Ultraviolet Properties of the Spinless, One-Particle Yukawa Model

TL;DR

This paper investigates the ultraviolet behavior of the spinless Yukawa model, showing that the model becomes trivial as the ultraviolet cutoff approaches infinity, with results valid in the small coupling regime.

Contribution

It provides a detailed analysis of the ultraviolet limit of the spinless Yukawa model, demonstrating triviality in the infinite cutoff limit under small coupling conditions.

Findings

Nucleon states are well-defined for finite cut-offs

Ground state energy depends on the cutoff and coupling

Model becomes trivial as cutoff approaches infinity

Abstract

We consider the one-particle sector of the spinless Yukawa model, which describes the interaction of a nucleon with a real field of scalar massive bosons (neutral mesons). The nucleon as well as the mesons have relativistic dispersion relations. In this model we study the dependence of the nucleon mass shell on the ultraviolet cut-off $\Lambda$. For any finite ultraviolet cut-off the nucleon one-particle states are constructed in a bounded region of the energy-momentum space. We identify the dependence of the ground state energy on $\Lambda$ and the coupling constant. More importantly, we show that the model considered here becomes essentially trivial in the limit $\Lambda\to\infty$ regardless of any (nucleon) mass and self-energy renormalization. Our results hold in the small coupling regime.