Validation of the finite-volume quantization condition for two spinless particles

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we present a way to validate the higher-order quantization conditions. This is an important step given the involved derivations of these formulae. We derive and validate quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states zero and non-zero total momentum. For all 45 quantization conditions we considered (22 in cubic box, 23 in elongated box) we find perfect agreement.Comment: 55 pages, 8 figures, 45 tables, 1 supplemen

Estimating the two-particle KK-matrix for multiple partial waves and decay channels from finite-volume energies

An implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the L\"uscher formalism and involving a Hermitian matrix known as the "box matrix" is described. The method includes higher partial waves and multiple decay channels. Two fitting procedures for estimating the $K$-matrix parameters, which properly incorporate all statistical covariances, are discussed. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are obtained for total momenta in several directions. First tests involving $\rho$-meson decay to two pions include the $L=3$ and $L=5$ partial waves, and the contributions from these higher waves are found to be negligible in the elastic energy range.Comment: 32 pages, 1 figur

Scattering from finite-volume energies including higher partial waves and multiple decay channels

A new implementation of estimating the two-to-two $K$-matrix from finite-volume energies based on the Luescher formalism is described. The method includes higher partial waves and multiple decay channels, and the fitting procedure properly includes all covariances and statistical uncertainties. The method is also simpler than previously used procedures. Formulas and software for handling total spins up to $S=2$ and orbital angular momenta up to $L=6$ are presented.Comment: 8 pages. Presented at Lattice 2017, the 35th International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June 201

Determination of \u3cem\u3es\u3c/em\u3e- and \u3cem\u3ep\u3c/em\u3e-wave \u3cem\u3eI\u3c/em\u3e = 1/2 \u3cem\u3eKπ\u3c/em\u3e Scattering Amplitudes in \u3cem\u3eN\u3c/em\u3e\u3csub\u3ef\u3c/sub\u3e = 2 + 1 Lattice QCD

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 Nf = 2+1 flavors of dynamical Wilson-clover fermions at mπ = 230MeV. A large spatial extent of L = 3.7fm enables a good energy resolution while partial wave mixing due to the reduced symmetries of the finite volume is treated explicitly. The p-wave amplitude is well described by a Breit–Wigner shape with parameters mK⁎/mπ = 3.808(18) and gBWK⁎Kπ = 5.33(20) which are insensitive to the inclusion of d-wave mixing and variation of the s-wave parametrization. An effective range description of the near-threshold s-wave amplitude yields mπα0 = –0.353(25)

Including Tetraquark Operators in the Low-Lying Scalar Meson Sectors in Lattice QCD

Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing the $K_0^*(700)$ ($\kappa$) and the $a_0(980)$ in $N_f = 2 + 1$ QCD, with $m_\pi \approx 230$ MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.Comment: 6 pages, 4 figures, proceedings for The 15th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon, MENU-201