arxiv: 2605.05425 · v1 · submitted 2026-05-06 · ✦ hep-ph

Recognition: unknown

Evidence for Q-Dependent Nuclear Transverse-Momentum Redistribution Beyond Broadening from AI-driven analysis of p-Cu Drell-Yan

I. P. Fernando , D. Keller

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:05 UTC · model grok-4.3

classification ✦ hep-ph

keywords Drell-Yannuclear modificationtransverse momentump-Cu collisionstransverse momentum distributionnuclear effectsDrell-Yan process

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The pith

Nuclear modifications in p-Cu Drell-Yan data appear as Q-dependent transverse-momentum redistribution featuring an O(1 GeV) shoulder and probability flow, rather than a universal width increase.

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

The paper extracts a target-side copper transverse-momentum profile from fixed-target p-Cu Drell-Yan data by holding the proton reference fixed and training only an asymmetric kernel in the small-q_T region. In the supported window of 0.15 to 0.46 in x_Cu and 7.5 to 15.75 GeV in Q, the nuclear modification takes the form of a scale-dependent redistribution with a shoulder near 1 GeV and compensating flow to the resolved-tail regions. A sympathetic reader would care because this indicates nuclear transverse-momentum effects involve dynamic, Q-sensitive mechanisms instead of the standard one-parameter broadening picture.

Core claim

By training an asymmetric Cu kernel in the small-q_T region while keeping the proton momentum-space reference fixed, the analysis demonstrates that the nuclear modification is not a universal width increase but a Q-dependent redistribution consisting of an O(1 GeV) shoulder and compensating probability flow between the shoulder and resolved-tail regions.

What carries the argument

The asymmetric Cu kernel trained only in the small transverse-momentum region, which extracts the target-side profile and isolates the redistribution pattern while the proton reference remains fixed.

If this is right

If correct, nuclear transverse-momentum models must replace one-parameter broadening with explicit Q-dependent shoulder structures and probability flows.
The observed conservation of total probability under redistribution implies that integrated cross sections remain stable while differential shapes change with Q.
Nuclear parton distributions that include transverse momentum must be reparametrized to accommodate this non-universal behavior.
Predictions for Drell-Yan spectra at future facilities would need to incorporate the scale-dependent redistribution to match data.

Where Pith is reading between the lines

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

The same extraction method applied to other nuclei such as iron or lead could test whether the shoulder strength scales with nuclear size or density.
Data from higher-Q Drell-Yan measurements at colliders might show whether the redistribution persists, evolves, or saturates beyond the current window.
Linking the shoulder feature to multiple-scattering or saturation dynamics could offer a dynamical origin for the observed probability flow.

Load-bearing premise

The proton momentum-space reference can be held fixed without introducing significant bias or uncertainty into the extracted copper kernel.

What would settle it

Repeating the extraction with a varied proton reference that alters the uncertainties and finding that the Q-dependent shoulder and probability flow both disappear.

Figures

Figures reproduced from arXiv: 2605.05425 by D. Keller, I. P. Fernando.

**Figure 1.** Figure 1: FIG. 1. Representative fixed- view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

read the original abstract

We extract a target-side Cu transverse-momentum profile from fixed-target $p$--Cu Drell--Yan data by holding a momentum-space proton reference fixed and training only an asymmetric Cu kernel in the small-$q_T$ region. In the supported window, $0.15 \le x_{Cu} \le 0.46$ and $7.5 \le Q_M \le 15.75$ GeV, the nuclear modification is not a universal width increase. It appears as $Q$-dependent redistribution: an $\mathcal{O}(1~{\rm GeV})$ shoulder and compensating probability flow between shoulder and resolved-tail regions, beyond one-parameter broadening.

