Momentum-Current Gravitational Multipoles of Hadrons

Abstract

We study multipole expansion of the momentum currents in hadrons, with three series $S^{(J)}$, ${\tilde{T}}^{(J)}$, and $T^{(J)}$, in connection with the gravitational fields generated nearby. The momentum currents are related to their energy-momentum form factors, which in principle can be probed through processes like deeply-virtual Compton scattering currently studied at JLab 12 GeV facility and future Electron Ion Collider. We define the leading momentum-current multipoles, tensor monopole $\tau$ ($T0$) and scalar quadrupole ${\hat{\sigma }}^{ij}$ ($S2$) moments, relating the former to the so-called $D$-term in the literature. We calculate the momentum current distribution in hydrogen atom and its monopole moment in the basic unit of ${\tau }_0={\hslash }^2/4M$, showing that the sign of $D$-term has little to do with mechanical stability. The momentum current distribution also strongly modifies the static gravitational field inside hadrons.

12 pages, 6 figures

References in corpus (9)

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• QCD Analysis of Near-Threshold Photon-Proton Production of Heavy Quarkonium
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• Energy momentum tensor and the D-term in the bag model
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Cited by in corpus (19)

• Gravitational form factors of the proton from lattice QCD
• Updated analysis of near-threshold heavy quarkonium production for probe of proton's gluonic gravitational form factors
• Nucleon D-term in holographic QCD
• Perturbative Calculations of Gravitational Form Factors at Large Momentum Transfer
• Mechanical structure of a spin-1 particle
• Forces inside a strongly-coupled scalar nucleon
• Generalized parton distributions in spin-3/2 particles
• Dominance of gluonic scale anomaly in confining pressure inside nucleon and D-term
• Quantum stresses in the hydrogen atom
• Gravitational form factor $D$ of charmonium from shear stress
• Internal force distributions in 't Hooft-Polyakov monopole and Julia-Zee dyon
• Gravitational form factors of the nucleon in the Skyrme model based on scale-invariant chiral perturbation theory
• Electromagnetic and gravitational local spatial densities for spin-1 systems
• A Journey of Seeking Pressure and Forces in the Nucleon
• Mechanical form factors and densities of non-relativistic fermions
• One-loop electron mass and QED trace anomaly
• Scale-anomaly-induced binding pressure in hadrons
• Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon
• Quantum stress and torsion distributions in the deuteron