Facilitating neutron and energy reconstruction in neutrino events using the direction of tagged neutrons

David Last; Hilary Utaegbulam; Mitchell Lahare; Steven Manly

REVIEW 4 major objections 6 minor 18 references

Facilitating neutron and energy reconstruction in neutrino events using the direction of tagged neutrons

T0 review · 4 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that combining a tagged neutron's direction with missing transverse momentum recovers the neutron's kinetic energy and noticeably improves reconstructed neutrino energy resolution.

desk verdict A plausible new estimator for neutron kinetic energy that improves reconstructed Eν in simulation, but the gains rest on an untested no-scattering direction assumption and a per-channel bias correction fitted on the same sample. read the letter →

arxiv 2509.17123 v2 pith:OVUGP3PC submitted 2025-09-21 hep-ex nucl-ex

Steven Manly , Mitchell Lahare , Hilary Utaegbulam , David Last This is my paper · ORCID

classification hep-exnucl-ex

keywords neutrinoenergyreconstructionneutrontaggingkineticmissingtransversemomentumliquidargondetectorsscintillatorcharged-currentinteractionsMonteCarlosimulation

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

This paper proposes a way to include neutrons in event-by-event neutrino energy reconstruction, something accelerator neutrino experiments have struggled to do. The idea is to combine the direction of a detected neutron energy deposit, pointing back to the neutrino interaction vertex, with the missing transverse momentum of the reconstructed charged particles. A simple ratio identity then gives the neutron's momentum magnitude and kinetic energy, and adding that estimate to the calorimetric sum improves the reconstructed neutrino energy resolution and makes its distribution more symmetric about the true value. In the paper's simulation, the neutrino energy width drops from about 16% to 10% for muon neutrinos on argon, and from about 11% to 6.5% for antineutrinos on argon.

What carries the argument

The load-bearing object is the lever-arm ratio identity of Eq. (1), $|\vec{p}_n| = |\vec{p}_{T,n}|\,|\vec{R}_n|/|\vec{R}_{T,n}|$, which converts a transverse-plane momentum balance into a full three-dimensional neutron momentum. It is used in two steps: first project the missing transverse momentum onto the transverse direction of the tagged neutron to get $|\vec{p}_{T,n}|$; then scale by the ratio of the full vertex-to-tag distance to its transverse projection, which accounts for motion out of the transverse plane. The identity's validity rests on the tagged neutron being the dominant missing transverse momentum and on the vertex-to-tag direction approximating the neutron's initial direction. The angle $\Delta\theta_T$ between $\vec{p}_{T,\mathrm{miss}}$ and $\vec{R}_{T,n}$ functions as a diagnostic of when those assumptions break down.

What would settle it

In a Monte Carlo that records both the true initial neutron direction and the direction at the energy deposit, compare the Eq. (1) $T_n$ with the true $T_n$ for events where the neutron scatters before depositing; if the reconstructed $T_n$ is biased exactly in those events, the no-scatter assumption is the cause. Equivalently, in a detector with independent time-of-flight neutron energy measurements, check whether events with large $\Delta\theta_T$ show the predicted loss of accuracy.

Watch

Extended reading notes

Core claim

The paper's central claim is that when a neutron produced in a charged-current neutrino interaction leaves a detectable energy deposit, the three-dimensional vector from the interaction vertex to that deposit is a serviceable stand-in for the neutron's initial direction, and that direction is enough to turn the usual missing-transverse-momentum imbalance into an event-by-event estimate of the neutron's kinetic energy. Concretely, with $\vec{R}_n$ the vertex-to-tag vector and $\vec{R}_{T,n}$ its component transverse to the neutrino beam, the component of the missing transverse momentum $\vec{p}_{T,\mathrm{miss}}$ parallel to $\vec{R}_{T,n}$ is taken to be the neutron's transverse momentum, and the full momentum magnitude follows from the lever-arm identity $|\vec{p}_n| = |\vec{p}_{T,n}|\,|\vec{R}_n|/|\vec{R}_{T,n}|$. From $|\vec{p}_n|$ the neutron kinetic energy $T_n$ follows using the known neutron mass. The paper argues, using generator-level simulations with detector-like thresholds and smearing, that including this $T_n$ in the calorimetric neutrino energy sum yields a reconstructed neutrino energy that is more centered on the true value and has a narrower width: the width measure $\sigma'$ drops from 15.9% to 9.8% for $\nu_\mu$ on argon and from 10.9% to 6.5% for $\bar{\nu}_\mu$ on argon. The same idea is shown to improve the neutron kinetic energy estimate relative to simply identifying $|\vec{p}_n|$ with $|\vec{p}_{T,\mathrm{miss}}|$, and a cut on the angle $\Delta\theta_T$ between the two vectors can enrich hydrogen interactions and suppress flat backgrounds.

