Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

TL;DR

This paper explores a linear sigma model with vector mesons to understand the chiral partner of the nucleon, revealing that a significant part of the nucleon mass arises from sources beyond the chiral condensate.

Contribution

It introduces a model incorporating the nucleon and its chiral partner with a chirally invariant mass term, and constrains this mass using experimental and lattice data.

Findings

Estimated the invariant mass parameter m_0 to be around 500 MeV.

Demonstrated that a substantial portion of the nucleon mass is not solely due to chiral symmetry breaking.

Validated the model through decay processes and scattering length calculations.

Abstract

We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions for the axial coupling constants of the nucleon, $g_{A}^{N}$, and its partner, $g_{A}^{N^{*}}$. Using experimental data for the decays $N^{*} \to N \pi$ and $a_{1} \to\pi\gamma$, as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0}\sim500$ MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay $N^{*} \to N \eta$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$.