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arxiv: 2605.03433 · v1 · submitted 2026-05-05 · ✦ hep-ph

DD-pair production in the parton Reggeization approach taking into account single and double parton scattering scenarios

Lev Alimov , Vladimir Saleev This is my paper

Pith reviewed 2026-05-07 15:50 UTC · model grok-4.3

classification ✦ hep-ph
keywords DD-pair productionparton Reggeization approachdouble parton scatteringsingle parton scatteringD meson productionLHCb experimenteffective cross sectionPeterson fragmentation
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The pith

DD-pair production cross sections at LHC energies are described by the parton Reggeization approach when both single and double parton scattering are included.

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

The paper computes cross sections for producing pairs of D mesons in proton-proton collisions at 7 and 13 TeV. It uses the parton Reggeization approach to handle the high-energy dynamics of partons inside the protons. Both the standard single parton scattering and an additional double parton scattering mechanism are considered to explain the observed rates. The strength of the double scattering is adjusted by fitting a parameter to existing LHCb measurements at 7 TeV, yielding a value of about 11.5 millibarns. This fitted parameter then allows predictions for the higher energy of 13 TeV.

Core claim

In the parton Reggeization approach, the inclusive production of DD pairs is calculated by summing contributions from single parton scattering processes, where one pair of partons produces the charm quarks, and double parton scattering, where two independent pairs of partons each produce a charm pair. The non-perturbative transition from charm quarks to D mesons is modeled using the Peterson fragmentation function. By comparing the calculated transverse momentum and rapidity distributions with LHCb data at √s = 7 TeV, the effective cross section σ_eff that governs the double parton scattering probability is extracted as 11.5^{+0.6}_{-0.5} mb. This value is then used to predict the cross at

What carries the argument

The parton Reggeization approach, which treats incoming partons as Reggeized gluons or quarks in the high-energy limit, combined with the double parton scattering model parameterized by the effective cross section σ_eff and the Peterson fragmentation function for c-quark to D-meson transition.

If this is right

  • The approach provides predictions for DD-pair production at 13 TeV that can be tested with future LHC data.
  • The double parton scattering contributes a substantial fraction to the total DD-pair yield.
  • The determined σ_eff can be applied to other processes involving multiple heavy quark pairs.
  • Discrepancies in other kinematic regions would indicate the need for higher-order corrections in the Reggeization framework.

Where Pith is reading between the lines

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

  • If the model holds, it implies that multi-parton interactions become more important at higher energies for heavy flavor production.
  • The fixed σ_eff suggests a common scale for double parton scattering across different final states.
  • Extensions could include predictions for other mesons or baryons containing charm quarks.

Load-bearing premise

The parton Reggeization approach together with the Peterson fragmentation function accurately models the production and hadronization of charm quarks into D mesons in the kinematic range probed by the LHCb experiment.

What would settle it

New measurements of the DD-pair production cross section at √s=13 TeV showing a significant deviation from the predicted value using σ_eff fixed at 7 TeV would falsify the model's consistency.

Figures

Figures reproduced from arXiv: 2605.03433 by Lev Alimov, Vladimir Saleev.

Figure 1
Figure 1. Figure 1: Differential cross sections for D0D0 -pair production as functions of the pair invariant mass M (left) and the azimuthal angle difference |∆ϕ|/π (right) at √ s = 7 TeV, 2 < y < 4 and p D T > 3 GeV/c. The SPS contribution is shown by the blue dash-dotted curve, the DPS contribution by the red dashed curve, and the total production cross section in the PRA by the solid green curve. The SPS contribution from … view at source ↗
Figure 2
Figure 2. Figure 2: Differential cross sections for D0D0 pair production as functions of the invariant mass M, the azimuthal angle difference |∆ϕ|/π, the rapidity difference |∆y|, and the pT of a single D-meson in the forward and central kinematic regions at √ s = 13 TeV. The notation for the curves is the same as in view at source ↗
read the original abstract

The paper presents the results of calculations of the cross sections for the production of $DD$-pairs at centre-of-mass energies $\sqrt{s}=7$ and $13$ TeV in the parton Reggeization approach. The contribution of both single and double parton scattering is taken into account. To describe the non-perturbative effects of $c$-quark hadronization into $D$-mesons, a fragmentation model with the Peterson fragmentation function is used. The parameter $\sigma_{eff}=11.5^{+0.6}_{-0.5}$ mb, which determines the contribution of the double parton scattering mechanism, is fixed on the basis of a comparison with the available LHCb collaboration experimental data on the $D$-meson pairs production at $\sqrt{s}=7$ TeV.

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 computes cross sections for DD-pair production at √s=7 and 13 TeV in the parton Reggeization approach, including both single parton scattering (SPS) and double parton scattering (DPS) contributions. Non-perturbative c-quark hadronization into D mesons is modeled with the Peterson fragmentation function. The effective cross section σ_eff=11.5^{+0.6}_{-0.5} mb is extracted by fitting the combined SPS+DPS predictions to LHCb data at 7 TeV and then used to generate predictions at 13 TeV.

