The $σ$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach

Nico Santowsky; Gernot Eichmann; Christian S. Fischer; Paul C. Wallbott; Richard Williams

doi:10.1103/PhysRevD.102.056014

paper

The $σ$ -meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach

arXiv:2007.06495 · doi:10.1103/PhysRevD.102.056014

Abstract

We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q q ˉ q q ˉ$ and $q q ˉ$ components of the Bethe-Salpeter wave function (with light quarks $q \in {u, d}$ ) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $π π$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $σ / f_{0} (500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}.

10 pages, 7 figures, v2: minor changes, version accepted by PRD

The σ-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach

Abstract

References in corpus (12)

The $σ$ -meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach