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arxiv: 2607.00962 · v1 · pith:WTHAVSXNnew · submitted 2026-07-01 · ✦ hep-ph · hep-ex

Higher-order effects in amplitude-assisted polarisation extraction with machine-learning techniques

Juan M. Cruz-Martinez , Jakob Linder , Mathieu Pellen , Giovanni Pelliccioli , Emanuele Re This is my paper

Pith reviewed 2026-07-02 09:51 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords polarization extractionmachine learningNLO QCDdi-boson productionelectroweak bosonsregressionparton shower
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0 comments X

The pith

Machine learning extracts longitudinal boson production rates from NLO QCD simulations of di-boson events.

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

This paper introduces a regression method that uses machine learning on simulated collision events to determine the fraction of longitudinally polarized electroweak bosons. The approach reaches next-to-leading-order accuracy in QCD and includes parton-shower effects, advancing beyond earlier leading-order techniques. Multiple neural-network designs are tested and compared to a random-forest baseline, showing consistent performance for processes like vector-boson pair production at the LHC. If the method works as described, it supplies a practical tool for measuring polarization fractions with higher theoretical precision.

Core claim

We present the first amplitude-assisted regression procedure at next-to-leading-order accuracy in QCD, supplemented with parton-shower effects, using machine-learning techniques to extract the rate of longitudinal-boson production in high-energy collisions. Several neural-network architectures are presented and benchmarked against a standard random-forest regressor, demonstrating the robustness of the results for di-boson production at the LHC.

What carries the argument

Amplitude-assisted regression procedure that feeds precise theoretical amplitudes into machine-learning models to regress polarization fractions from event-level kinematics.

If this is right

  • The regression works at NLO QCD plus parton showers for di-boson final states.
  • Neural-network models yield results comparable in robustness to random-forest models.
  • The method supplies a concrete extraction procedure for longitudinal boson rates.
  • Inclusion of higher-order corrections improves the accuracy of the polarization extraction.

Where Pith is reading between the lines

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

  • The same training strategy could be adapted to other final states containing polarized vector bosons.
  • Validation against real data would test whether NLO training reduces theory uncertainties in polarization measurements.
  • If the method proves stable, it might be combined with existing experimental analyses to tighten limits on electroweak parameters.

Load-bearing premise

The simulated events used for training accurately represent the polarization fractions that will be observed in real LHC data.

What would settle it

Apply the trained regressor to actual LHC collision data and compare the extracted longitudinal rates against independent experimental measurements of the same polarization fractions.

Figures

Figures reproduced from arXiv: 2607.00962 by Emanuele Re, Giovanni Pelliccioli, Jakob Linder, Juan M. Cruz-Martinez, Mathieu Pellen.

Figure 1
Figure 1. Figure 1: Differential distributions in the transverse momentum of the four-lepton system for doubly polarised [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Differential distributions with respect to the positron polar decay angle for doubly polarised ZZ [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Architecture of our FFNN model, namely a NN with 10 hidden layers and a constant width of 707. [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Structure of the autoencoder-like NN (AE). The decoder part of the network on the right, not [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Architecture of the PN model used in this work, as obtained from the LO hyperparameter scan [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Differential distributions in the positron decay angle in the corresponding Z-boson rest frame [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Distributions in the truth and predicted [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Differential distributions in the positron rapidity (left) and in the positron–electron azimuthal [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Differential distributions in the transverse momentum of the four-lepton system at LO [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Same cos θ ∗ e+ and pT, e+ distributions as in [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Training history for the FFNN at LO (left panel) and LO [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Loss values according to Eq. (29) for different batch sizes and learning rates for the FFNN at LO (left panel) and LO+Sud. (right panel). The colour of the dots indicates the trial number, with darker shades of blue corresponding to later trials. tion 3.3, since no prior implementation exists for this problem to use as a baseline and the architecture is too different from both FNNN and AE to reutilize the… view at source ↗
read the original abstract

With increasing experimental precision, the prospect of extracting the polarisation of electroweak gauge bosons is becoming particularly attractive. To this end, regression and classification procedures based on precise and accurate theoretical predictions are becoming increasingly important. In this work, we present the first amplitude-assisted regression procedure at next-to-leading-order accuracy in QCD, supplemented with parton-shower effects, using machine-learning techniques to extract the rate of longitudinal-boson production in high-energy collisions. Several neural-network architectures are presented and benchmarked against a standard random-forest regressor, demonstrating the robustness of the results for di-boson production at the LHC.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript presents the first amplitude-assisted regression procedure at next-to-leading-order accuracy in QCD, supplemented with parton-shower effects, using machine-learning techniques to extract the rate of longitudinal-boson production in di-boson processes at the LHC. Several neural-network architectures are benchmarked against a random-forest regressor, with claims of robust performance in closure tests.

Significance. If the central results hold, the work would advance polarization extraction methods by incorporating higher-order QCD effects and parton showers into an ML framework, a timely development for LHC precision measurements. Credit is due for the systematic benchmarking across multiple architectures and the explicit inclusion of NLO + shower effects, which strengthens the methodology over leading-order approaches.

major comments (1)
  1. [Results section] Results section (around the performance tables): the reported stability of the regression across architectures lacks quantitative metrics such as mean absolute error, correlation coefficients, or pull distributions with uncertainties; without these, the claim that the procedure extracts rates at NLO accuracy cannot be fully assessed for precision.
minor comments (2)
  1. [Abstract] The abstract would benefit from including at least one key numerical result (e.g., extracted fraction or closure-test accuracy) to substantiate the robustness claim.
  2. [§2] Notation for the amplitude-assisted features should be defined more explicitly in §2 to clarify how NLO matrix elements enter the input variables.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Results section] Results section (around the performance tables): the reported stability of the regression across architectures lacks quantitative metrics such as mean absolute error, correlation coefficients, or pull distributions with uncertainties; without these, the claim that the procedure extracts rates at NLO accuracy cannot be fully assessed for precision.

    Authors: We agree that the inclusion of additional quantitative metrics would strengthen the presentation. The current manuscript reports performance tables for multiple architectures in closure tests and benchmarks against random forests, but does not explicitly provide mean absolute errors, correlation coefficients, or pull distributions with uncertainties. In the revised manuscript we will augment the results section with these metrics (including uncertainties) to allow a fuller assessment of the NLO precision. revision: yes

Circularity Check

0 steps flagged

No significant circularity; method is a standard ML regression on simulated data

full rationale

The paper introduces an amplitude-assisted ML regression at NLO QCD + parton shower for extracting longitudinal boson polarization fractions from di-boson production. The procedure trains regressors (NNs and random forests) on simulated events whose polarization labels are known by construction from the generator; the output is a trained model whose performance is validated on held-out simulated samples. No derivation, uniqueness theorem, or ansatz is invoked that reduces the reported extraction to a fitted parameter or self-citation by construction. The simulation-to-data transfer assumption is stated as a standard caveat in the abstract and is not presented as a derived result. The central claim therefore remains an empirical demonstration of a computational technique rather than a closed logical loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; all such elements remain unknown.

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discussion (0)

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Reference graph

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