Load-bearing premise

The method assumes the straight line from the neutrino vertex to the tagged neutron energy deposit is the neutron's initial direction, with no significant scattering before the deposit and no smearing of that direction.

Editorial extensions

If this is right

Detectors that can tag a neutron's three-dimensional energy deposition and point it back to the interaction vertex can reconstruct that neutron's kinetic energy event by event, without needing time-of-flight.
In the paper's simulation, including the reconstructed neutron narrows the argon neutrino energy width from $\sigma'=15.9\%$ to $9.8\%$ for $\nu_\mu$ and from $10.9\%$ to $6.5\%$ for $\bar{\nu}_\mu$.
A cut on the angle $\Delta\theta_T$ between the missing transverse momentum and the neutron's transverse direction can enrich samples of neutrino interactions on hydrogen and suppress flat backgrounds.
The approach is compatible with liquid argon detectors and with the three-dimensional scintillator detector in the T2K near detector, and it can complement time-of-flight neutron energy measurements.
The largest relative improvement in reconstructed neutrino energy width appears for antineutrino interactions, where neutron production is more important.

Reading between the lines

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

Because the method is most reliable at small $\Delta\theta_T$, that same angle could serve as a per-event quality flag or event weight, providing a simple way to suppress biased events without a full unfolding.
The underlying lever-arm identity is not specific to neutrons; a similar vertex-to-tag direction plus transverse-momentum projection could constrain the energy of other neutral final-state particles that leave a localized energy deposit.
The paper itself notes that a more sophisticated simulation including backgrounds, detection inefficiencies, and better detector effects is needed, especially for hydrogen interactions; the size of the resolution gain in a realistic analysis remains an open question.
Where independent time-of-flight neutron energy is available, combining it with the direction-based estimate would give a cross-check of the no-scatter assumption and potentially a joint estimator with better resolution than either method alone.

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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

What you should know: this paper proposes a new kinematic estimator—Eq. (1)—that combines the 3D direction of a tagged neutron with the missing transverse momentum to infer the neutron's kinetic energy and fold it into the reconstructed neutrino energy. The combination is genuinely new, building on Myatt's old transverse-balance idea but using the tagged neutron's direction instead of the total hadronic momentum. The paper is clearly written, the estimator is sensible, and the authors are honest about several limitations. It is a methods study, not a final demonstration.

What it does well: the GENIE-based setup is straightforward, the detection thresholds and smearing are stated, and they define a robust width metric σ′ for non-Gaussian distributions. They also report channel-dependent results rather than cherry-picking. The idea that a small ΔθT cut could enrich hydrogen interactions in CH is interesting and plausible. The paper explicitly flags that a more sophisticated simulation with backgrounds and better detector effects is needed, which is credit where it is due.

The soft spots are real but proportionate. The load-bearing assumption, stated in Sec. III A, is that the vector from the neutrino vertex to the tagged energy deposition equals the neutron's initial direction, and that this quantity was not smeared. Real neutrons scatter before depositing energy, especially in argon. The stress-test note is right: this is the main reason the reported gains may be optimistic. The paper does not model neutron transport or multi-neutron events, where the other neutrons corrupt pT,miss,reco.

More telling: Table II shows that the new method's Tn resolution σ′ is worse than the pT-balance method in every channel (e.g., 1.340 vs 0.781 for νμ on C). The neutrino energy resolution improves not because the Tn estimate is tighter, but because it is better centered after a per-channel mean bias correction fitted to the same simulation used for scoring. That circularity is not fatal for a methods study, but it means the reported Eν gains are not yet evidence of a robust improvement. No error bars, background model, or code are provided.