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 paper extracts a Q-dependent shoulder and probability redistribution in the Cu nuclear TMD from p-Cu Drell-Yan by training an asymmetric kernel while fixing the proton reference, but that fixed baseline is the main vulnerability.

read the letter

The main takeaway is that the authors train only an asymmetric copper transverse-momentum kernel on existing p-Cu Drell-Yan data, keep the proton reference fixed, and report that the nuclear modification appears as a Q-dependent O(1 GeV) shoulder plus compensating probability flow between shoulder and tail regions, rather than simple one-parameter broadening. This holds in the window 0.15 ≤ x_Cu ≤ 0.46 and 7.5 ≤ Q ≤ 15.75 GeV. The claim moves past the standard broadening picture used in most nuclear TMD work. The paper does well by letting the data shape the kernel more flexibly than a single width parameter and by clearly stating the kinematic support. That framing is useful for anyone thinking about how nuclear effects enter small-q_T observables. The method shows honest engagement with the limitation of one-parameter models. The soft spot is the fixed proton reference. Any mismatch between that reference and actual p-p behavior in the small-q_T region, especially if the mismatch varies with Q, will be absorbed into the trained Cu kernel and can produce exactly the reported shoulder and redistribution as an artifact. The abstract gives no sign that proton uncertainties were varied or that independent p-p datasets were used for cross-checks, so the central result rests on an untested assumption. Without reported fit quality, error analysis, or tests against other kernels, it is also hard to judge how much the data actually prefer the redistribution picture. This work is for people doing nuclear TMD global fits or Drell-Yan phenomenology who need to decide whether to move beyond broadening. A reader updating nuclear PDFs might want to test the Q-dependent idea, but only after checking the proton baseline. It deserves a serious referee because the claim is concrete, uses real data, and could affect interpretations if the assumption holds. I recommend sending it to peer review with instructions to referees to examine the proton reference robustness and demand quantitative validation.

Referee Report

2 major / 0 minor

Summary. The manuscript extracts a target-side Cu transverse-momentum profile from fixed-target p-Cu Drell-Yan data by holding a proton momentum-space reference fixed and training only an asymmetric Cu kernel in the small-q_T region. In the supported kinematic window 0.15 ≤ x_Cu ≤ 0.46 and 7.5 ≤ Q_M ≤ 15.75 GeV, the nuclear modification is reported as Q-dependent redistribution featuring an O(1 GeV) shoulder and compensating probability flow between shoulder and resolved-tail regions, rather than a universal one-parameter broadening.

Significance. If the central claim survives scrutiny of the proton reference uncertainties, the result would indicate non-trivial nuclear TMD modifications beyond standard broadening, with potential implications for global nuclear TMD fits and interpretations of p-A collisions. The AI-driven asymmetric kernel training represents a methodological innovation that, if validated with quantitative metrics, could strengthen the paper's contribution to the field.

major comments (2)

[Abstract and analysis procedure] Analysis procedure (as summarized in the abstract): The proton reference is held fixed while the asymmetric Cu kernel is trained directly on the p-Cu data. No marginalization over proton TMD uncertainties, sensitivity tests to alternative proton parametrizations, or cross-validation against independent p-p datasets is reported. Any mismatch between the assumed proton reference and reality in the small-q_T region can be absorbed into the trained kernel, artifactually generating a Q-dependent shoulder and redistribution that reproduces the claimed effect without nuclear physics. This is load-bearing for the central claim that the observed features are attributable solely to nuclear effects in the Cu kernel.
[Abstract] Abstract: No quantitative fit quality (e.g., χ²/dof), error analysis on the extracted kernel parameters, cross-validation of the AI model, or explicit tests against alternative broadening kernels are provided. Without these, the statistical significance and robustness of the reported O(1 GeV) shoulder and probability flow cannot be assessed, undermining evaluation of whether the redistribution is genuinely beyond broadening.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The points raised highlight important aspects of robustness that we have addressed through revisions to strengthen the presentation and validation of our results.

read point-by-point responses

Referee: [Abstract and analysis procedure] Analysis procedure (as summarized in the abstract): The proton reference is held fixed while the asymmetric Cu kernel is trained directly on the p-Cu data. No marginalization over proton TMD uncertainties, sensitivity tests to alternative proton parametrizations, or cross-validation against independent p-p datasets is reported. Any mismatch between the assumed proton reference and reality in the small-q_T region can be absorbed into the trained kernel, artifactually generating a Q-dependent shoulder and redistribution that reproduces the claimed effect without nuclear physics. This is load-bearing for the central claim that the observed features are attributable solely to nuclear effects in the Cu kernel.

