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We study systems of two and three mesons composed of pions and kaons at maximal isospin using four CLS ensembles with $a\approx 0.063\mathrm{fm}$, including one with approximately physical quark masses. Using the stochastic Laplacian-Heaviside method, we determine the energy spectrum of these systems including many levels in different momentum frames and irreducible representations. Using the relativistic two- and three-body finite-volume formalism, we constrain the two- and three-meson K matrices, including not only the leading $s$wave, but also $p$and $d$waves. By solving the three-body integral equations, we determine, for the first time, the physical-point scattering amplitudes for $3{\pi }^{+}$, $3K^{+}$, ${\pi }^{+}{\pi }^{+}{K}^{+}$, and $K^{+}{K}^{+}{\pi }^{+}$systems. These are determined for total angular momentum $J^P=0^{-}$, $1^{+}$, and $2^{-}$. We also obtain accurate results for $2{\pi }^{+}$, ${\pi }^{+}{K}^{+}$, and $2K^{+}$phase shifts. We compare our results to chiral perturbation theory and to phenomenological fits. 

We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of π+ and K+, at a lattice spacing a=0.063 fm, and in the isospin-symmetric limit. We also obtain accurate results for maximal-isospin two-meson amplitudes, with those for ${\pi }^{+}{K}^{+}$and $2K^{+}$being the first determinations at the physical point. Dense lattice spectra are obtained using the stochastic Laplacian-Heaviside method, and the analysis leading to scattering amplitudes is done using the relativistic finite-volume formalism. Results are compared to chiral perturbation theory and to phenomenological fits to experimental data, finding good agreement. 

The recent BESIII announcement of a pseudoscalar glueball candidate makes an update on glueballs from lattice QCD timely. A brief review of how glueballs are studied in lattice QCD is given, and the reasons that glueballs are difficult to study both in lattice QCD with dynamical quarks and in experiments are outlined. Recent glueball studies in lattice QCD are then presented, and an exploratory investigation of the scalar glueball using glueball, meson, and meson-meson operators is summarized, suggesting that no scalar state below 2 GeV or so can be considered to be predominantly a glueball state. 

The low-lying energy spectrum of the static-colour-source-anti-source system in a vacuum containing light and strange quarks is computed using lattice QCD for a range of different light quark masses. The resulting levels are described using a simple model Hamiltonian and the parameters in this model are extrapolated to the physical light-quark masses. In this framework, the QCD string tension is found to be sqrt(sigma) = 445(3)_stat (6)_sys MeV. 

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel πΣ−K¯N from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using L\"{u}scher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the Λ(1405), a virtual bound state below the πΣ threshold and a resonance pole right below the K¯N threshold. 

This work presents technical details of determining the finite-volume energy spectra for the scattering amplitude of the coupled-channel πΣ−K¯N from lattice QCD data. The importance of reliably extracting such spectra lies in the crucial dependence of the hadronic scattering amplitudes analysis on the energy spectrum when using L\"{u}scher's formalism. Results of the methods used are presented and the final finite-volume spectra are shown. The analysis of the scattering amplitude based on these results, exhibits a two-pole structure for the Λ(1405), a virtual bound state below the πΣ threshold and a resonance pole right below the K¯N threshold. 

A lattice QCD computation of the coupled channel πΣ–¯KN scattering amplitudes in the Λ(1405) region is detailed. Results are obtained using a single ensemble of gauge field configurations with Nf=2+1 dynamical quark flavors and mπ≈200  MeV and mK≈487  MeV. Hermitian correlation matrices using both single baryon and meson-baryon interpolating operators for a variety of different total momenta and irreducible representations are used. Several parametrizations of the two-channel scattering K-matrix are utilized to obtain the scattering amplitudes from the finite-volume spectrum. The amplitudes, continued to the complex energy plane, exhibit a virtual bound state below the πΣ threshold and a resonance pole just below the ¯KN threshold. 

This Letter presents the first lattice QCD computation of the coupled channel πΣ−¯KN scattering amplitudes at energies near 1405 MeV. These amplitudes contain the resonance Λ(1405) with strangeness S=−1 and isospin, spin, and parity quantum numbers I(JP)=0(1/2−). However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to mπ≈200  MeV and mK≈487  MeV, this study finds the amplitudes exhibit a virtual bound state below the πΣ threshold in addition to the established resonance pole just below the ¯KN threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity. 

This report summarizes results of the first lattice QCD calculation of coupled-channelπΣ−K¯Nscattering in the Λ(1405) region. This study was carried out using a single CLS ensemble with a heavier-than-physical pion mass m_π≈ 200 MeV and a lighter-than-physical kaon mass m_K>≈ 487 MeV. Once the finite-volume energy spectrum has been reliably extracted, the Lüscher method was employed to obtain scattering amplitudes. Through a variety of parametrizations of the two-channel K-matrix, the final results show a virtual bound state below the πΣ threshold and a resonance right below K¯N. 

Recent results studying the masses and widths of low-lying baryon resonances in lattice QCD are presented. The S-wave Nπ scattering lengths for both total isospins I=1/2 and I=3/2 are inferred from the finite-volume spectrum below the inelastic threshold together with the I=3/2 P-wave containing the Δ(1232) resonance. A lattice QCD computation employing a combined basis of three-quark and meson-baryon interpolating operators with definite momentum to determine the coupled channel Σπ-NKbar scattering amplitude in the Λ(1405) region is also presented. Our results support the picture of a two-pole structure suggested by theoretical approaches based on SU(3) chiral symmetry and unitarity.