Bottom line: the core idea is worth taking seriously, but the central claims as stated overreach the simulation. A serious referee should push for a validation on a separate sample, a realistic neutron-scattering model, and a clearer statement of which channels actually benefit. For someone working on neutron reconstruction in LArTPCs or SuperFGD, this is a useful starting point.

Recommendation: send it to peer review. It deserves referee time, even though heavy revision is likely.

Referee Report

4 major / 6 minor

Summary. The paper proposes a method to estimate the kinetic energy of a tagged neutron in charged-current neutrino interactions by combining the direction from the interaction vertex to the tagged energy deposition with the reconstructed missing transverse momentum. Equation (1) sets the neutron momentum magnitude using the component of the missing transverse momentum parallel to the projected neutron direction. The method is evaluated with GENIE simulations for carbon and argon targets under T2K-like and DUNE-like fluxes, with nominal detection thresholds and momentum/angular smearing; the resulting neutron kinetic energy is added to a calorimetric sum to reconstruct the neutrino energy. The authors report improved centeredness and, for most channels, improved width (sigma') of the reconstructed neutrino energy, and they suggest that a cut on the opening angle Delta_theta_T can enrich a sample of interactions on hydrogen. The paper is a generator-level methods study with explicit acknowledgement that a more sophisticated simulation, including backgrounds and detector effects, is needed.

Significance. If the technique survives a more realistic simulation, it would be a useful and inexpensive addition to neutron-inclusive reconstruction in liquid argon and scintillator detectors, complementing time-of-flight methods and providing a way to include a fraction of produced neutrons in event-by-event neutrino energy reconstruction. The paper is commendable for defining a robust non-Gaussian width metric, making generator and flux choices explicit, and comparing against two baseline algorithms. However, the quantitative claims are conditionally supported by an idealized simulation: the neutron direction is taken as the unsmeared vertex-to-deposit vector, non-tagged neutrons are ignored in the missing transverse momentum, and the mean kinetic energy bias is corrected using the same simulated sample that is used to evaluate the resolution. These limitations make the reported resolutions optimistic and model-dependent, so the significance of the result is not yet established at the level claimed in the abstract.

major comments (4)

[Sec. III A, Eq. (1)] The central estimator assumes that the initial neutron direction is equal to the spatial vector from the neutrino interaction point to the tagged energy deposition, and the text states 'This quantity was not smeared.' Real neutrons can scatter before depositing energy, especially in argon and at higher kinetic energies, so the vertex-to-deposit vector need not point along the initial neutron direction. Because this assumption directly feeds Eq. (1), the reported Tn and neutrino-energy resolutions are likely optimistic. I request a sensitivity study that smears or perturbs the neutron direction according to a scattering model, or a generator-level study including final-state interactions and neutron transport, with the effect on the quoted sigma' values quantified.
[Sec. III A] The study selects only the highest-kinetic-energy neutron as the tagged candidate and states that 'Produced neutrons, other than the one considered to be tagged, were ignored as undetected particles.' In events with more than one produced neutron, the reconstructed missing transverse momentum p_T,miss,reco contains contributions from all unreconstructed particles, not just the tagged neutron, so the identification of p_T,miss,reco with the tagged neutron's transverse momentum fails. The paper should report the fraction of selected events with additional neutrons above the detection threshold and show how the Tn and neutrino-energy resolutions change when such events are excluded or treated differently.
[Table II] The claim that including the neutron improves the neutrino energy resolution is not uniform across channels. For nu_mu on carbon, the full correction yields sigma' = 0.151 for E_nu, slightly worse than the no-correction value of 0.149; for the Tn reconstruction, the full-direction method has a larger sigma' than the transverse-balance method in every channel (for example, 1.340 versus 0.781 for nu_mu on carbon). The abstract and conclusions emphasize improved resolution and symmetry, but the actual improvement for Tn is in centeredness rather than width. This distinction should be made explicitly, and the channel dependence should be discussed rather than glossed over.
[Sec. III B] The 'correction for the mean kinetic energy bias using the simulation' is an in-sample calibration: a per-channel offset is derived from the same simulated sample that is then used to compute the reported sigma' values. This procedure can artificially center the reconstructed distributions and makes the quoted resolutions dependent on the generator tune and flux model. The authors should specify how many parameters are fitted, how large the offsets are relative to the signal, and ideally validate the correction on an independent simulated sample or with a different generator configuration.

