Chromoelectric projections of light-front gluonic gravitational distributions in near-threshold quarkonium scattering

Abstract: We apply the established Drell-Yan-frame light-front EMT/GFF density framework to the gluonic response selected by compact-quarkonium chromoelectric scattering. The analysis separates the scalar trace form factor from the non-scalar gluon EMT combination governed by $A_g(t)$, $D_g(t)$, and $\bar C_g(t)$. The forward chromoelectric strength is fixed externally by the threshold ratio $R_{\rm LF}^{\rm int}=N_{\rm nt}(0)/N_θ(0)\simeq 0.15$, while the transverse profile is controlled by the normalized off-forward form-factor shape. We show that scalar and non-scalar responses can have different transverse localization and that near-threshold quarkonium production probes a chromoelectric EMT projection rather than an individual gravitational form-factor slope or a universal mass density.

• The paper introduces a rigorous separation of the chromoelectric and scalar EMT projections in near-threshold quarkonium scattering, clarifying that the chromoelectric component contributes approximately 15% of the scalar strength.
• The paper employs the light-front formalism and Fourier–Bessel transforms to derive impact-parameter distributions of gluonic form factors, enabling precise spatial characterization of transverse localization.
• The paper emphasizes that conventional extractions of geometric radii are insufficient, advocating for precise dσ/dt measurements to disentangle process-dependent EMT projections.

Chromoelectric Projections of Light-Front Gluonic Gravitational Distributions in Near-Threshold Quarkonium Scattering

Overview

The paper "Chromoelectric projections of light-front gluonic gravitational distributions in near-threshold quarkonium scattering" (2606.14304) addresses the spatial characterization of gluonic energy-momentum tensor (EMT) distributions in the context of near-threshold heavy-quarkonium interactions with nucleons. It constructs light-front transverse gravitational distribution functions (GDFs) corresponding both to the scalar EMT trace and to a specific non-scalar combination, selected by the compact-quarkonium chromoelectric operator. The analysis rigorously distinguishes between off-forward spatial shape functions and forward normalization strengths, establishing that quarkonium production near threshold probes a chromoelectric EMT projection with distinct transverse localization properties.

Light-Front EMT Structure and Form Factors

The treatment adopts the light-front formalism in the Drell-Yan frame—where $t = -\bm{\Delta}_\perp^2$—to construct longitudinal-boost-invariant impact-parameter distributions for various gluonic form factors. Scalar and non-scalar gluon EMT matrix elements are decomposed in terms of the gravitational form factors $A_g(t)$, $D_g(t)$, and $\bar C_g(t)$, with individual scheme- and scale-dependence handled at $\mu=2{\rm\ GeV}$. The scalar trace form factor $G_\theta(t)$ encodes the overall mass decomposition, while $A_g(0)$ yields the gluon momentum fraction and $D_g(t)$ captures mechanical contributions with nontrivial sign structure.

Transverse distributions are generated by two-dimensional Fourier–Bessel transforms of these form factors, providing spatial profiles at fixed light-front time. The slope conventions adopted allow quantitative definition of light-front radii, although the paper emphasizes that these are not direct physical sizes in the three-dimensional rest frame.

Chromoelectric Shape–Strength Separation

The analysis introduces a rigorous shape–strength separation for the chromoelectric EMT projection relevant to compact-quarkonium scattering. A specific linear combination of gluon form factors, $G_{\rm nt}^{\rm LF}(t;\omega,\zeta)$, is selected by the operator structure of the chromoelectric interaction. Critically, the integrated forward strength $N_{\rm nt}(0)$ is fixed externally by threshold theorems and is distinct from the raw forward value of the off-forward shape combination; for typical parameters, $A_g(t)$0. The normalized transverse spatial profile is governed by the off-forward behavior of the constituent form factors.

This explicit separation clarifies that the total chromoelectric strength is not the simple integral of the spatial distribution, and underscores why extraction of geometric radii or densities from EMT slopes is not straightforward in this context.

Numerical Modeling and Transverse Localization

Employing analytic pole models for $A_g(t)$1, $A_g(t)$2, and $A_g(t)$3 with reference inputs from lattice QCD and phenomenological studies, the paper computes normalized transverse distributions for scalar and non-scalar chromoelectric projections. Derivative-weighted stress kernels, implementing light-front analogs of pressure and shear distributions, are considered to illustrate the spatial mechanical content carried by $A_g(t)$4. The non-scalar chromoelectric distribution exhibits distinct localization relative to the scalar trace, confirming that near-threshold quarkonium production does not simply probe a universal mass density.

Cumulative Response Diagnostics

A cumulative response ratio $A_g(t)$5 is introduced to quantify the relative spatial distribution of chromoelectric and scalar trace responses as a function of transverse impact parameter cutoff $A_g(t)$6. This ratio converges rapidly and robustly to the externally determined normalization $A_g(t)$7, independent of the detailed shape of the scalar or non-scalar profiles. The integrated limit is always $A_g(t)$8, though the rate of convergence is shape-dependent, a fact demonstrated in sensitivity scans across form-factor parameters.

Physical and Theoretical Implications

The paper makes several formal claims:

1. Near-threshold quarkonium scattering accesses a chromoelectric projection of the gluonic EMT, not a standalone GDF or gravitational radius.

2. The scalar and non-scalar responses differ in both normalization and spatial shape; in particular, the non-scalar strength is a fraction ($A_g(t)$915%) of the scalar reference with distinct transverse localization.

3. Extraction of spatial densities or geometric sizes from EMT form-factor slopes is not justified in relativistic QFT; light-front impact-parameter distributions are the appropriate spatial language.

4. Precision measurements of $D_g(t)$0 near threshold, including channel comparisons ($D_g(t)$1, $D_g(t)$2), helicity asymmetries, and $D_g(t)$3-dependence, have the potential to disentangle these projections experimentally.

Practically, this framework mandates a future phenomenological analysis in which scalar trace and chromoelectric non-scalar contributions are treated as distinct transverse spatial profiles, with normalizations fixed externally. The results caution against conflating mass distributions, mechanical distributions, and process-dependent projections in interpreting hadronic spatial structure.

Conclusion

This work establishes a formal light-front spatial representation for both scalar and chromoelectric non-scalar gluonic EMT distributions in near-threshold quarkonium–nucleon scattering, separating forward normalization from off-forward spatial shape. The cumulative response diagnostic confirms robust normalization independence from spatial profile assumptions, and emphasizes that the relevant object is a chromoelectric projection of EMT structures—distinct from universal mass densities or simple geometric radii. These insights lay the foundation for more precise phenomenological treatments of quarkonium production and gluonic structure in QCD.