Nonperturbative study of the action parameters for anisotropic-lattice quarks

The anisotropic lattice has proved an invaluable tool for simulations of a variety of physical quantities. The precision calculation of the glueball spectrum was an early application of the approach [1] and it was recognized that anisotropic actions may also be advantageous in heavy quark physics calculations [2]. Correlators of heavy particles such as glueballs and hadrons with a charm or bottom quark have a signal which decays rapidly. Monte Carlo estimates of these correlation functions can be noisy, making it difficult to resolve a plateau over a convincing range of lattice time steps. Increasing the number of time slices for which the effective mass of a particle has reached a plateau solves this problem and also decreases the statistical error in the fitted mass. Since this value may be used as an input to determine many physical parameters this decrease is very beneficial. Second, improved precision in effective mass fits means that momentum-dependent errors of O ap can be disentangled from other discretization effects and larger particle momenta may be considered. This is particularly relevant for the determination of semileptonic decay form factors where the overlap of momentum regions accessible to both experiments and lattice calculations is currently very small. Typically, experiments have more events with daughter particle momentum at or above 1 GeV. This is also the region where large momentum-dependent errors are expected in lattice calculations. The form factors of decays like B! ‘ and B! K are inputs to determinations of Cabibbo-Kobayashi-Maskawa quark-mixing matrix (CKM) parameters so that increased precision in lattice calculations can lead to tighter constraints on the standard model. This has motivated a study of 2 2 anisotropic lattices where the temporal and one spatial direction are made fine and all momentum is injected along this fine spatial axis. Details of the progress to date in this work are in Refs. [3,4]. The 2 2 formulation has also proved useful for a precision determination of the static interquark potential over large separations, which is described in Ref. [3]. In this paper we consider a 3 1 anisotropic