minor comments (6)

[Sec. II] The sentence beginning 'Under the assumption that p_T,miss,reco cos Delta_theta_T ...' is grammatically incomplete and should be rewritten to state that the magnitude |p_T,miss,reco| cos Delta_theta_T is taken to equal the transverse momentum of the tagged neutron.
[Eq. (1)] The notation p_T,n is used both as a vector and as a magnitude; please define it explicitly as a magnitude to avoid confusion.
[Table II] The column labels 'No corr.', 'Trans. corr.', and 'Full corr.' are not defined in the caption or in the text; please define them clearly and relate them to the three algorithms shown in Fig. 5.
[Figs. 3-6] The figures would benefit from self-contained legends and captions that identify the solid, hatched, and dotted histograms; currently the reader must infer the correspondence from the text.
[Sec. III B] The definition of sigma' as the 'half-width of the length that would encompass the central 68% of the events' is ambiguous for asymmetric distributions; please specify whether the quoted values are the average of the two half-widths or the full width divided by two.
[Tables and figures] No statistical uncertainties are quoted for the sigma' values; given the finite simulated sample sizes, a statement about statistical precision would be useful.

Circularity Check

1 steps flagged · score 6.0 of 10

The Tn-centeredness claim is imposed by a simulation-fitted mean-bias correction; the direction-method width is actually worse than pT-balance, so the headline Tn gain reduces to the fit.

fitted input called prediction [Sec. III B (Fig. 4 and Table II)]
"After implementing a ΔθT <30◦ cut and correcting for the mean kinetic energy bias using the simulation, the neutron candidate kinetic energy resolution determined using the technique presented in Sec. II is shown in Fig. 4 in the solid gray histogram."

The mean-bias correction is derived from the same GENIE sample on which the Tn and Eν resolutions are evaluated. Applying that correction to Tn,reco forces the average of (Tn,reco − Tn,true) toward zero, so the abstract's claim that the technique is 'more centered' than assigning |pT,miss,reco| to the neutron is true by construction rather than being an independent property of Eq. (1). Table II confirms the direction method has larger σ′ for KEn than the pT-balance method in every channel (e.g., 1.340 vs 0.781 for νμ on C), so the reported Tn advantage is essentially the fitted centering. The pT-balance comparator is not given the same correction, making the comparison partly an artifact of the fit.

full rationale

The core estimator in Eq. (1) is a kinematic construction, not a fit: it combines the tagged-neutron direction with pT,miss,reco to infer |pn|, and the paper acknowledges the similarity to Myatt's transverse-momentum-balance approach. That part is not circular. The circularity is concentrated in the evaluation: the 'full' Tn and Eν results are presented after 'correcting for the mean kinetic energy bias using the simulation' on the same events used to build the resolution plots. Because the correction is an in-sample fit to the very quantity being reported, the improved centeredness of Tn is enforced rather than demonstrated. Table II strengthens this reading: the full direction-based KEn width is worse than the pT-balance width in every channel, so the only Tn gain claimed is the fitted centering. The Eν improvements, particularly for argon, may have some independent content, but they too are reported after the same simulation-derived correction and without a validation sample. The unsmeared assumption that the vertex-to-deposit vector equals the neutron direction is a modeling limitation, not circularity, as are the ignored extra neutrons. There are no load-bearing self-citations. Overall, the central Tn prediction partially reduces to a fitted input, while the Eν claim retains some independent content, giving a score of 6.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The method relies on two kinematic assumptions (transverse balance and the projection identity), the untested tag-direction assumption, and a simulation-derived bias correction. There are no new physical entities. The free parameters are the bias correction and two hand-chosen cuts; each is fitted or selected on the same simulation used for the resolution claims.

