Ordinary and exotic mesons in the extended Linear Sigma Model

TL;DR

The paper presents an extended Linear Sigma Model (eLSM) that incorporates various mesons and glueballs, successfully describing mesonic phenomenology up to 2 GeV and exploring chiral symmetry restoration and the QCD phase diagram.

Contribution

It introduces an expanded eLSM including exotic and hybrid mesons, chiral multiplets, and glueballs, providing a comprehensive framework aligned with experimental data.

Findings

eLSM describes meson masses and decay widths up to 2 GeV accurately.

Exotic and hybrid mesons are incorporated with consistent chiral multiplet structures.

Scalar glueball is predominantly gluonic, with other glueballs coupling to specific mesons.

Abstract

The extended Linear Sigma Model (eLSM) is a hadronic model based on the global symmetries of QCD and the corresponding explicit, anomalous, and spontaneous breaking patterns. In its basic three-flavor form, its mesonic part contains the dilaton/glueball as well as the nonets of (pseudo)scalar and (axial-)vector mesons, thus chiral symmetry is linearly realized. In the chiral limit and neglecting the chiral anomaly, only one term -- within the dilaton potential -- breaks dilatation invariance. Spontaneous symmetry breaking is implemented by a generalization of the Mexican-hat potential, with explicit symmetry breaking responsible for its tilting. The overall mesonic phenomenology up to 2 GeV is in agreement with the PDG compilation of masses and decay widths. The eLSM was enlarged to include other conventional quark-antiquark nonets (pseudovector and orbitally excited vector mesons, (axial-)tensor mesons, etc.), as well as two nonets of hybrid mesons, the lightest one with exotic quantum numbers $J^{PC} = 1^{-+}$ not allowed for $\bar{q}q$ objects such as the resonance $\pi_1(1600)$ and the recently discovered $\eta_1(1855)$. In doing so, different types of chiral multiplets are introduced: heterochiral and homochiral multiplets, which differ in the way they transform under chiral transformations. Moreover, besides the scalar glueball, the tensor, the pseudoscalar and the vector glueballs were coupled to the eLSM: the scalar $f_0(1710)$ turns out to be mostly gluonic, the tensor glueball couples strongly to vector mesons, and the pseudoscalar glueball couples can be assigned to $X(2370)$ or $X(2600)$. The eLSM contains chiral partners on an equal footing and is therefore well suited for studies of chiral symmetry restoration at nonzero temperature and densities. The QCD phase diagram and the location of the critical endpoint were investigated within this framework.