Momentum-Current Gravitational Multipoles of Hadrons

TL;DR

This paper explores the multipole expansion of momentum currents in hadrons, linking them to gravitational fields and energy-momentum form factors, with calculations in hydrogen atoms and implications for gravitational fields inside hadrons.

Contribution

It introduces new momentum-current multipoles, relates them to the D-term, and calculates their distributions, providing insights into gravitational effects in hadrons.

Findings

Momentum-current multipoles are defined and related to the D-term.

The distribution of momentum currents in hydrogen atoms is calculated.

The sign of the D-term is shown to be unrelated to mechanical stability.

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 $\tau_0 =\hbar^2/4M$, 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.