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arxiv: 2606.25685 · v1 · pith:HL37GQ54new · submitted 2026-06-24 · ✦ hep-ph · hep-th

Quark Reggeization in QCD from the Wilson line formalism

Tolga Altinoluk , Guillaume Beuf , Jules Favrel , Michael Fucilla This is my paper

Pith reviewed 2026-06-25 20:33 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords quark ReggeizationWilson lineshigh-energy QCDRegge trajectoryrapidity evolutionshockwave formalismeikonal approximation
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The pith

An interpolating operator of semi-infinite Wilson lines yields the nonlinear rapidity evolution for the Reggeized quark in QCD.

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

The paper constructs an interpolating operator for the Reggeized quark from semi-infinite Wilson lines inside the eikonal shockwave formalism of high-energy QCD. It then derives the nonlinear rapidity renormalization-group evolution of this operator using the background-field method at leading logarithmic accuracy. In the dilute limit after projection onto definite signature, the positive-signature channel recovers the power-law scaling set by the one-loop quark Regge trajectory. The negative-signature channel mixes Reggeized quark and gluon exchanges, yet this mixing vanishes in the large-Nc limit where Regge-pole behavior appears without projection. The construction supplies a Wilson-line language for systematic all-order treatment of amplitudes carrying t-channel quark quantum numbers.

Core claim

The central claim is that an interpolating operator for the Reggeized quark, built from semi-infinite Wilson lines, obeys a nonlinear rapidity renormalization-group equation obtained via the background-field method in the eikonal approximation; this equation reproduces the one-loop quark Regge trajectory in the positive-signature dilute limit while exhibiting signature mixing that disappears at large Nc, thereby enabling all-order analyses of high-energy amplitudes with t-channel quark exchange entirely in the Wilson-line formalism.

What carries the argument

Interpolating operator for the Reggeized quark expressed in terms of semi-infinite Wilson lines, with its nonlinear rapidity renormalization-group evolution derived using the background-field method.

If this is right

  • The positive-signature channel reproduces the characteristic power-law scaling dictated by the one-loop quark Regge trajectory.
  • The negative-signature channel exhibits mixing between Reggeized quark and gluon exchanges.
  • In the large-Nc limit this mixing disappears and Regge-pole behaviour emerges without the need for signature projection.
  • The framework enables a systematic all-order analysis of high-energy QCD amplitudes with t-channel quark quantum-number exchange in terms of eikonal Wilson lines.

Where Pith is reading between the lines

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

  • The nonlinear evolution equation could be solved in specific kinematic regimes to generate resummed predictions for quark-exchange amplitudes beyond leading log.
  • The Wilson-line operator may furnish a bridge to other high-energy factorization schemes that treat quark Reggeons.
  • Numerical or analytic solutions of the evolution in the dilute regime could be compared against existing perturbative calculations of quark Reggeization.

Load-bearing premise

The eikonal approximation together with the background-field method at leading logarithmic accuracy fully captures the nonlinear evolution of the Wilson-line operators without missing higher-order or non-eikonal corrections.

What would settle it

An explicit extraction of the one-loop quark Regge trajectory from the derived evolution equation that matches the known result, or a direct measurement of the predicted power-law energy dependence in a high-energy scattering process dominated by t-channel quark exchange.

Figures

Figures reproduced from arXiv: 2606.25685 by Guillaume Beuf, Jules Favrel, Michael Fucilla, Tolga Altinoluk.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) A fast-moving photon interacting with the tar [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) A projectile built from an arbitrary number of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Left: the diagram contributing to the one-loop evolution of a single Wilson line. Right: the diagram contributing to [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

We derive quark Reggeization in QCD at leading logarithmic accuracy within the eikonal Wilson-line (shockwave) approach. An interpolating operator for the Reggeized quark is identified in terms of semi-infinite Wilson lines, and its nonlinear rapidity renormalization-group evolution is derived using the background-field method. In the dilute limit, after projecting onto operators of definite signature, the positive-signature channel reproduces the characteristic power-law scaling dictated by the one-loop quark Regge trajectory, whereas the negative-signature channel exhibits mixing between Reggeized quark and gluon exchanges. In the large-$N_c$ limit, this mixing disappears, and Regge-pole behaviour emerges without the need for signature projection, recovering the expected degeneracy by signature. This paves the way to a systematic all-order analysis of high-energy QCD amplitudes with $t$-channel quark quantum-number exchange in terms of eikonal Wilson lines.

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

0 major / 0 minor

Summary. The manuscript derives quark Reggeization in QCD at leading logarithmic accuracy in the eikonal Wilson-line (shockwave) formalism. It identifies an interpolating operator for the Reggeized quark built from semi-infinite Wilson lines and obtains its nonlinear rapidity renormalization-group evolution equation via the background-field method. In the dilute limit, after projection onto definite-signature operators, the positive-signature channel reproduces the one-loop quark Regge trajectory power-law scaling, the negative-signature channel exhibits mixing with gluon exchange, and this mixing vanishes in the large-N_c limit, recovering signature degeneracy.

Significance. If the derivation holds, the work supplies a parameter-free Wilson-line framework for systematic LLA analysis of high-energy QCD amplitudes with t-channel quark quantum numbers, extending the established gluon case. The explicit reproduction of the known one-loop trajectory provides an internal consistency test, and the approach uses only standard eikonal and background-field techniques without ad-hoc parameters or fitted inputs.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. There are no major comments requiring a point-by-point response.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper starts from the standard eikonal Wilson-line shockwave formalism and background-field method to identify the interpolating operator for the Reggeized quark and derive its nonlinear rapidity RG evolution equation at LLA. The only explicit verification is that, after signature projection in the dilute limit, the positive-signature channel reproduces the known one-loop power-law scaling of the quark Regge trajectory. This is presented as a consistency check against an external benchmark result, not as a fitted parameter renamed as prediction or a self-referential definition. No load-bearing self-citations, uniqueness theorems imported from prior author work, or ansatze smuggled via citation are used to force the central result. The derivation chain remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The work rests on the standard eikonal Wilson-line formalism of high-energy QCD and the background-field method; the new element is the specific quark operator and its evolution equation.

axioms (2)
  • domain assumption Eikonal approximation holds for the high-energy limit of QCD scattering
    Invoked throughout the shockwave/Wilson-line approach described in the abstract.
  • domain assumption Leading logarithmic accuracy is sufficient to derive the evolution
    Stated explicitly as the accuracy level of the derivation.
invented entities (1)
  • Interpolating operator for the Reggeized quark no independent evidence
    purpose: To represent the Reggeized quark state in terms of semi-infinite Wilson lines
    Identified in the paper but no independent falsifiable prediction outside the derivation is supplied.

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discussion (0)

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Reference graph

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