Forces inside a strongly-coupled scalar nucleon

TL;DR

This paper non-perturbatively calculates gravitational form factors of a strongly coupled scalar theory mimicking nucleon-pion interactions, revealing internal energy and pressure distributions using light-front Hamiltonian methods.

Contribution

It introduces a Fock sector dependent renormalization scheme and systematically analyzes the energy-momentum tensor to extract form factors free of spurious contributions.

Findings

Form factors obey momentum conservation and stability conditions

Computed energy and pressure distributions inside the system

Converted off-diagonal Fock sector contributions to diagonal ones

Abstract

We investigate the gravitational form factors of a strongly coupled scalar theory that mimic the interaction between the nucleon and the pion. The non-perturbative calculation is based on the light-front Hamiltonian formalism. We renormalize the energy-momentum tensor with a Fock sector dependent scheme. We also systematically analyze the Lorentz structure of the energy-momentum tensor and identify the suitable hadron matrix elements to extract the form factors, avoiding the contamination of spurious contributions. We verify that the extracted form factors obey momentum conservation as well as the mechanical stability condition. From the gravitational form factors, we compute the energy and pressure distributions of the system. Furthermore, we show that utilizing the Hamiltonian eigenvalue equation, the off-diagonal Fock sector contributions from the interaction term can be converted to diagonal Fock sector contributions, yielding a systematic non-perturbative light-front wave function representation of the energies and forces inside the system.