Color dependence of tensor and scalar glueball masses in Yang-Mills theories

Ed Bennett,Jong-Wan Lee,Jack Holligan,Davide Vadacchino,Deog Ki Hong,Biagio Lucini,Maurizio Piai,C.-J David Lin

doi:10.1103/physrevd.102.011501

Abstract

We report the masses of the lightest spin-0 and spin-2 glueballs obtained in an extensive lattice study of the continuum and infinite volume limits of $Sp(N_c)$ gauge theories for $N_c=2,4,6,8$. We also extrapolate the combined results towards the large-$N_c$ limit. We compute the ratio of scalar and tensor masses, and observe evidence that this ratio is independent of $N_{c}$. Other lattice studies of Yang-Mills theories at the same space-time dimension provide a compatible ratio. We further compare these results to various analytical ones and discuss them in view of symmetry-based arguments related to the breaking of scale invariance in the underlying dynamics, showing that a constant ratio might emerge in a scenario in which the $0^{++}$ glueball is interpreted as a dilaton state.

Highlights

In D 1⁄4 3 þ 1 space-time dimensions, Yang-Mills (YM) theories are classically scale-invariant
The notation G 1⁄4 Eþþ; Aþ1 þ; Tþ2 þ, refers explicitly to the representations of the octahedral group, which describes the symmetry of the discretized space-time, and to P and C
Ref. [5] reports continuum limits for the glueball masses expressed in units of the string tension σ, but the variational method uses a smaller basis of operators of the octahedral group in respect to our work, and the T2 channel is not measured

Summary

INTRODUCTION

In D 1⁄4 3 þ 1 space-time dimensions, Yang-Mills (YM) theories are classically scale-invariant. We update the measurements for the Spð4Þ group, by doubling the size of the combined statistical ensemble, and proceed to the step of this program, by performing detailed studies of the YM theory (with no matter content) with gauge groups Spð2Þ, Spð6Þ, and Spð8Þ R ≡ m2þþ ; ð1Þ m0þþ defined as the ratio of masses of the glueballs with quantum number JPC 1⁄4 2þþ and JPC 1⁄4 0þþ, captures some universal, intrinsic properties of YM theories, in the sense that. It depends only on the dimensionality of the space-time and of the operators of the field theory. A comprehensive report on the physics of SpðNcÞ YM theories, which details the results for excited states and for extended objects, is in preparation [4]

NEW LATTICE RESULTS

EARLIER LATTICE RESULTS

GLUEBALL MASSES: A BRIEF SURVEY OF ANALYTICAL RESULTS

DISCUSSIONS AND UNIVERSAL RATIO

OUTLOOK