Monte Carlo study of glueball masses in the Hamiltonian limit of SU(3) lattice gauge theory

TL;DR

This paper uses Monte Carlo techniques to accurately determine glueball masses in SU(3) lattice gauge theory's Hamiltonian limit, demonstrating consistency with Euclidean results and confirming the reliability of the Euclidean approach.

Contribution

It provides improved glueball mass estimates in the Hamiltonian limit by extrapolating from anisotropic lattices, confirming universality between Euclidean and Hamiltonian formulations.

Findings

Glueball masses are consistent with previous Euclidean estimates.

The Euclidean Monte Carlo method is validated for Hamiltonian studies.

Significant improvement in mass ratio accuracy.

Abstract

Using Standard Euclidean Monte Carlo techniques, we discuss in detail the extraction of the glueball masses of 4-dimensional SU(3) lattice gauge theory in the Hamiltonian limit, where the temporal lattice spacing is zero. By taking into account the renormalization of both the anisotropy and the Euclidean coupling, we calculate the string tension and masses of the scalar, axial vector and tensor states using standard Wilson action on increasingly anisotropic lattices, and make an extrapolation to the Hamiltonian limit. The results are compared with estimates from various other Hamiltonian and Euclidean studies. We find that more accurate determination of the glueball masses and the mass ratios has been achieved and the results are a significant improvement upon previous Hamiltonian estimates. The continuum predictions are then found by extrapolation of results obtained from smallest values of spatial lattice spacing. For the lightest scalar, tensor and axial vector states we obtain masses of $m_{0^{++}}=1654 \pm 83$ MeV, $m_{2^{++}}=2272\pm 115$ MeV and $m_{1^{+-}}=2940\pm 165$ MeV, respectively. These are consistent with the estimates obtained in the previous studies in the Euclidean limit. The consistency is a clear evidence of universality between Euclidean and Hamiltonian formulations. From the accuracy of our estimates, we conclude that the standard Euclidean Monte Carlo method is a reliable technique for obtaining results in the Hamiltonian version of the theory, just as in Euclidean case.