Update on the computation of the quenched $SU(6)$ Yang-Mills lattice spectrum

Abstract

We report on our continued efforts to measure the glueball and meson spectra in SU($N$) Yang-Mills theory and QCD with the aim of extrapolating to the large-$N$ limit. In particular, we document the computation of the low-lying SU($6$) spectrum. We employ a multilevel sampling algorithm to measure glueball correlators to reduce statistical noise in the large-time separation limit. The gluon operator basis is composed of spatial Wilson loop measured at different levels of (APE) smearing, with vanishing momentum selected to maximise the orthonogality of the operators and their overlap with the lowest lying states. We also report on analogous computations for the $J=0,1$ non-singlet meson spectrum with two degenerate quark flavors.

Figures (6)

• Figure 1: Summary of the loop shapes used in the glueball spectrum measurements.
• Figure 2: Example flow diagram for 2-level sampling of glueball operators for a lattice of temporal extent of $32a$ and $\Delta = 8$.
• Figure 3: Average distribution of the statistical weights in the sink/source average over diagonal correlators in the scalar channel measured in lattice 2.
• Figure 4: Example comparison for the $E^{++}$ ground state channel between the GEVP estimate and the effective mass average from the 8 operator with biggest ground state overlap.
• Figure 5: Results of preliminary glueball spectrum extraction in different symmetry channels for both lattices