arxiv: 2604.22953 · v1 · submitted 2026-04-24 · ✦ hep-ph · hep-th

Recognition: unknown

Light-front mass operator with dressed quarks

J. A. O. Marinho , J. P. B. C. de Melo , T. Frederico , W. de Paula

Authors on Pith no claims yet

Pith reviewed 2026-05-08 10:55 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords light-front dynamicsquark dressingmass operatorpion structureTMD distributionsparton distribution functionsdistribution amplitudesrunning quark mass

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The pith

An effective light-front mass-squared operator incorporates quark dressing for quark-antiquark systems.

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 mass-squared operator that includes quark dressing effects for use in Hamiltonian approaches to hadrons. It starts from a quark propagator parametrized to match lattice QCD and derives a resolvent that separates instantaneous parts before projecting onto helicity states. This yields an operator whose application to the pion produces TMDs, PDFs, and distribution amplitudes with notable infrared changes from dressing. Such a framework matters because it offers a way to embed nonperturbative QCD features directly into light-front calculations without losing perturbative control at high momenta.

Core claim

What carries the argument

The effective dressed mass-squared operator obtained by projecting the disconnected light-front resolvent of dressed quark propagators onto the constituent-quark helicity basis.

If this is right

Quark dressing induces sizable infrared modifications in hadron distributions.
The operator preserves controlled ultraviolet behavior.
It provides a framework to incorporate nonperturbative QCD dynamics into light-front descriptions of hadrons.
Applications to the pion produce unpolarized TMDs, PDFs and distribution amplitudes.

Where Pith is reading between the lines

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

The method could be applied to other mesons to test consistency of the running mass across the hadron spectrum.
Tuning the lattice-inspired propagator parameters against specific parton distribution data would allow direct validation of the infrared modifications.
The separation of instantaneous terms may simplify numerical diagonalization of light-front bound-state equations for higher states.

Load-bearing premise

The generalized spectral representation of the quark propagator cleanly separates instantaneous contributions and that projection onto the helicity basis yields a valid effective operator for dynamics.

What would settle it

If the computed pion TMDs, PDFs or distribution amplitudes deviate significantly from experimental data or lattice results in the infrared region while ultraviolet behavior is checked, the incorporation of dressing effects would be shown insufficient.

Figures

Figures reproduced from arXiv: 2604.22953 by J. A. O. Marinho, J. P. B. C. de Melo, T. Frederico, W. de Paula.

**Figure 1.** Figure 1: FIG. 1. Ratio view at source ↗

**Figure 2.** Figure 2: FIG. 2. Effective quark self-energy as a function of the mo view at source ↗

**Figure 4.** Figure 4: FIG. 4. Unpolarized Transverse Momentum Distribution view at source ↗

**Figure 6.** Figure 6: FIG. 6 view at source ↗

**Figure 7.** Figure 7: FIG. 7 view at source ↗

read the original abstract

We construct an effective light-front mass-squared operator for quark-antiquark systems that incorporates quark dressing effects through a running quark mass. Starting from a Minkowski-space quark propagator constrained by lattice-QCD-inspired parametrization, we derive the disconnected light-front resolvent for a light quark-antiquark system using a generalized spectral representation of an individual quark propagator separating out the instantaneous contributions. By projecting the resolvent onto a constituent-quark helicity basis, we obtain an effective dressed mass-squared operator suitable for light-front Hamiltonian approaches. We introduce an effective light-front quark self-energy and analyze its momentum dependence. As an application, we study pion structure using representative light-front wave-function models and compute unpolarized transverse-momentum-dependent distributions, unpolarized parton distribution functions and distribution amplitudes. Our results show that quark dressing induces sizable infrared modifications while preserving controlled ultraviolet behavior, providing a framework to incorporate nonperturbative QCD dynamics into light-front descriptions of hadrons.

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 gives a concrete recipe for folding a lattice-inspired running quark mass into an effective light-front mass-squared operator for quark-antiquark systems via spectral representation and helicity projection.

read the letter

The central new piece is the step that starts from a Minkowski-space quark propagator with running mass, builds the disconnected light-front resolvent through a generalized spectral representation, strips out the instantaneous terms, and projects onto the constituent helicity basis to produce a usable M^2 operator. That construction is the actual advance; the rest of the paper applies it to existing pion light-front wave-function models to compute TMDs, PDFs, and distribution amplitudes as a consistency check. The results show the expected infrared softening from dressing while the ultraviolet stays well behaved, which is a clean demonstration that the operator can be dropped into standard light-front Hamiltonian work without blowing up. The approach follows the usual light-front dressed-quark playbook but packages the lattice input more directly than earlier attempts. The main limitation is that everything downstream inherits the uncertainties of the chosen lattice parametrization; there is no independent derivation or error propagation shown for how those parameters affect the final distributions. The calculations also stay at the level of representative wave functions rather than solving a dynamical equation, so the structure functions remain illustrative. The paper is aimed at the small group of people who already do light-front Hamiltonian calculations for hadrons and want a systematic way to import nonperturbative quark-mass effects. It is technically sound enough and the steps are spelled out clearly enough that a serious referee should see it; the subfield can use the method even if the numerical gains are modest.

