A Journey of Seeking Pressure and Forces in the Nucleon

Abstract

Momentum current density (MCD) $T^{ij}$ is a general physics concept describing the momentum conservation through momentum flow generated from both the kinetic motion of particles and the interacting forces among them. It has been suggested by M. Polyakov et al. that the MCD in the nucleon, characterized by the form factor $C/D$ of the QCD energy-momentum tensor, can be interpreted as the pressure and shear forces between adjacent parts of the system because the nucleon interior approximates a continuous medium. While intuitively appealing, we find that the interpretation is hard to justify from a detailed examination of the physical mechanisms for the momentum flow in QCD. After reviewing through a broad range of classical and quantum systems, we find that while thermal and/or quantum average of isotropic motion contributes to kinetic MCD a pressure term proportional to ${\delta }^{ij}$, when there is an anisotropic motion, the pressure cannot simply be identified from the MCD tensor. Furthermore, kinetic pressure cannot be considered as the surface force between adjacent parts of a system. More importantly, at the scale of the nucleon dimension, the color forces among quarks and gluons is by no means short-ranged as in a continuous medium, and the resulting interaction MCD cannot be interpreted as normal or shear ``stress'' force, although an isotropic term from the QCD trace anomaly may be interpreted as a ``vacuum pressure.'' Following our previous study of force densities through divergences of kinetic MCDs, we affirm that the vacuum pressure term provides a confining potential on the quarks through color Lorentz forces.

58 pages, 8 figures, accepted by Nuclear Physics B

References in corpus (65)

• Insights into the Emergence of Mass from Studies of Pion and Kaon Structure
• Nucleon form-factors of the energy momentum tensor in the chiral quark-soliton model
• Unpolarized and helicity generalized parton distributions of the proton within lattice QCD
• The mass radius of the proton
• The nucleon form-factors of the energy momentum tensor in the Skyrme model
• QCD Analysis of Near-Threshold Photon-Proton Production of Heavy Quarkonium
• Gravitational form factors of the proton from lattice QCD
• Revisiting the proton mass decomposition
• Forces within hadrons on the light front
• Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
• Hard-core deconfinement and soft-surface delocalization from nuclear to quark matter
• Nucleon mass radii and distribution: Holographic QCD, Lattice QCD and GlueX data
• Ambiguities in the definition of local spatial densities in light hadrons
• Single diffractive hard exclusive processes for the study of generalized parton distributions
• Phenomenological assessment of proton mechanical properties from deeply virtual Compton scattering
• Gravitational form factors and mechanical properties of proton in a light-front quark-diquark model
• Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case
• Energy momentum tensor and the D-term in the bag model
• Gravitational form factors within light-cone sum rules at leading order
• The energy-momentum tensor of spin-1 hadrons: formalism
• Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions
• On the definition of local spatial densities in hadrons
• Contact interaction analysis of pion GTMDs
• Nucleon D-term in holographic QCD
• Measures of pion and kaon structure from generalised parton distributions
• Extraction of the proton mass radius from the vector meson photoproductions near thresholds
• Chiral theory of nucleons and pions in the presence of an external gravitational field
• Momentum-Current Gravitational Multipoles of Hadrons
• The gravitational form factor D(t) of the electron
• Gravitational form factors of the baryon octet with flavor SU(3) symmetry breaking
• Cosmic Axion Force
• Determination of the generalized parton distributions through the analysis of the world electron scattering data considering two-photon exchange corrections
• Gravitational form factors and mechanical properties of a quark at one loop in light-front Hamiltonian QCD
• Scale symmetry breaking, quantum anomalous energy and proton mass decomposition
• Quadrupole pressure and shear forces inside baryons in the large $N_c$ limit
• Pion Valence-Quark Generalized Parton Distribution at Physical Pion Mass
• A bound on the nucleon Druck-term from chiral EFT in curved space-time and mechanical stability conditions
• Lattice gauge theory computation of the static force
• Stability of the pion and the pattern of chiral symmetry breaking
• Forces inside a strongly-coupled scalar nucleon
• Mechanical structure of a spin-1 particle
• Hadronic structure on the light-front IV: Heavy and light Baryons
• Mass sum rule of hadrons in the QCD instanton vacuum
• Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon
• Dominance of gluonic scale anomaly in confining pressure inside nucleon and D-term
• Gravitational form factors of hyperons in light-cone QCD
• Magnetic enhancement of baryon confinement modeled via a deformed Skyrmion
• Local spatial densities for composite spin-3/2 systems
• Pion gravitational form factors in the QCD instanton vacuum II
• Effect of the pion field on the distributions of pressure and shear in the proton
• Gravitational form factors of $N(1535)$ in QCD
• Gravitational transverse-momentum distributions
• Flavor structure of the energy-momentum tensor form factors of the proton
• Spatial densities of the photon on the light front
• Transverse force distributions in the proton from lattice QCD
• Internal force distributions in 't Hooft-Polyakov monopole and Julia-Zee dyon
• Regularization dependence of pion generalised parton distributions
• Stress out of charmonia
• Electromagnetic and gravitational local spatial densities for spin-1 systems
• Gluon gravitational form factors of protons from charmonium photoproduction
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• Transverse Force on Transversely Polarized Quarks in Longitudinally Polarized Nucleons
• Medium modification of the nucleon mechanical properties: Abel tomography case
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon

Cited by in corpus (5)

• Quantum stress and torsion distributions in the deuteron
• Energy-momentum tensor form factor D(t) of proton and neutron
• Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons
• Reconstruction of Gravitational Form Factors using Generative Machine Learning
• The energy-momentum tensor in a classical model of the electron