Glueball spectroscopy in lattice QCD using gradient flow

TL;DR

This paper explores the use of spatial gradient flow in lattice QCD to improve glueball spectroscopy by reducing ultraviolet noise, introducing a new smearing method, and calculating the masses of the lowest-lying glueball states.

Contribution

It proposes a spatial gradient flow technique for constructing glueball operators, enhancing the accuracy of glueball mass calculations in lattice QCD.

Findings

Spatial gradient flow effectively reduces noise in glueball correlators.

The method accurately determines the masses of the lowest-lying glueball states.

Comparison shows improved efficiency over traditional methods.

Abstract

Removing ultraviolet noise from the gauge fields is necessary for glueball spectroscopy in lattice QCD. It is known that the Yang-Mills gradient flow method is an alternative approach instead of link smearing or link fuzzing in various aspects. In this work we study the application of the gradient flow technique to the construction of the extended glueball operators. We examine a simple application of the gradient flow method, which has some problems in glueball mass calculations at large flow time because of its nature of diffusion in space-time. To avoid this problem, the spatial links are evolved by the ``spatial gradient flow'', that is defined to restrict the diffusion to spatial directions only. We test the spatial gradient flow in calculations of glueball two-point functions and Wilson loops as a new smearing method, and then discuss its efficiency in comparison with the original gradient flow method and the conventional method. Furthermore, to demonstrate the feasibility of our proposed method, we determine the masses of the three lowest-lying glueball states, corresponding to the $0^{++}$, $2^{++}$ and $0^{-+}$ glueballs, in the continuum limit in the pure Yang-Mills theory.