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

Lakaschus, Phillip (Institute for Theoretical Physics, Goethe University, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany) ; Mauldin, Justin L.P. (Institute for Theoretical Physics, Goethe University, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany) ; Giacosa, Francesco (Institute of Physics, Jan Kochanowski University, PL-25406 Kielce, Poland) ; Rischke, Dirk H. (Institute for Theoretical Physics, Goethe University, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany) (Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China)

09 April 2019

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 ${f}_{0}\left(1710\right)\right]$, as well as the nucleon and its chiral partner. We extend this model by the additional light scalar meson ${f}_{0}\left(500\right)$, 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 $\text{U}{\left(1\right)}_{A}$ 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 ${f}_{0}\left(500\right)$ improves the description of pion-pion and pion-nucleon scattering lengths.

Published in: Physical Review C 99 (2019)
Published by: APS
DOI: 10.1103/PhysRevC.99.045203
arXiv: 1807.03735
License: CC-BY-4.0

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