arxiv: 2604.07509 · v1 · submitted 2026-04-08 · ✦ hep-ph · hep-th· nucl-th

Recognition: unknown

Forward trijet production in proton-nucleus collisions: gluon initiated channel

Paul Caucal , Marcos Guerrero Morales , Farid Salazar

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:11 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th

keywords trijet productiongluon initiatedproton-nucleus collisionsColor Glass Condensatedilute-dense approximationJIMWLK evolutionWilson linesforward kinematics

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The pith

The gluon-initiated forward trijet production cross section is computed at leading order in proton-nucleus collisions using the Color Glass Condensate effective theory.

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

This paper computes the leading-order differential cross section for forward trijet production in the gluon-initiated channel for proton-nucleus collisions. Calculations are performed in the Color Glass Condensate framework under the dilute-dense approximation, separating amplitudes into regular and instantaneous contributions via covariant perturbation theory. The results take the form of convolutions between multiparton color correlators of light-like Wilson lines and perturbative impact factors for both q qbar g and g g g final states. Notably, the g g g channel shows a four-gluon vertex topology akin to instantaneous terms. Integrating out one final-state gluon demonstrates that rapidity divergences feed into the JIMWLK evolution of the color correlator while collinear divergences contribute to the evolution of the gluon parton distribution function and fragmentation functions.

Core claim

The leading-order calculation of gluon-initiated forward trijet production in pA collisions is performed in the CGC dilute-dense framework. Amplitudes for q bar q g and g g g final states are computed using effective vertices and separated into regular and instantaneous parts. The cross sections are organized as convolutions of Wilson line color correlators with impact factors in bare diagram topologies. For the ggg channel the four-gluon vertex shares the structure of instantaneous contributions. Integrating a final-state gluon yields rapidity divergences that match the real part of the JIMWLK kernel acting on the LO correlator and collinear divergences that match DGLAP evolution of the glu

What carries the argument

Effective vertices for quark and gluon propagators in the small-x background field, allowing separation of regular and instantaneous contributions, with results expressed via multiparton color correlators of light-like Wilson lines convoluted with perturbative impact factors.

If this is right

These calculations validate the dilute-dense hybrid formalism at one-loop order.
The results provide key ingredients for the complete next-to-leading-order calculation of dijet and dihadron production in proton-nucleus collisions.
The observed structure of the four-gluon vertex in the ggg final state extends the understanding of instantaneous contributions.
Divergences identified upon gluon integration confirm consistency with JIMWLK evolution of color correlators and collinear evolution of PDFs and fragmentation functions.

Where Pith is reading between the lines

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

Similar techniques may apply to other forward multi-jet observables in small-x physics.
Numerical evaluations of these expressions could enable direct comparisons with data from the LHC or future electron-ion colliders.
The compact topological organization might simplify extensions to higher orders or different kinematic regimes.

Load-bearing premise

The dilute-dense approximation together with the effective vertices for quark and gluon propagators interacting with the small-x background gluon field remains valid for the kinematics considered.

What would settle it

A failure of the extracted rapidity divergence to match the real part of the JIMWLK kernel, or of the collinear divergence to reproduce the known evolution of the gluon PDF and fragmentation functions, upon integration over a final-state gluon.

read the original abstract

In this paper, we present the results for the forward trijet production differential cross section in the gluon initiated channel at leading order in proton-nucleus collisions. The calculations are carried out within the Color Glass Condensate (CGC) effective theory, and in the dilute-dense approximation, using effective vertices for the quark and gluon propagators interacting with the small-$x$ background gluon field. We employ the covariant perturbation theory approach and disentangle the amplitudes into regular and instantaneous contributions. Our results are expressed as convolutions of multiparton color correlators of light-like Wilson lines and perturbative impact factors, organized in compact expressions in terms of the ``bare" topologies of the contributing diagrams. The gluon initiated channel receives contributions from a $q\bar{q}g$ and a $ggg$ final state. Interestingly, when considering the $ggg$ final state, we observe, for the first time, that the four-gluon vertex topology follows a structure similar to the instantaneous contributions. Furthermore, when integrating (one of) the real gluon(s) in the final state, we identify that: i) the rapidity divergence contributes to the real part of JIMWLK of the leading-order color correlator; and ii) the collinear divergence contribute to the evolution of initial-state gluon parton distribution function, and final state fragmentation functions. These results validate the dilute-dense hybrid formalism at one-loop order, and are key ingredients towards the complete next-to-leading order calculation of dijet/dihadron production in proton--nucleus collisions.

