Particle level screening of scalar forces in 1+1 dimensions

TL;DR

This paper studies how scalar fields, specifically the symmetron, screen point sources in 1+1 dimensions, revealing conditions for mass screening and source behavior depending on separation, with implications for particle physics.

Contribution

It provides an exact analysis of scalar field responses to point sources in 1+1 dimensions, including screening effects and source interactions, and explores related fermion mass generation constraints.

Findings

Mass of a point source can be screened if above a critical value.

Two sources behave independently at large separation, but merge at small separation.

Fermion mass generated via Yukawa coupling is limited by the Higgs mass.

Abstract

We investigate how non-linear scalar field theories respond to point sources. Taking the symmetron as a specific example of such a theory, we solve the non-linear equation of motion in one spatial dimension for (i) an isolated point source and (ii) two identical point sources with arbitrary separation. We find that the mass of a single point source can be screened by the symmetron field, provided that its mass is above a critical value. We find that two point sources behave as independent, isolated sources when the separation between them is large, but, when their separation is smaller than the symmetron's Compton wavelength, they behave much like a single point source with the same total mass. Finally, we explore closely related behavior in a toy Higgs-Yukawa model, and find indications that the maximum fermion mass that can be generated consistently via a Yukawa coupling to the Higgs in 1+1 dimensions is roughly the mass of the Higgs itself, with potentially intriguing implications for the hierarchy problem.