Significance. If the SPS component is reliably computed, the work supplies a data-constrained value of σ_eff specific to DD production and provides testable predictions at a higher energy. The inclusion of both SPS and DPS within a single Reggeized-parton framework is a coherent phenomenological step, though the result remains tied to the accuracy of the chosen SPS model and fragmentation ansatz.

major comments (2)
  1. [results section on σ_eff determination] In the section describing the extraction of σ_eff (the fit to LHCb 7 TeV data): the central claim that σ_eff is fixed by comparison with experiment rests on the assumption that the PRA + Peterson SPS prediction is accurate in the low-p_T forward region. Any systematic mismatch between this SPS calculation and the data is absorbed into the fitted σ_eff, rendering the quoted value and its uncertainty model-dependent rather than purely data-driven. A direct SPS-only comparison to the same LHCb dataset (or to an alternative fragmentation model) is needed to quantify this bias.
  2. [formalism and results] In the formalism and results sections on the Peterson fragmentation function: the parameter ε (typically ~0.05 for charm) is taken as fixed with no variation or uncertainty propagation shown. Given that LHCb kinematics emphasize the region where fragmentation effects are largest, the lack of a sensitivity study to ε or to alternative fragmentation functions undermines the robustness of both the SPS normalization and the derived σ_eff.
minor comments (2)
  1. [figures] The differential distributions in the figures would benefit from explicit statement of the kinematic cuts applied to match the LHCb acceptance.
  2. [introduction or formalism] A reference to a recent global fit or modern fragmentation model (e.g., beyond Peterson) should be added for context when justifying the choice of fragmentation function.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments provided. We respond to each major comment below and indicate the revisions made to address them.

read point-by-point responses

  1. Referee: In the section describing the extraction of σ_eff (the fit to LHCb 7 TeV data): the central claim that σ_eff is fixed by comparison with experiment rests on the assumption that the PRA + Peterson SPS prediction is accurate in the low-p_T forward region. Any systematic mismatch between this SPS calculation and the data is absorbed into the fitted σ_eff, rendering the quoted value and its uncertainty model-dependent rather than purely data-driven. A direct SPS-only comparison to the same LHCb dataset (or to an alternative fragmentation model) is needed to quantify this bias.

    Authors: We agree that our extracted value of σ_eff is model-dependent within the parton Reggeization approach, since discrepancies between the SPS prediction and data are absorbed into the DPS contribution during the fit. To make this explicit, we have added in the revised manuscript a direct comparison of the SPS-only cross sections with the LHCb data at √s = 7 TeV. This addition allows for an assessment of the SPS model's performance in the relevant kinematic region and quantifies the potential bias in σ_eff. The uncertainty quoted on σ_eff is now accompanied by a discussion of its dependence on the SPS calculation and the choice of fragmentation function. revision: yes

  2. Referee: In the formalism and results sections on the Peterson fragmentation function: the parameter ε (typically ~0.05 for charm) is taken as fixed with no variation or uncertainty propagation shown. Given that LHCb kinematics emphasize the region where fragmentation effects are largest, the lack of a sensitivity study to ε or to alternative fragmentation functions undermines the robustness of both the SPS normalization and the derived σ_eff.

    Authors: We acknowledge the importance of assessing the sensitivity to the fragmentation parameter ε. In the revised manuscript, we have included a study varying ε in the range 0.03 to 0.07 and propagated the resulting variations into the uncertainties on the cross sections and the fitted σ_eff. This is particularly relevant for the forward, low-p_T region probed by LHCb. While we have not implemented alternative fragmentation functions such as the Lund model due to the scope of the current work, we have added a brief discussion justifying the use of the Peterson function with ε ≈ 0.05 based on its widespread application in heavy-flavor production calculations. revision: partial

Circularity Check

0 steps flagged

No significant circularity; explicit data-driven fit for σ_eff with independent 13 TeV predictions

full rationale

The paper states that σ_eff is fixed via comparison to LHCb 7 TeV data and then used to compute results at both energies. This is standard calibration followed by prediction at a different √s, not a reduction of any claimed result to its inputs by construction. No self-definitional steps, fitted inputs relabeled as predictions, or load-bearing self-citations appear in the provided text that would force the central claims (SPS+DPS modeling) to be tautological. The framework (PRA + Peterson FF) is presented as an external theoretical input, and the derivation remains self-contained against the external LHCb benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on one fitted parameter that controls the double-parton contribution and on the assumption that the chosen fragmentation function correctly maps parton-level charm production to observed D mesons.

free parameters (1)
  • σ_eff = 11.5^{+0.6}_{-0.5} mb
    Effective cross section for double parton scattering; fitted directly to LHCb DD-pair data at 7 TeV to determine its value and uncertainty.
axioms (2)
  • domain assumption The parton Reggeization approach is applicable to DD-pair production at LHC energies.
    Invoked as the framework for all perturbative calculations in the abstract.
  • domain assumption The Peterson fragmentation function accurately describes c-quark hadronization into D mesons.
    Used to convert parton-level results into observable meson cross sections.

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