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arxiv: 2506.05337 · v2 · pith:ERMRVVSLnew · submitted 2025-06-05 · ✦ hep-ph

Momentum fraction and hard scale dependence of double parton scattering

Joao Vitor C. Lovato , Edgar Huayra , Emmanuel G. de Oliveira This is my paper

Pith reviewed 2026-05-19 10:37 UTC · model grok-4.3

classification ✦ hep-ph
keywords double parton scatteringeffective cross sectiondouble parton distributionsGaussian transverse profileLHCTevatronparton momentum fractionhard scale
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The pith

Double parton effective cross section varies with momentum fraction and hard scale

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

The paper establishes that the effective cross section measured in double parton scattering is not a fixed universal value but changes with the chosen final state, kinematics, and experiment. The authors build this variation into the model by letting the width of a Gaussian transverse profile in the double parton distributions depend on both the parton momentum fraction x and the hard scale μ. They then fit one set of parameters to a collection of LHC and Tevatron measurements spanning different processes and energies. If the fit holds, the effective cross section becomes a calculable output of proton structure rather than an input constant, allowing predictions for observables not yet measured.

Core claim

Incorporating the dependence on both the parton longitudinal momentum fraction x and the process energy hard scale μ into the transverse part of the double parton distributions using a Gaussian profile, the authors perform a global fit to experimental data from the LHC and Tevatron covering different processes, kinematic configurations, and center-of-mass energies, extract the parameters that describe the proton structure, and provide predictions for future measurements at the LHC.

What carries the argument

An x- and μ-dependent Gaussian profile for the transverse dependence of double parton distributions, which sets the size of the effective cross section for each observable and kinematic point.

Load-bearing premise

The transverse dependence of double parton distributions can be captured by a single Gaussian whose width is a function of x and μ, with one parameter set remaining valid across other observables and kinematic regions.

What would settle it

A precise LHC measurement of the effective cross section in a new double parton scattering final state that lies well outside the range predicted by the fitted x- and μ-dependent Gaussian model would falsify the central claim.

Figures

Figures reproduced from arXiv: 2506.05337 by Edgar Huayra, Emmanuel G. de Oliveira, Joao Vitor C. Lovato.

Figure 1
Figure 1. Figure 1: Double parton scattering effective cross section [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parameterization of the variance function [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Predictions of σeff, DPS in pp collisions for various final states from the global fit of our model. The kinematic cuts are the same as those used by the experiments in DPS analyses (when available) or in corresponding SPS analyses. The purple arrows indicate upper or lower experimental limits for D0 Ref. [50], ATLAS Ref. [51], and UA2 Ref. [52]. depending on the specific final state considered. To model t… view at source ↗
read the original abstract

The effective cross section of double parton scattering in high-energy hadron collisions has been measured in proton--proton collisions, with significant variation among final-state observables, contrary to the idea of a universal value. Building upon our previous work, we incorporate the dependence on both the parton longitudinal momentum fraction $x$ and the process energy hard scale $\mu$ into the transverse part of the double parton distributions, using a Gaussian profile. Employing the experimental data from the LHC and Tevatron experiments (covering different processes, kinematic configurations, and center--of--mass energies), we perform a global fit of the model, extracting the parameters that describe the proton structure. With this result, it becomes possible to calculate the effective cross section for others observables, and we provide predictions for future measurements 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

2 major / 2 minor

Summary. The manuscript extends a model of double parton scattering by introducing explicit dependence on the parton momentum fraction x and the hard scale μ into the transverse profile of the double parton distributions, adopting a Gaussian form whose width varies with both variables. Using data on the effective cross section from multiple LHC and Tevatron measurements that span different processes, kinematics, and center-of-mass energies, the authors perform a global fit to determine the model parameters and then employ the fitted parameters to predict the effective cross section for additional observables at the LHC.

