Isoscalar $\pi\pi, K\overline{K}, \eta\eta$ scattering and the $\sigma, f_0, f_2$ mesons from QCD

TL;DR

This lattice QCD study investigates coupled isoscalar meson scattering, revealing states analogous to known mesons like the sigma, f0(980), and f2 resonances, and provides insights into their properties from first-principles calculations.

Contribution

First lattice QCD analysis of coupled isoscalar meson scattering, identifying and characterizing sigma, f0(980), and f2 states from discrete finite-volume spectra.

Findings

Sigma appears as a stable bound state below pi-pi threshold.

f0(980) manifests as a dip near the K-Kbar threshold.

Two f2 states resemble f2(1270) and f2'(1525), with distinct decay patterns.

Abstract

We present the first lattice QCD study of coupled isoscalar $\pi\pi,K\overline{K},\eta\eta$ $S$- and $D$-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the quark mass corresponding to $m_\pi\sim391$ MeV. In the $J^P=0^+$ sector we find analogues of the experimental $\sigma$ and $f_0(980)$ states, where the $\sigma$ appears as a stable bound-state below $\pi\pi$ threshold, and, similar to what is seen in experiment, the $f_0(980)$ manifests itself as a dip in the $\pi\pi$ cross section in the vicinity of the $K\overline{K}$ threshold. For $J^P=2^+$ we find two states resembling the $f_2(1270)$ and $f_2'(1525)$, observed as narrow peaks, with the lighter state dominantly decaying to $\pi\pi$ and the heavier state to $K\overline{K}$. The presence of all these states is determined rigorously by finding the pole singularity content of scattering amplitudes, and their couplings to decay channels are established using the residues of the poles.