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

This paper computes the gluon-initiated forward trijet cross section in the CGC dilute-dense setup and shows that integrating out one gluon reproduces the expected JIMWLK rapidity divergence plus DGLAP collinear pieces.

read the letter

The main takeaway is that the authors have worked out the leading-order gluon channel for forward trijet production in proton-nucleus collisions inside the Color Glass Condensate framework. They separate the amplitudes into regular and instantaneous pieces, write the cross section as convolutions of Wilson-line correlators with impact factors, and note that the four-gluon vertex in the ggg final state follows the same structure as the instantaneous terms. When one gluon is integrated out, the rapidity pole feeds the real part of JIMWLK evolution of the color correlator while the collinear poles match the gluon PDF and fragmentation-function kernels. That matching is a clean consistency check on the hybrid formalism at real-emission level one-loop order. The expressions stay compact by organizing around bare diagram topologies, which is practical for later use in NLO dijet or dihadron work. The calculation is entirely analytic and stays within established CGC tools, so the internal logic appears consistent with no obvious missing topologies or contradictory assumptions. The dilute-dense approximation is the main limitation; it restricts the kinematic range where the results can be applied directly, and there are no numerical evaluations or comparisons to other approaches here. This is a methods paper aimed at specialists already working in small-x QCD and saturation phenomenology. A reader who needs the explicit trijet impact factors or the divergence mapping for their own NLO codes will get concrete value. It is technically grounded enough to deserve a serious referee rather than a desk rejection, even though the practical impact will depend on how these pieces are implemented downstream.

Referee Report

0 major / 2 minor

Summary. The paper computes the leading-order differential cross section for forward trijet production in the gluon-initiated channel (q qbar g and g g g final states) in proton-nucleus collisions within the Color Glass Condensate effective theory under the dilute-dense approximation. It employs covariant perturbation theory to separate amplitudes into regular and instantaneous contributions, expresses the results as convolutions of multiparton Wilson-line color correlators with perturbative impact factors organized by diagram topologies, and shows that integrating out one final-state gluon reproduces the expected rapidity divergences feeding into JIMWLK evolution of the leading-order color correlator together with collinear divergences matching DGLAP evolution of the initial-state gluon PDF and final-state fragmentation functions.

Significance. If the derivation holds, this work supplies a non-trivial consistency check of the dilute-dense hybrid formalism at the real-emission one-loop level. The explicit treatment of the four-gluon vertex topology and the compact correlator expressions constitute useful technical ingredients for the ongoing program of next-to-leading-order calculations of dijet and dihadron observables in pA collisions.

minor comments (2)

[Abstract] The abstract states that the four-gluon vertex topology 'follows a structure similar to the instantaneous contributions,' but the manuscript would be clearer if this similarity were stated explicitly (e.g., by comparing the resulting color factors or kinematic dependence) in the main text.
A short table or paragraph comparing the gluon-channel impact factors derived here with the corresponding quark-channel results from prior work would help readers assess the completeness of the one-loop real-emission structure.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation for minor revision. The referee's summary accurately describes the scope of our calculation of the gluon-initiated trijet channel at leading order in the dilute-dense CGC framework, including the separation into regular and instantaneous contributions, the role of the four-gluon vertex, and the consistency checks with JIMWLK and DGLAP evolution upon integration of a final-state gluon.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper derives the LO forward trijet cross section in the gluon-initiated channel from the CGC dilute-dense hybrid formalism using effective vertices and covariant perturbation theory. Amplitudes are disentangled into regular and instantaneous pieces, with the cross section expressed as convolutions of Wilson-line correlators and impact factors organized by diagram topologies. The subsequent identification of rapidity divergences feeding the real JIMWLK kernel and collinear divergences feeding DGLAP evolution of the gluon PDF and fragmentation functions follows directly from phase-space integration of those derived expressions. No parameter is fitted to the target result, no ansatz is smuggled via self-citation, and the central computation does not reduce to its own inputs by definition. The consistency check is a derived validation against known external evolution equations rather than a circular renaming or self-referential prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Color Glass Condensate effective theory and the dilute-dense approximation, both standard in the field; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)

domain assumption Color Glass Condensate effective theory for small-x gluon fields
Framework invoked to describe the dense nuclear gluon background.
domain assumption Dilute-dense approximation for proton-nucleus kinematics
Assumption that the proton is dilute while the nucleus is dense, used throughout the calculation.

pith-pipeline@v0.9.0 · 5582 in / 1468 out tokens · 44564 ms · 2026-05-10T17:11:37.207305+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Probing Saturation Effect in Heavy Meson Pair Correlation in Forward $pA$ Collisions
hep-ph 2026-05 unverdicted novelty 5.0

Heavy meson pair correlations in forward pA collisions are computed in the CGC framework with Sudakov resummation, reproducing LHCb data and showing a mass hierarchy in R_pA that strengthens at higher rapidity.

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