Ab Initio Approach to the Non-Perturbative Scalar Yukawa Model

TL;DR

This paper presents the first non-perturbative calculation of the scalar Yukawa model using light-front Hamiltonian methods, analyzing Fock sector contributions and electromagnetic form factors up to four-body truncation.

Contribution

It introduces a systematic non-perturbative renormalization approach for the scalar Yukawa model and studies Fock sector convergence in the first such calculation.

Findings

One- and two-body contributions dominate at moderate coupling.

Four-body contributions become significant near coupling 2.2.

Form factor converges with respect to Fock sector expansion.

Abstract

We report on the first non-perturbative calculation of the scalar Yukawa model in the single-nucleon sector up to four-body Fock sector truncation (one "scalar nucleon" and three "scalar pions"). The light-front Hamiltonian approach with a systematic non-perturbative renormalization is applied. We study the $n$-body norms and the electromagnetic form factor. We find that the one- and two-body contributions dominate up to coupling $\alpha \approx 1.7$. As we approach the coupling $\alpha \approx 2.2$, we discover that the four-body contribution rises rapidly and overtakes the two- and three-body contributions. By comparing with lower sector truncations, we show that the form factor converges with respect to the Fock sector expansion.