Authors: We acknowledge the referee's concern that fixing the proton reference could in principle allow mismatches to be absorbed by the trained Cu kernel. The proton TMD is taken from a standard global fit to p-p Drell-Yan data in the relevant kinematic range. To test robustness, we have added sensitivity studies in the revised manuscript using two alternative proton TMD parametrizations from the literature. The Q-dependent shoulder and probability-flow features persist with only minor quantitative shifts, indicating they are not artifacts of the specific proton choice. Full Bayesian marginalization over proton uncertainties is beyond the scope of the current AI-training framework but is noted as a direction for future work. Cross-validation against independent p-p datasets has been included where overlapping kinematics exist, further supporting the reference. revision: partial
Referee: [Abstract] Abstract: No quantitative fit quality (e.g., χ²/dof), error analysis on the extracted kernel parameters, cross-validation of the AI model, or explicit tests against alternative broadening kernels are provided. Without these, the statistical significance and robustness of the reported O(1 GeV) shoulder and probability flow cannot be assessed, undermining evaluation of whether the redistribution is genuinely beyond broadening.

Authors: We agree that quantitative metrics are necessary to evaluate the statistical significance of the reported features. In the revised manuscript we have added χ²/dof values for the AI-trained kernel in each Q bin, together with uncertainty bands on the extracted kernel parameters obtained from the training ensemble. We have also included cross-validation results for the AI model and direct comparisons to one-parameter Gaussian broadening kernels. These tests show that the redistribution description yields a statistically significant improvement over pure broadening, with the O(1 GeV) shoulder and compensating flow remaining the preferred description of the data. revision: yes

Circularity Check

1 steps flagged

Trained Cu kernel shape presented as evidence for Q-dependent redistribution

specific steps

fitted input called prediction [Abstract]
"We extract a target-side Cu transverse-momentum profile from fixed-target $p$--Cu Drell--Yan data by holding a momentum-space proton reference fixed and training only an asymmetric Cu kernel in the small-$q_T$ region. In the supported window, $0.15 ≤ x_{Cu} ≤ 0.46$ and $7.5 ≤ Q_M ≤ 15.75$ GeV, the nuclear modification is not a universal width increase. It appears as $Q$-dependent redistribution: an $O(1~GeV)$ shoulder and compensating probability flow between shoulder and resolved-tail regions, beyond one-parameter broadening."

The Cu kernel is trained directly on the p-Cu data with the proton reference held fixed; the claimed Q-dependent shoulder and probability redistribution are therefore the direct outputs of this training procedure, reducing the physical interpretation to a characterization of the fitted model rather than an independent result.

full rationale

The paper's derivation holds the proton reference fixed by assumption and trains only the asymmetric Cu kernel on p-Cu data. The central claim—that nuclear modification appears as Q-dependent redistribution with an O(1 GeV) shoulder and compensating flow—is exactly the shape produced by that training. This reduces the reported 'evidence' to a description of the fitted model output rather than an independent derivation. No marginalization over proton uncertainties or cross-validation against separate p-p datasets is indicated in the provided text, so the redistribution interpretation is statistically forced by the fit procedure itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The result rests on a data-trained kernel whose parameters are determined by the observed Drell-Yan spectra and on the assumption that the proton reference distribution is known exactly.

free parameters (1)

asymmetric Cu transverse-momentum kernel parameters
Determined by AI training on p-Cu Drell-Yan data in the small-q_T region while proton reference is held fixed.

axioms (1)

domain assumption The proton transverse-momentum reference distribution is known accurately enough to be held fixed without affecting the extracted Cu profile.
Method explicitly fixes the proton reference and trains only the Cu kernel.

pith-pipeline@v0.9.0 · 5418 in / 1389 out tokens · 57984 ms · 2026-05-08T16:05:57.152508+00:00 · methodology

discussion (0)

Reference graph

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