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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. 

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential ${\mu }_I$bounds the partition function for a baryon chemical potential ${\mu }_B=3{\mu }_I/2$, these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society2025 

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. 

A<sc>bstract</sc> We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specificallyπ⁺K⁺,π⁺π⁺K⁺andK⁺K⁺π⁺. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLSN_f= 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up topwaves. This requires also results for theπ⁺π⁺andK⁺K⁺spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix inπ⁺π⁺K⁺andK⁺K⁺π⁺systems, finding statistically significant nonzero results in most cases. We includesandpwaves in the K matrix forπ⁺K⁺scattering, finding evidence for an attractivep-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory. 

A bstract We study the properties of three-body resonances using a lattice complex scalar φ 4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory. 

Abstract Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally.