Non-Perturbative Calculation of the Scalar Yukawa Theory in Four-Body Truncation

TL;DR

This paper presents a non-perturbative calculation of the quenched scalar Yukawa theory using light-front Tamm-Dancoff approach with up to four constituents, revealing sector dominance and convergence properties.

Contribution

It introduces a Fock sector dependent renormalization scheme and analyzes the dominance of low Fock sectors in the four-body truncation.

Findings

Lowest two Fock sectors dominate even at large coupling

One-body sector shows convergence with truncation

Four-body norm surpasses three-body norm at coupling ~1.7

Abstract

The quenched scalar Yukawa theory is solved in the light-front Tamm-Dancoff approach including up to four constituents (one scalar nucleon, three scalar pions). The Fock sector dependent renormalization is implemented. By studying the Fock sector norms, we find that the lowest two Fock sectors dominate the state even in the large-coupling region. The one-body sector shows convergence with respect to the Fock sector truncation. However, the four-body norm exceeds the three-body norm at the coupling $\alpha \approx 1.7$.