An $a_0$ resonance in strongly coupled $\pi \eta$, $K \overline{K}$ scattering from lattice QCD

Abstract

We present the first calculation of coupled-channel meson-meson scattering in the isospin = 1, G-parity negative sector, with channels πη, KK and πη , in a first-principles approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the S-matrix, and find that the S-wave features a prominent cusp-like structure in πη → πη close to KK threshold coupled with a rapid turn on of amplitudes leading to the KK final-state. This behavior is traced to an a0(980)-like resonance, strongly coupled to both πη and KK, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of D-wave scattering suggests a narrow tensor resonance at higher energy.

Tetraquark mixing supported by the partial decay widths of two light-meson nonets

“…Or one can think about combining our mixing model with the hadronic molecular picture [4][5][6] or other pictures as in Refs. [3,[7][8][9] with a hope that certain improvement is achieved. However, it seems that all these scenarios are not easy to proceed at this point.…”

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“…Indeed, there have been various approaches to describing the two nonets. They include hadronic molecular picture for f 0 (980), a 0 (980) [3][4][5][6], a two-quark picture with hadronic intermediate states [7,8], tetraquarks mixed with a glueball [9], the mixing model of the P-wave q q with the four-quark qq q q scalar nonet [10,11], and the tetraquarks including instantons [12].…”

A simple alternative to the relativistic Breit–Wigner distribution

“…We stress that the examples that we shall present are illustrative and aim to show the utility of the Sill distribution as a useful function to fit data in first approximation. Yet, for each of the presented resonances, more detailed and advanced studies have been performed (e.g, see [75,76] for a review of various methods as well as the PDG review on Resonances [1]). The Sill is not a substitute of such advanced studies, but a simple useful tool to study resonances by taking into account threshold effects.…”

“…On the other hand, care is needed, since the resonance a 0 (980) has been studied in a variety of works as a exotic meson candidate (e.g. in the form of a molecular state or a companion pole) (e.g, [75,[87][88][89][90], for a review on the status of exotic hadrons, see [91]). We thus proceed as follows.…”