Momentum Flow Mechanisms and Color-Lorentz Forces on Quarks in the Nucleon

Momentum conservation in the nucleon is examined in terms of continuous flow of the momentum current density (or, in short, momentum flow), which receives contributions from both kinetic motion and interacting forces involving quarks and gluons. While quarks conduct momentum flow through their kinetic motion and the gluon scalar (anomaly) contributes via pure interactions, the gluon stress tensor has both effects. The quarks momentum flow encodes the information of the color-Lorentz force density on them, and the momentum conservation allows to trace its origin to the gluon tensor and anomaly (a "negative pressure" potential). From the state-of-the-art lattice calculations and experimental fits on the form factors of the quantum chromodynamics energy-momentum tensor, we exhibit pictures of the momentum flow and the color-Lorentz forces on the quarks in the nucleon. In particular, the anomaly contributes a critical attractive force with a strength similar to that of a heavy-quark confinement potential.