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

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 toward 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.