High Statistics Analysis using Anisotropic Clover Lattices: (I) Single Hadron Correlation Functions

We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292, 500 sets of measurements are made using 1194 gauge configurations of size 203 x 128 with an anisotropy parameter ζ = bs/bt = 3.5, a spatial lattice spacing of bs = 0.1227 ± 0.0008 fm, and pion mass of Mπ ∼ 390 MeV. Ground state baryons masses are extracted with fully quantified uncertainties that are at or below the ∼ 0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the Nπ threshold and, therefore, the isospin-1/2 πN s-wave scattering phase-shift can be extracted using Luescher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time-slices. This is due to backward propagating states arising from the anti-periodic boundary conditions imposed on the quark-propagators in the time-direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables