Isoscalar ππ; KK; ηη Scattering and the σ; f0; f2 Mesons from QCD

We present the first lattice QCD study of coupled isoscalar ππ;K ¯K; ηη S- and D-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the light quark mass corresponding to mπ ∼ 391 MeV. In the JP = 0+ sector we find analogues of the experimental σ and f0 (980) states, where the σ appears as a stable bound-state below ππ threshold, and, similar to what is seen in experiment, the f0 (980) manifests itself as a dip in the ππ cross section in the vicinity of the K ¯K threshold. For JP = 2+ we find two states resembling the f2 (1270) and f 2 (1525) observed as narrow peaks, with the lighter state dominantly decaying to ππ and the heavier state to K ¯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

Isoscalar pi pi, K(K)over-bar, eta eta scattering and the sigma, f(0),f(2) mesons from QCD

We present the first lattice QCD study of coupled isoscalar pi pi, K (K) over bar, eta eta S- and D-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the light quark mass corresponding to m(pi) similar to 391 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 (K) over bar threshold. For J(P) = 2(+) we find two states resembling the f(2)(1270) and f\u27(2)(1525), observed as narrow peaks, with the lighter state dominantly decaying to pi pi and the heavier state to K (K) over bar. 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

Energy-Dependent π^{+}π^{+}π^{+} Scattering Amplitude from QCD.

Focusing on three-pion states with maximal isospin ($\pi^+\pi^+\pi^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structures and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate

Energy-Dependent π^{+}π^{+}π^{+} Scattering Amplitude from QCD.

Focusing on three-pion states with maximal isospin (π^{+}π^{+}π^{+}), we present the first nonperturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate

Isoscalar ππ Scattering and the σ Meson Resonance from QCD

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the $\textit{S}$-wave phase shift up to the $K\overline{K}$ threshold. Calculations are performed at two values of the $\textit{u}$, $\textit{d}$ quark mass corresponding to $\textit{m}_{\pi} = 236, 391$ MeV , and the resulting amplitudes are described in terms of a σ meson which evolves from a bound state below the ππ threshold at the heavier quark mass to a broad resonance at the lighter quark mass.The research was supported in part under an Advanced Scientific Computing Research (ASCR), Advanced Leadership Computing Challenge (ALCC) grant, and used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This research is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Grants No. OCI-0725070 and No. ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing computing resources. Gauge configurations were generated using resources awarded from the U.S. Department of Energy Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program at Oak Ridge National Lab and also resources awarded at NERSC. R. A. B., R. G. E., and J. J. D. acknowledge support from U.S. Department of Energy Contract No. DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab. J. J. D. acknowledges support from the U.S. Department of Energy Early Career Contract No. DE-SC0006765. D. J. W. acknowledges support from the Isaac Newton Trust/University of Cambridge Early Career Support Scheme [RG74916]

Electroweak three-body decays in the presence of two- and three-body bound states

Abstract : Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors

Foreign policy of the New Left: explaining Brazil's Southern partnerships

Abstract The purpose of this study is to consider the relationship between domestic change and foreign policy in Brazil, a country seeking to become Latin America's hegemon, and achieve greater global status. It focuses on Brazil's partnerships with other countries in the Global South. It argues that, due to the combination of institutions and interests behind foreign policy-making in Brazil, there is no coherent project of South-South engagement. As a result, South-South ties tend to contradict the Brazilian government's foreign policy objective of acting as a global equaliser. The study also examines the drivers of Brazil's foreign conduct, and argues that the politico-economic determinants of foreign policy differ from those of domestic policy