Referee Report

1 major / 3 minor

Summary. The manuscript constructs an effective light-front mass-squared operator for quark-antiquark systems that incorporates quark dressing via a running quark mass taken from a lattice-QCD-inspired parametrization of the Minkowski-space propagator. Starting from a generalized spectral representation of the individual quark propagator, the authors derive the disconnected light-front resolvent while isolating instantaneous contributions, project onto the constituent-quark helicity basis to obtain the dressed M² operator, introduce an effective light-front quark self-energy, and apply the framework to pion TMDs, PDFs, and DAs using representative light-front wave-function models, reporting sizable infrared modifications with controlled ultraviolet behavior.

Significance. If the derivation holds, the work supplies a concrete route to embed nonperturbative quark dressing into light-front Hamiltonian dynamics for hadrons. The lattice-inspired input and the explicit consistency checks on pion observables constitute a strength; the approach follows standard LF techniques while addressing the incorporation of running-mass effects without introducing new free parameters beyond the input parametrization.

major comments (1)

The central construction rests on the generalized spectral representation of the quark propagator to obtain the disconnected resolvent and cleanly separate instantaneous pieces (as described in the abstract). Without an explicit check that this representation reproduces the known free-quark limit or matches standard LF resolvent constructions when the running mass is set constant, the projection step to the helicity basis remains unverified as load-bearing for the effective operator.

minor comments (3)

The abstract and introduction should explicitly state the section or equation where the effective light-front self-energy is defined and its momentum dependence is analyzed, to improve traceability.
When presenting the pion TMD/PDF/DA results, the manuscript should include a brief comparison to the undressed (constant-mass) case to quantify the size of the infrared modifications claimed.
Notation for the running mass function M(p²) versus the effective operator should be clarified to avoid confusion with standard constituent-mass symbols.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the recommendation for minor revision. We address the major comment below.

read point-by-point responses

Referee: The central construction rests on the generalized spectral representation of the quark propagator to obtain the disconnected resolvent and cleanly separate instantaneous pieces (as described in the abstract). Without an explicit check that this representation reproduces the known free-quark limit or matches standard LF resolvent constructions when the running mass is set constant, the projection step to the helicity basis remains unverified as load-bearing for the effective operator.

Authors: We thank the referee for this observation. The generalized spectral representation employed in the derivation is constructed to reduce exactly to the standard Dirac propagator when the mass function is taken to be a constant. In that limit the disconnected light-front resolvent recovers the known free-quark expression, the instantaneous pieces match the standard separation, and the projection onto the constituent-quark helicity basis follows the usual light-front procedure without modification. Nevertheless, we agree that an explicit verification would remove any residual ambiguity and strengthen the presentation. In the revised manuscript we will add a short subsection (or appendix) that explicitly sets the running mass to a constant, recovers the free resolvent, and confirms consistency with established light-front constructions before performing the helicity projection. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from external input

full rationale

The paper takes a lattice-QCD-inspired Minkowski-space quark propagator (with running mass parametrization) as an external input. It then applies a generalized spectral representation to construct the disconnected light-front resolvent, isolates instantaneous terms, and projects onto the constituent helicity basis to obtain the effective M^2 operator. These steps follow standard light-front techniques and do not reduce the output to the input by algebraic identity or by renaming a fit. The subsequent introduction of an effective self-energy is presented as a derived quantity from the same resolvent, and the TMD/PDF/DA calculations are explicit applications using separate model wave functions rather than predictions forced by the propagator fit. No self-citations, uniqueness theorems, or ansatz smuggling are invoked in the provided chain. The construction therefore adds independent structure on top of the chosen input.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on a lattice-QCD-inspired parametrization whose parameters are fitted externally, plus standard domain assumptions in light-front dynamics about spectral representations and basis projections; no new entities are postulated.

free parameters (1)

running quark mass function parameters
The quark propagator is constrained by a lattice-QCD-inspired parametrization that introduces momentum-dependent mass parameters fitted to lattice data.

axioms (2)

domain assumption Generalized spectral representation of the quark propagator separates instantaneous contributions
Invoked to derive the disconnected light-front resolvent for the quark-antiquark system.
domain assumption Projection onto constituent-quark helicity basis yields a suitable effective mass operator
Assumed without further justification to be appropriate for light-front Hamiltonian approaches.

pith-pipeline@v0.9.0 · 5473 in / 1354 out tokens · 44775 ms · 2026-05-08T10:55:24.984712+00:00 · methodology

discussion (0)

Reference graph

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