Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD

Abstract

Multihadron operators are crucial for reliably extracting the masses of excited states lying above multihadron thresholds in lattice QCD Monte Carlo calculations. The construction of multihadron operators with significant coupling to the lowest-lying multihadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gauge-covariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on ${24}^{3}\ifmmode\times\else\texttimes\fi{}128$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}256$ anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as $\ensuremath{\eta}\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\eta}$ in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, $\ensuremath{\pi}\ensuremath{\pi}$, and $\ensuremath{\eta}\ensuremath{\eta}$ operators is shown to be feasible.