Effects of scalar mesons in a Skyrme model with hidden local symmetry

TL;DR

This paper investigates how light scalar mesons influence skyrmion properties within a mesonic model that includes pions, rho, omega, and scalar mesons, revealing how mixing and coupling affect soliton mass and size.

Contribution

It introduces a mesonic model with mixing of two- and four-quark scalar mesons and analyzes their impact on skyrmion properties, highlighting the effects of coupling and mixing.

Findings

Lighter scalar mesons lead to smaller soliton mass and larger size when no direct coupling is present.

Increasing coupling strength results in heavier solitons and larger baryon density radius.

Enhanced two-quark component in scalar mesons decreases soliton mass and increases size.

Abstract

We study the effects of light scalar mesons on the skyrmion properties by constructing and examining a mesonic model including pion, rho meson, and omega meson fields as well as two-quark and four-quark scalar meson fields. In our model, the physical scalar mesons are defined as mixing states of the two- and four-quark fields. We first omit the four-quark scalar meson field from the model and find that when there is no direct coupling between the two-quark scalar meson and the vector mesons, the soliton mass is smaller and the soliton size is larger for lighter scalar mesons; when direct coupling is switched on, as the coupling strength increases, the soliton becomes heavy, and the radius of the baryon number density becomes large, as the repulsive force arising from the $\omega$ meson becomes strong. We then include the four-quark scalar meson field in the model and find that mixing between the two-quark and four-quark components of the scalar meson fields also affects the properties of the soliton. When the two-quark component of the lighter scalar meson is increased, the soliton mass decreases and the soliton size increases.