Role of a four-quark and a glueball state in pion-pion and pion-nucleon scattering

Abstract

We consider the two-flavor version of the extended linear sigma model (eLSM), which contains (pseudo)scalar and (axial-)vector quark-antiquark mesons, a scalar glueball (predominantly corresponding to $f_0(1710)$), as well as the nucleon and its chiral partner. We extend this model by the additional light scalar meson $f_0(500)$, predominantly a putative four-quark state. We investigate various interaction terms of the four-quark and glueball states with the other particles, some of which preserve and some of which explicitly break the $U(1{)}_{\text{A}}$ symmetry. We test our model by performing a global fit to masses and decay widths of the scalar resonances and pion-pion scattering lengths. We also discuss the influence of the scalar four-quark state and the glueball on the baryon sector by evaluating pion-nucleon scattering parameters. We find that the inclusion of $f_0(500)$ improves the description of pion-pion and pion-nucleon scattering lengths.

arXiv commentCorrected several typos, replaced old experimental pion-nucleon scattering data with up-to-date data, corresponds now to the published version

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• Remarks on nuclear matter: how an ${\omega }_0$ condensate can spike the speed of sound, and a model of $Z(3)$ baryons
• Comprehensive study of mass modifications of light mesons in nuclear matter in the three-flavor extended Linear Sigma Model
• The fate of the critical endpoint at large $N_c$
• Glueball-glueball scattering and the glueballonium
• Ordinary and exotic mesons in the extended Linear Sigma Model
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• Chiral anomaly and strange-nonstrange mixing