Trace anomaly and non-scalar gluon EMT contributions in near-threshold quarkonium scattering on the light front

Arkadiy I. Syamtomov

arxiv: 2606.08835 · v1 · pith:EDRICNKAnew · submitted 2026-06-07 · ✦ hep-ph

Trace anomaly and non-scalar gluon EMT contributions in near-threshold quarkonium scattering on the light front

Arkadiy I. Syamtomov This is my paper

Pith reviewed 2026-06-27 17:47 UTC · model grok-4.3

classification ✦ hep-ph

keywords light fronttrace anomalygluon EMTquarkonium scatteringchromoelectric OPEmass decompositiontransverse densitiesDrell-Yan frame

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The pith

The forward light-front ratio reproduces the QCD EMT result for gluon contributions without spurious boost enhancement

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

The paper develops a light-front formulation for the scalar trace-anomaly and non-scalar gluon energy-momentum tensor parts of the compact quarkonium chromoelectric interaction with a nucleon. It separates the trace-anomaly contribution from the forward normal gluon-energy term in light-front variables, where the gluon momentum fraction comes from the T_g^{++} matrix element and the energy factor from projecting the traceless EMT. This ensures the forward ratio matches the combination of QCD EMT mass decomposition and chromoelectric OPE without introducing artificial boost effects. The work also equates the off-forward form-factor combination to its covariant counterpart and reinterprets the scalar form-factor radius as a transverse light-front radius with longitudinal-boost invariance in the Drell-Yan frame.

Core claim

The forward light-front ratio reproduces the result obtained by combining the QCD EMT mass decomposition with the compact-quarkonium chromoelectric operator-product expansion, without introducing any spurious boost enhancement. The off-forward light-front form-factor combination is equivalent to the corresponding covariant expression, and the scalar form-factor radius is reinterpreted as a transverse light-front radius providing a longitudinal-boost-invariant transverse-density interpretation.

What carries the argument

The projection of the traceless gluon energy-momentum tensor onto the threshold chromoelectric structure in light-front variables, which isolates the normal gluon-energy factor matching the covariant decomposition

If this is right

Gluon momentum fraction follows from the T_g^{++} matrix element in light-front variables
Normal gluon-energy factor arises only after projecting the traceless EMT onto the threshold chromoelectric structure
Off-forward light-front form-factor combination equals the covariant expression for the non-scalar gluon-EMT contribution
Scalar form-factor radius admits interpretation as transverse light-front radius in the Drell-Yan frame

Where Pith is reading between the lines

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

The equivalence opens the possibility of computing these EMT contributions using light-front wave functions or basis light-front quantization methods
The transverse light-front radius interpretation may provide new insights into the spatial distribution of gluon energy in the nucleon
This formulation could be tested against results from covariant calculations in different frames to confirm the absence of boost artifacts

Load-bearing premise

The traceless part of the gluon EMT, when projected onto the threshold chromoelectric structure in light-front variables, yields exactly the normal gluon-energy factor that appears in the covariant mass decomposition

What would settle it

An explicit computation of the forward light-front ratio in a solvable model or lattice simulation that deviates from the expected value from the QCD EMT mass decomposition combined with the chromoelectric OPE would falsify the claimed reproduction

Figures

Figures reproduced from arXiv: 2606.08835 by Arkadiy I. Syamtomov.

**Figure 2.** Figure 2: FIG. 2. Light-front transverse densities in the Drell–Yan frame [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

read the original abstract

We present a light-front formulation of the scalar trace-anomaly and non-scalar gluon energy-momentum-tensor contributions entering the compact-heavy-quarkonium chromoelectric interaction with a nucleon. The construction reformulates, in light-front variables, the separation between the scalar trace-anomaly contribution to the compact-quarkonium chromoelectric interaction and the forward normal gluon-energy contribution appearing in the QCD EMT mass decomposition. In light-front variables, the gluon momentum fraction follows from the $T_g^{++}$ matrix element, while the normal gluon-energy factor arises only after projecting the traceless EMT onto the threshold chromoelectric structure. In this way the forward light-front ratio reproduces the result obtained by combining the QCD EMT mass decomposition with the compact-quarkonium chromoelectric operator-product expansion (OPE), without introducing any spurious boost enhancement. We also construct the off-forward light-front form-factor combination controlling the non-scalar gluon-EMT contribution and show its equivalence to the corresponding covariant expression. Finally, the scalar form-factor radius is reinterpreted as a transverse light-front radius, providing a longitudinal-boost-invariant transverse-density interpretation in the Drell--Yan frame. The work is therefore not a new mass-radius extraction, but a light-front operator formulation connecting the QCD EMT mass decomposition, the compact-quarkonium chromoelectric OPE, modern gluon momentum fractions, and light-front transverse densities.

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 reformulates the trace anomaly and gluon EMT separation for near-threshold quarkonium in light-front variables, showing equivalence to covariant results without new numbers or predictions.

read the letter

The core contribution is an explicit light-front operator setup for the scalar trace-anomaly piece and the non-scalar gluon EMT term in the compact quarkonium chromoelectric interaction. They define the gluon momentum fraction from the T_g^{++} matrix element and show that the traceless projection onto the threshold structure recovers the standard gluon-energy factor from the QCD EMT decomposition. The forward ratio matches the earlier covariant result with no extra boost term, and they give the matching off-forward form-factor combination plus a transverse light-front reading of the scalar radius in the Drell-Yan frame.

