We determine elastic and coupled-channel amplitudes for isospin-1 meson-meson scattering in $P$-wave, by calculating correlation functions using lattice QCD with light quark masses such that $m_pi = 236$ MeV in a cubic volume of $sim (4 ,mathrm{fm})^
3$. Variational analyses of large matrices of correlation functions computed using operator constructions resembling $pipi$, $Koverline{K}$ and $qbar{q}$, in several moving frames and several lattice irreducible representations, leads to discrete energy spectra from which scattering amplitudes are extracted. In the elastic $pipi$ scattering region we obtain a detailed energy-dependence for the phase-shift, corresponding to a $rho$ resonance, and we extend the analysis into the coupled-channel $Koverline{K}$ region for the first time, finding a small coupling between the channels.
We explore the use of optimized operators, designed to interpolate only a single meson eigenstate, in three-point correlation functions with a vector-current insertion. These operators are constructed as linear combinations in a large basis of meson
interpolating fields using a variational analysis of matrices of two-point correlation functions. After performing such a determination at both zero and non-zero momentum, we compute three-point functions and are able to study radiative transition matrix elements featuring excited state mesons. The required two- and three-point correlation functions are efficiently computed using the distillation framework in which there is a factorization between quark propagation and operator construction, allowing for a large number of meson operators of definite momentum to be considered. We illustrate the method with a calculation using anisotopic lattices having three flavors of dynamical quark all tuned to the physical strange quark mass, considering form-factors and transitions of pseudoscalar and vector meson excitations. The dependence on photon virtuality for a number of form-factors and transitions is extracted and some discussion of excited-state phenomenology is presented.
Coupled-channel $pi K$ and $eta K$ scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a $
qbar{q}$ construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at ${m_pi=391,mathrm{MeV}}$, we find a gradual increase in the $J^P=0^+$ $pi K$ phase-shift which may be identified with a broad scalar resonance that couples strongly to $pi K$ and weakly to $eta K$. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the $kappa$ resonance. A bound state with $J^P=1^-$ is found very close to the $pi K$ threshold energy, whose coupling to the $pi K$ channel is compatible with that of the experimental $K^star(892)$. Evidence is found for a narrow resonance in $J^P=2^+$. Isospin--3/2 $pi K$ scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.
We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic JPC isoscalars. The use of a novel quark field construction has en
abled us to overcome the long-standing challenge of efficiently including quark-annihilation contributions. Hidden-flavor mixing angles are extracted and while most states are found to be close to ideally flavor mixed, there are examples of large mixing in the pseudoscalar and axial sectors in line with experiment. The exotic JPC isoscalar states appear at a mass scale comparable to the exotic isovector states.
