Exotic meson decay widths using lattice quantum chromodynamics

Most experiments in particle physics are scattering experiments, the analysis of which leads to masses, scattering phases, decay widths and other properties of one or multi-particle systems. Until the advent of Lattice Quantum Chromodynamics (LQCD) it was difficult to compare experimental results on low energy hadron-hadron scattering processes to the predictions of QCD, the current theory of strong interactions. The reason being, at low energies the QCD coupling constant becomes large and the perturbation expansion for scattering; amplitudes does not converge. To overcome this, one puts the theory onto a lattice, imposes a momentum cutoff, and computes the integral numerically. For particle masses, predictions of LQCD agree with experiment, but the area of decay widths is largely unexplored. ^ LQCD provides ab initio access to unusual hadrons like exotic mesons that are predicted to contain real gluonic structure. To study decays of these type resonances the energy spectra of a two-particle decay state in a finite volume of dimension L can be related to the associated scattering phase shift δ(k) at momentum k through exact formulae derived by Lüscher. Because the spectra can be computed using numerical Monte Carlo techniques, the scattering phases can thus be determined using Lüscher's formulae, and the corresponding decay widths can be found by fitting Breit-Wigner functions. ^ Results of such a decay width calculation for an exotic hybrid( h) meson (JPC = 1-+) are presented for the decay channel h → πa 1. This calculation employed Lüscher's formulae and an approximation of LQCD called the quenched approximation. Energy spectra for the h and πa1 systems were extracted using eigenvalues of a correlation matrix, and the corresponding scattering phase shifts were determined for a discrete set of πa1 momenta. Although the number of phase shift data points was sparse, fits to a Breit-Wigner model were made, resulting in a decay width of about 60 MeV. ^