Low-energy limit of the extended Linear Sigma Model

TL;DR

This paper derives the low-energy limit of the extended Linear Sigma Model (eLSM) for two flavors, showing it aligns with Chiral Perturbation Theory (ChPT) and determining some low-energy constants from experimental data.

Contribution

It demonstrates the formal equivalence of the eLSM's low-energy limit to ChPT and provides a method to determine low-energy constants from hadron data.

Findings

Two low-energy constants are fitted to hadron masses and decay widths.

The tree-level values of these constants agree with ChPT.

Predictions are made for other constants based on ChPT values.

Abstract

The extended Linear Sigma Model (eLSM) is an effective hadronic model based on the linear realization of chiral symmetry $SU(N_f)_L \times SU(N_f)_R$, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the eLSM for $N_f=2$ flavors by integrating out all fields except for the pions, the (pseudo-)Nambu--Goldstone bosons of chiral symmetry breaking. We only keep terms entering at tree level and up to fourth order in powers of derivatives of the pion fields. Up to this order, there are four low-energy coupling constants in the resulting low-energy effective action. We show that the latter is formally identical to Chiral Perturbation Theory (ChPT), after choosing a representative for the coset space generated by chiral symmetry breaking and expanding up to fourth order in powers of derivatives of the pion fields. Two of the low-energy coupling constants of the eLSM are uniquely determined by a fit to hadron masses and decay widths. We find that their tree-level values are in reasonable agreement with the corresponding low-energy coupling constants of ChPT. The other two low-energy coupling constants are functions of parameters that can in principle be determined by $\pi\pi$ scattering, which has not yet been studied within the eLSM. Therefore, we use the respective values from ChPT to make a prediction for the values of these parameters in the eLSM Lagrangian.