free parameters (3)

Mean Tn bias correction per channel = Not quoted; applied per channel in Sec. III B
Correcting for the mean kinetic energy bias using the simulation is a per-event-type offset inferred from the same simulation sample used to evaluate the resolution. It directly improves the apparent centering of Tn and neutrino energy distributions.
Delta_theta_T selection threshold = 30 degrees for inclusive samples; 10 degrees for H-enriched CH sample
Chosen by hand. The cut is motivated by the expected flat background distribution, but its value is not optimized or justified quantitatively.
Neutron candidate selection threshold = Tn > 20 MeV; highest-Tn neutron chosen
Hand-chosen requirement that a neutron could leave a detectable deposition. It affects all results and is not varied or justified with a dedicated study.

assumptions (4)

domain assumption Transverse momentum is conserved for the reconstructed charged particles and the tagged neutron.
The method assumes the transverse momentum sum of reconstructed particles plus the tagged neutron balances, ignoring nuclear effects, recoil, and other unreconstructed particles (Sec. II). The paper acknowledges this and uses Delta_theta_T as a diagnostic.
domain assumption The missing transverse momentum component parallel to the neutron transverse direction equals the neutron transverse momentum magnitude.
Eq. (1) and the text: 'Under the assumption that p_T,miss,reco cos Delta_theta_T ... is equal to the magnitude of the transverse momentum of the tagged neutron.' This is the core kinematic assumption; the paper partially tests it against truth in simulation.
ad hoc to paper The spatial vector from the neutrino vertex to the neutron energy deposition gives the initial neutron direction.
Stated in Sec. III A: 'it was assumed that the spatial vector from the neutrino interaction point to the tagged energy deposition gave a good measure of the initial direction of the neutron. This quantity was not smeared.' Neutron scattering before the tag is not modeled.
domain assumption GENIE 3.04.02 with tune G18_02a_00_000 faithfully models the neutrino interactions and nuclear effects.
All conclusions depend on this generator and tune for the truth-level events; detector effects are simplified thresholds and Gaussian smears (Table I). No comparison to data is made.

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Cite this review

Pith. "Pith review of Facilitating neutron and energy reconstruction in neutrino events using the direction of tagged neutrons." pith.science (2026). https://pith.science/paper/OVUGP3PC

@misc{pith2026250917123,
  author       = {Pith},
  title        = {Pith review of: Facilitating neutron and energy reconstruction in neutrino events using the direction of tagged neutrons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OVUGP3PC}},
  note         = {Machine review of arXiv:2509.17123}
}

read the original abstract

To date, accelerator neutrino experiments have had only limited success including neutrons in the neutrino event reconstruction event by event. Produced neutrons often interact in a detector leaving an energy deposition that does not correlate strongly with the kinetic energy of the neutron. This work explores the inclusion of the direction of a neutron tagged by such an energy deposition in concert with the missing transverse momentum of the reconstructed particles to determine the approximate kinetic energy of the neutron and modify the reconstruction of the energy of the incoming neutrino. The technique significantly increases the neutron kinetic energy estimation relative to one that assigns the neutron kinetic energy by enforcing transverse momentum balance alone. When included in the neutrino energy calculation, the neutrino energy resolution is improved and the reconstructed energy is distributed more symmetrically around the true value. The technique shows promise and might be used to good effect to analyze data taken with experiments able to tag neutron energy deposits with good neutron direction resolution such as the T2K near detector and the liquid argon detectors in the SBN program and DUNE.

Figures

Figures reproduced from arXiv: 2509.17123 by the authors.

**Figure 2.** FIG. 2. View of transverse plane of the interaction toward the incoming neutrino direction showing [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3. These plots show ∆ [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. These plots show the reconstructed T [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: FIG. 5. These plots show the reconstructed (anti)neutrino energy resolution for the selected events. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: FIG. 6. The energy resolution for antineutrino interactions on CH in a T2K-like flux. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

Review history (2 revisions) →

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Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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Abreuet al.(SoLid Collaboration), A novel segmented-scintillator antineutrino detector, Journal of Instrumentation12(04), P04024–P04024

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