detector effects in LArTPCs, are not included in the current implementation. To address this, we will add an explicit discussion in the revised manuscript justifying the use of independent variations for the purposes of this study and noting the limitations regarding generalizability to fully correlated scenarios. We believe that this approach still supports our conclusions about the relative performance of the estimators, as the independent variations represent a conservative test of robustness. revision: partial

Circularity Check

0 steps flagged

No circularity in estimator definition or validation

full rationale

The W²-based estimator is defined directly from the physical observable of final-state hadronic invariant mass for events with at least one proton. Performance claims (smallest bias as function of true neutrino energy, stability under mismodelling of lepton kinematics, missing energy, hadronic mass, and FSI) are obtained by explicit comparison against four other estimators inside an independent toy long-baseline oscillation analysis that uses separate Monte Carlo samples. No step equates a derived quantity to its own fitting procedure, no load-bearing self-citation supplies a uniqueness theorem, and the central results are externally falsifiable against the toy benchmarks rather than being tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the toy simulation as a proxy for real experimental conditions and on the assumption that hadronic invariant mass can be reconstructed with sufficient accuracy in LArTPCs.

axioms (1)

domain assumption The toy long-baseline oscillation analysis accurately represents the dominant experimental uncertainties and reconstruction effects in real LArTPC data.
Used to evaluate impact on δ_CP and Δm²_23 and to compare estimator performance under mismodelling.

pith-pipeline@v0.9.0 · 5560 in / 1392 out tokens · 34806 ms · 2026-05-17T22:39:10.740734+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

EW²_est = W_vis² − n_p²(m_n − E_b)² − m_l² + 2 n_p (m_n − E_b) E_l / [2(n_p m_n − n_p E_b − E_l + p_l cos θ)]

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · 3 internal anchors

[1]

K. Abeet al.(T2K), Constraint on the mat- ter–antimatter symmetry-violating phase in neutrino os- cillations, Nature580, 339 (2020), [Erratum: Nature 583, E16 (2020)], arXiv:1910.03887 [hep-ex]

work page arXiv 2020
[2]

P. A. Machado, O. Palamara, and D. W. Schmitz, The Short-Baseline Neutrino Program at Fermilab, Ann. Rev. Nucl. Part. Sci.69, 363 (2019), arXiv:1903.04608 [hep- ex]

work page arXiv 2019
[3]

R. Acciarriet al.(DUNE), Long-Baseline Neutrino Fa- cility (LBNF) and Deep Underground Neutrino Exper- iment (DUNE): Conceptual Design Report, Volume 2: The Physics Program for DUNE at LBNF, (2015), arXiv:1512.06148 [physics.ins-det]

work page arXiv 2015
[4]

R. Acciarriet al.(DUNE), Long-Baseline Neutrino Facil- ity (LBNF) and Deep Underground Neutrino Experiment (DUNE): Conceptual Design Report, Volume 1: The LBNF and DUNE Projects, (2016), arXiv:1601.05471 [physics.ins-det]

work page arXiv 2016
[5]

A. P. Furmanski and J. T. Sobczyk, Neutrino energy re- construction from one muon and one proton events, Phys. Rev. C95, 065501 (2017), arXiv:1609.03530 [hep-ex]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[6]

J. Kopp, P. Machado, M. MacMahon, and I. Martinez- Soler, Improving neutrino energy reconstruction with machine learning, (2024), arXiv:2405.15867 [hep-ph]

work page arXiv 2024
[7]

The GENIE Neutrino Monte Carlo Generator

C. Andreopouloset al., The GENIE Neutrino Monte Carlo Generator, Nucl. Instrum. Meth. A614, 87 (2010), arXiv:0905.2517 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[8]

Sobczyk, A

J. Sobczyk, A. Ankowski, K. Graczyk, C. Juszczak, K. Niewczas, R. Banerjee, H. Prasad,et al., NuWro: Monte Carlo Neutrino Event Generator User’s Guide,https://nuwro.github.io/user-guide/(2024), accessed 2025

work page 2024
[9]

Hayato, NEUT, Acta Phys

Y. Hayato, NEUT, Acta Phys. Polon. B33, 2469 (2002)

work page 2002
[10]

O. Buss, T. Gaitanos, K. Gallmeister, H. van Hees, M. Kaskulov, O. Lalakulich, A. Larionov, T. Leupold, J. Weil, and U. Mosel, Transport-theoretical Description of Nuclear Reactions, Phys. Rept.512, 1 (2012)

work page 2012
[11]

Understanding the energy resolution of liquid argon neutrino detectors

A. Friedland and S. W. Li, Understanding the energy resolution of liquid argon neutrino detectors, Phys. Rev. D99, 036009 (2019), arXiv:1811.06159 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[12]

Abratenkoet al.(MicroBooNE), Measurement of sin- gle charged pion production in charged-currentν µ-Ar interactions with the MicroBooNE detector, (2025), arXiv:2509.03628 [hep-ex]

P. Abratenkoet al.(MicroBooNE), Measurement of sin- gle charged pion production in charged-currentν µ-Ar interactions with the MicroBooNE detector, (2025), arXiv:2509.03628 [hep-ex]

work page arXiv 2025
[13]

P. Abratenkoet al.(MicroBooNE), Measurement of the differential cross section for neutral pion produc- tion in charged-current muon neutrino interactions on argon with the MicroBooNE detector, Phys. Rev. D110, 092014 (2024), arXiv:2404.09949 [hep-ex]

work page arXiv 2024
[14]

Abratenkoet al.(MicroBooNE), First study of neu- trino angle reconstruction using quasielasticlike interac- tions in MicroBooNE, Phys

P. Abratenkoet al.(MicroBooNE), First study of neu- trino angle reconstruction using quasielasticlike interac- tions in MicroBooNE, Phys. Rev. D111, 113007 (2025), arXiv:2504.17758 [hep-ex]

work page arXiv 2025
[15]

Abratenkoet al.(MicroBooNE), Differential Cross Section Measurement of Charged Currentνe Interac- tions Without Pions in MicroBooNE, Phys

P. Abratenkoet al.(MicroBooNE), Differential Cross Section Measurement of Charged Currentνe Interac- tions Without Pions in MicroBooNE, Phys. Rev. D106, L051102 (2022), arXiv:2208.02348 [hep-ex]

work page arXiv 2022
[16]

C. Adamset al.(MicroBooNE), Calibration of the charge and energy loss per unit length of the MicroBooNE liquid argon time projection chamber using muons and protons, JINST15(03), P03022, arXiv:1907.11736 [physics.ins- det]

work page arXiv 1907
[17]

Abratenko et al

P. Abratenkoet al.(MicroBooNE), Search for an anoma- lous excess of charged-currentνe interactions without pi- ons in the final state with the MicroBooNE experiment, Phys. Rev. D105, 112004 (2022), arXiv:2110.14065 [hep- 19 ex]

work page arXiv 2022
[18]

P. Abratenkoet al.((MicroBooNE Collaboration)*, Mi- croBooNE), Search for an Anomalous Production of Charged-Currentνe Interactions without Visible Pions across Multiple Kinematic Observables in MicroBooNE, Phys. Rev. Lett.135, 081802 (2025), arXiv:2412.14407 [hep-ex]

work page arXiv 2025
[19]

See Supplemental Material

work page
[20]

Navaset al.(Particle Data Group), Review of particle physics, Phys

S. Navaset al.(Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

work page 2024