Properties of the ρ Resonance from ππ Elastic Scattering and the Spectrum of Excited ρ Mesons Using the Stochastic LapH Method in Lattice QCD

Inclusion of multi-meson operators allows lattice QCD calculations to extract energies of resonances above two-meson thresholds, as well as to study two-meson scattering. Previously, temporal correlations involving multi-hadron operators were difficult to evaluate due to contributions from quark propagators which begin and end on the same time slice. The stochastic LapH method allows for efficient computations of such contributions and is applied in this work to compute the low-energy spectrum of the I = 1, S = 0, T 1u channel, as well as the P -wave ππ scattering phase shift. The calculations use 412 gauge-field configurations generated by a Monte Carlo method utilizing clover-improved Wilson fermions on an anisotropic 32 × 256 lattice with a pion mass near 240 MeV. The masses of the ρ meson and several excited mesons are computed using a 63× 63 correlator matrix for total zero momentum and are shown to agree with experiment. Additionally, the low-energy spectrum of stationary states in several channels of nonzero total momenta are calculated. The ππ stationarystate energies in a finite box are used to calculate the infinite-volume I = 1 P -wave scattering phase shifts, from which the width of the ρ resonance is determined.