Related papers: Prospects for $\gamma^\star \gamma^\star \to \pi \…
We present a comprehensive analysis of the dispersion relations for the doubly-virtual process $\gamma^*\gamma^*\to\pi\pi$. Starting from the Bardeen-Tung-Tarrach amplitudes, we first derive the kernel functions that define the system of…
The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are calculated using a single ensemble of anisotropic lattice QCD gauge field configurations with $N_{\mathrm{f}} = 2+1$ flavors of dynamical Wilson-clover fermions at…
We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using…
We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and…
pi pi scattering at low energy is sensitive to the structure of the QCD vacuum. I review the calculations of the pi pi scattering lengths and phases, and group them in three cathegories: 1. those based on very general theoretical…
We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and…
A general prescription for the construction of $\pi \pi$ interaction potentials which preserve scattering length constraints from chiral symmetry when iterated in scattering equations is derived. The prescription involves only minor…
The pi+pi+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four lattice…
The extraction of two- and three-body hadronic scattering amplitudes and the properties of the low-lying hadronic resonances from the finite-volume energy levels in lattice QCD represents a rapidly developing field of research. The use of…
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…
Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The…
The elastic $I=1$ $p$-wave $\pi\pi$ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with $N_{\rm f}=2+1$ dynamical quark flavors. Wilson clover ensembles generated by the…
One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ with…
It is known that the high-energy quark-quark scattering amplitude can be described by the expectation value of two lightlike Wilson lines, running along the classical trajectories of the two colliding particles. Generalizing the results of…
Progress in computing various meson-baryon scattering amplitudes is presented on a single ensemble from the Coordinated Lattice Simulations (CLS) consortium with $m_\pi=200$ MeV and $N_f=2+1$ dynamical fermions. The finite-volume L\"uscher…
For resonances decaying in a finite volume, the simple identification of state and eigenvalue is lost. The extraction of the scattering amplitude is a major challenge as we demonstrate by extrapolating the physical S_{11} amplitude of…
We determine the energy-dependent amplitude for elastic {\pi}{\pi} P-wave scattering in isospin-1 by computing part of the discrete energy spectrum of QCD in finite cubic boxes. We observe a rapidly rising phase shift that can be well…
We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic…
We present $I=1/2$ $D^\ast\pi$ scattering amplitudes from lattice QCD and determine two low-lying $J^P=1^+$ axial-vector $D_1$ states and a $J^P=2^+$ tensor $D_2^\ast$. Computing finite-volume spectra at a light-quark mass corresponding to…
First-principles calculations of multi-hadron dynamics are a crucial goal in lattice QCD. Significant progress has been achieved in developing, implementing, and applying theoretical tools that connect finite-volume quantities to their…