A group-theoretic construction yields complete form factor bases for scalar, vector, and tensor operators on spin-1/2 to spin-2 particles, with new P and T structures for higher spins and identification of a redundant conserved structure for spin-2 in existing literature.
Gluon gravitational structure of hadrons of different spin
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, $\rho$ meson, and $\Delta$ baryon as functions of the squared momentum transfer $t$ in the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD study with pion mass $m_{\pi} = 450(5) \; \text{MeV}$. By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for the corresponding gluon mechanical and mass radii, as well as the forward-limit gluon contributions to the momentum fraction and angular momentum of the hadrons.
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Analytical expressions for quark gravitational TMDs are derived in the LFQDM, verified against standard TMD relations, and linked to transverse pressure and shear-force distributions.
An effective light-front wave function whose five-dimensional piece comes from holographic QCD yields pion gravitational form factors A(Q^{2}) and D(Q^{2}) that match lattice results after parameter tuning.
QCD sum rules yield numerical tensor form factors for Ω^-, Σ^{*+}, and Ξ^{*-} up to 10 GeV² together with forward-limit quark tensor charges.
σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
Transverse EMT distributions in polarized nucleons are derived in the quantum phase-space formalism; they reduce to standard light-front densities (including bad components) in the infinite-momentum frame.
Near-threshold charmonium chromoelectric scattering separates into a scalar anomaly channel and a traceless spin-two channel fixed by Ag(0) forward and by a specific GFF combination off forward, without a boost-enhanced mass radius.
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σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
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Transverse energy-momentum tensor distributions in polarized nucleons
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Scalar and spin-two energy-momentum-tensor structure in near-threshold charmonium probes of the proton
Near-threshold charmonium chromoelectric scattering separates into a scalar anomaly channel and a traceless spin-two channel fixed by Ag(0) forward and by a specific GFF combination off forward, without a boost-enhanced mass radius.