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Ambiguities in the definition of local spatial densities in light hadrons
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The relationship between the matrix element of a local operator and the Fourier transform of the associated form factor fails for systems such as the nucleon where its intrinsic size is of order its Compton wavelength. Although one can conceive of an intrinsic charge density distribution in the proton, there does not seem to be an unambiguous way to define, compute, or measure it precisely.
Forward citations
Cited by 13 Pith papers
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Lattice evidence that scalar glueballs are small
First lattice extraction of scalar glueball gravitational form factors gives a mass radius of 0.263(31) fm, smaller than typical hadrons.
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Mechanical form factors and densities of non-relativistic fermions
Non-relativistic fermion energy-momentum tensor matrix elements are decomposed into Galilei-covariant mechanical form factors using new eight-component spinors, with pilot-wave based density formulas separating intern...
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Polarized Nucleon as a Topological Dipole
A polarized nucleon generically hosts a topological charge dipole q_top ∝ S · r̂ whose moment equals −ΔΣ/N_f in the chiral limit.
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Quantum stress and torsion distributions in the deuteron
First complete non-relativistic impulse-approximation calculation of all eleven deuteron EMT form factors, including non-conserved c-bar and s-bar form factors that map to force and torsion distributions inside the nucleons.
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Quantum stresses in the hydrogen atom
For the hydrogen ground state, the \bar{c} gravitational form factor, not the D-term, carries the local force law, supporting a literal stress interpretation under pilot wave ontology.
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Transverse distributions of the energy-momentum tensor for a spin-$3/2$ baryon
The paper derives the longitudinal-boost dependence of transverse energy-momentum tensor distributions for a spin-3/2 baryon and matches the infinite-momentum limit to direct light-front results.
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Transverse energy-momentum tensor distributions in polarized nucleons
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.
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Reconstruction of Gravitational Form Factors using Generative Machine Learning
A diffusion model trained on synthetic physics-motivated curves reconstructs the proton's A(t), J(t), D(t) from sparse data, extracting c8=-4.6±0.8, c9=-0.61±0.19, and D(0)=-4.3±0.8.
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Gravitational form factors of the nucleon in the Skyrme model based on scale-invariant chiral perturbation theory
A Skyrme model with a dilaton field attributes the proton's negative internal pressure and confining force to the gluonic scale anomaly, and reproduces the lattice QCD D(t) form factor.
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Imaging the charge distributions of flavor-symmetric and -asymmetric mesons
Using a maximum-entropy inversion of DSE/BSE form factors, the authors map meson charge profiles and find quark-antiquark distances that shrink with quark mass and grow by 5-15% for spin-aligned mesons.
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Nucleon relativistic weak-neutral axial-vector four-current distributions
The 3D axial charge density of a spin-1/2 hadron is parity-odd and controlled by the induced pseudotensor form factor G_T^Z, while the second-class current drops out of the mean-square axial and spin radii.
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Misconceptions About the Physics of the QCD Trace Anomaly from Renormalization in a Reducible Basis
This paper critiques reducible-basis renormalization of the QCD trace anomaly, arguing it introduces unphysical scheme dependence and that the standard whole-anomaly decomposition is the only symmetry-allowed choice.
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Baryon Form Factors
A review of baryon form factors summarizing the authors' dispersion-theoretical fits, which yield r_p^E = 0.840 fm, r_p^M = 0.849 fm, and r_n^M = 0.864 fm.
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