What works is the clean translation into light-front language. The authors state up front that this is not a new mass or radius extraction, which keeps the claims proportionate. The construction connects the EMT mass decomposition, the chromoelectric OPE, modern gluon fractions, and light-front densities without introducing fitted parameters or circular loops.

The soft spot is that the abstract and summary assert the projection works exactly but do not display the intermediate steps or explicit checks against known limits. Without those, one cannot yet rule out a subtle kinematic mismatch, though the stress-test note finds no obvious inconsistency in the stated logic. The work is therefore plausible but still needs the full derivation verified.

This is for readers already using light-front methods who want the operator dictionary for these particular quantities. It will not interest people hunting new numerical results. The paper shows clear thinking and honest engagement with the literature, so it deserves a serious referee even if the final verdict is that it is mainly a useful reformulation.

Referee Report

1 major / 1 minor

Summary. The paper claims to provide a light-front formulation of the scalar trace-anomaly and non-scalar gluon EMT contributions entering the compact-heavy-quarkonium chromoelectric interaction with a nucleon. It reformulates the separation between the scalar trace-anomaly contribution and the forward normal gluon-energy contribution from the QCD EMT mass decomposition in light-front variables, showing that the forward light-front ratio (from T_g^{++} matrix element followed by traceless projection) reproduces the covariant result obtained by combining the QCD EMT mass decomposition with the compact-quarkonium chromoelectric OPE, without spurious boost enhancement. It also constructs the off-forward light-front form-factor combination and shows equivalence to the covariant expression, while reinterpreting the scalar form-factor radius as a transverse light-front radius providing a longitudinal-boost-invariant transverse-density interpretation in the Drell-Yan frame.

Significance. If the central equivalence holds, the work supplies a useful operator-level bridge connecting the QCD EMT mass decomposition, the compact-quarkonium chromoelectric OPE, modern gluon momentum fractions, and light-front transverse densities. This could facilitate light-front calculations of near-threshold quarkonium scattering and provide a boost-invariant density interpretation. The paper explicitly positions itself as a reformulation rather than a new mass-radius extraction.

major comments (1)

[Abstract (forward light-front ratio paragraph)] Abstract (paragraph on forward light-front ratio): the central claim that the traceless projection of the gluon EMT onto the threshold chromoelectric structure in light-front variables exactly recovers the normal gluon-energy factor (with no spurious boost terms) is asserted but the provided text supplies no explicit derivation steps, intermediate expressions, or checks against known covariant limits. This projection is load-bearing for the no-spurious-enhancement result.

minor comments (1)

The abstract mentions T_g^{++} for the momentum fraction but does not name the additional light-front operators or projectors used for the traceless part; adding one sentence would improve clarity without altering the technical content.

Simulated Author's Rebuttal

1 responses · 0 unresolved

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

read point-by-point responses

Referee: Abstract (paragraph on forward light-front ratio): the central claim that the traceless projection of the gluon EMT onto the threshold chromoelectric structure in light-front variables exactly recovers the normal gluon-energy factor (with no spurious boost terms) is asserted but the provided text supplies no explicit derivation steps, intermediate expressions, or checks against known covariant limits. This projection is load-bearing for the no-spurious-enhancement result.

Authors: We agree that the abstract, being a concise summary, does not contain the intermediate steps. The full derivation of the traceless projection of the gluon EMT in light-front variables, the resulting forward ratio, and its explicit equivalence to the covariant QCD EMT mass decomposition plus chromoelectric OPE (without spurious boost terms) are given in the main text. We will revise the abstract to include a brief reference to these steps and the relevant sections so that the central claim is more self-contained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; explicit reformulation of known results

full rationale

The paper's central claim is an explicit light-front reformulation of the QCD EMT mass decomposition combined with the compact-quarkonium chromoelectric OPE, showing that the forward ratio from T_g^{++} and traceless projection reproduces the covariant gluon-energy factor without spurious boost terms. This is presented as a coordinate re-expression connecting existing quantities (gluon momentum fractions, transverse densities) rather than a derivation that reduces to fitted inputs or self-referential premises. No self-citations are invoked as load-bearing uniqueness theorems, no parameters are fitted then renamed as predictions, and no ansatz is smuggled via prior work. The construction is self-contained against external benchmarks via operator definitions, warranting a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, ad-hoc axioms, or new entities are introduced in the provided text. The work relies on standard QCD EMT decomposition and OPE assumptions already present in the cited literature.

axioms (1)

domain assumption Standard QCD energy-momentum tensor decomposition and compact-quarkonium chromoelectric OPE remain valid when rewritten in light-front coordinates.
The equivalence claim rests on this background assumption stated in the abstract.

pith-pipeline@v0.9.1-grok · 5778 in / 1307 out tokens · 16139 ms · 2026-06-27T17:47:31.512000+00:00 · methodology

discussion (0)

Reference graph

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Pith/arXiv arXiv 1995

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arXiv 2022