How wide is the transition to deconfinement?

Abstract

Pure $SU(3)$ glue theories exhibit a deconfining phase transition at a nonzero temperature, ${T}_{c}$. Using lattice measurements of the pressure, we develop a simple matrix model to describe the transition region, when $T\ensuremath{\ge}{T}_{c}$. This model, which involves three parameters, is used to compute the behavior of the 't Hooft loop. There is a Higgs phase in this region, where off-diagonal color modes are heavy, and diagonal modes are light. Lattice measurements of the latter suggest that the transition region is narrow, extending only to about $\ensuremath{\sim}1.2{T}_{c}$. This is in stark contrast to lattice measurements of the renormalized Polyakov loop, which indicates a much wider width. The possible implications for the differences in heavy ion collisions between the Relativistic Heavy Ion Collider and the LHC are discussed.