Significance. If the functional form proves adequate and the fit is robust, the work supplies a data-driven parameterization that can account for the observed process dependence of the DPS effective cross section, thereby improving the reliability of predictions for future LHC measurements and reducing reliance on a single universal value.

major comments (2)
  1. [Section describing the global fit and parameter extraction] The central result is a global fit whose parameters are subsequently used for predictions, yet the manuscript provides no quantitative measures of fit quality (χ², degrees of freedom, or residual distributions) nor any discussion of parameter uncertainties or correlations. This information is required to judge whether the chosen x- and μ-dependent Gaussian adequately describes the input data sets without large systematic residuals.
  2. [Section on model assumptions and predictions] The assumption that a single Gaussian transverse profile with x- and μ-dependent width, fitted to the selected LHC and Tevatron data, remains valid for extrapolation to new observables and kinematic regions is load-bearing for the predictive claims, but no stability tests under dataset variations or alternative functional forms are reported.
minor comments (2)
  1. Notation for the hard scale μ and the momentum fraction x should be defined consistently when first introduced and used uniformly throughout the text and equations.
  2. [Abstract and Introduction] The abstract and introduction would benefit from a brief statement of the number of data points and the range of processes included in the global fit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report on our manuscript. We address the major comments point by point below. Where the comments identify omissions in the presentation of fit quality and robustness checks, we agree that revisions are warranted and will incorporate the requested information and tests in the revised version.

read point-by-point responses

  1. Referee: [Section describing the global fit and parameter extraction] The central result is a global fit whose parameters are subsequently used for predictions, yet the manuscript provides no quantitative measures of fit quality (χ², degrees of freedom, or residual distributions) nor any discussion of parameter uncertainties or correlations. This information is required to judge whether the chosen x- and μ-dependent Gaussian adequately describes the input data sets without large systematic residuals.

    Authors: We agree that quantitative measures of fit quality are essential for a proper assessment of the model. The original manuscript focused on the extracted parameters and their use for predictions but omitted explicit reporting of the global χ², degrees of freedom, parameter uncertainties, correlations, and residual distributions. In the revised manuscript we will add a dedicated subsection that reports the χ² per degree of freedom, tabulates the best-fit parameters with uncertainties, provides the correlation matrix, and includes residual plots comparing the model to each input data set. These additions will allow readers to evaluate the adequacy of the x- and μ-dependent Gaussian form directly. revision: yes

  2. Referee: [Section on model assumptions and predictions] The assumption that a single Gaussian transverse profile with x- and μ-dependent width, fitted to the selected LHC and Tevatron data, remains valid for extrapolation to new observables and kinematic regions is load-bearing for the predictive claims, but no stability tests under dataset variations or alternative functional forms are reported.

    Authors: The referee correctly identifies that the robustness of the model assumptions underpins the predictive results. While the global fit already incorporates data spanning different processes, center-of-mass energies, and kinematic ranges, we acknowledge that explicit stability tests (e.g., fits with subsets of the data or comparisons to alternative transverse profiles) were not presented. In the revision we will include a new subsection that reports the results of stability checks performed by excluding individual data sets (such as the Tevatron measurements or specific LHC channels) and that discusses the sensitivity to the choice of functional form. We will also add a brief statement on the limitations of the current parameterization when extrapolating outside the fitted kinematic domain. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central procedure is a global fit of an x- and μ-dependent Gaussian transverse profile to selected LHC and Tevatron double-parton-scattering data, from which parameters are extracted and then applied to compute effective cross sections for additional observables and to generate predictions for future measurements. This is a standard phenomenological workflow in which the fit itself constitutes the primary result and the subsequent calculations are direct applications of the fitted model; no algebraic step, equation, or self-citation is shown to reduce any claimed prediction or first-principles result back to the input data by construction. The functional form is adopted as an explicit ansatz, the data sets are external experimental measurements, and the predictions target observables or kinematic regions outside the fit, rendering the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the Gaussian transverse ansatz and the assumption that a single global fit across the selected data sets captures all relevant physics; no new particles or forces are introduced.

free parameters (1)
  • parameters of the x- and μ-dependent Gaussian width
    Fitted to the collection of LHC and Tevatron effective-cross-section measurements
axioms (1)
  • domain assumption Factorization and the Gaussian form for the transverse dependence of double parton distributions remain valid across the kinematic range of the fitted data
    Invoked when the model is applied to the experimental measurements

pith-pipeline@v0.9.0 · 5670 in / 1458 out tokens · 32780 ms · 2026-05-19T10:37:18.177505+00:00 · methodology

discussion (0)

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