QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector

Overview & Synopsis

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global $Z_2$ symmetry, two colourless boundstates, even and odd under $Z_2$, are identified. Their respective contributions (poles) in correlation functions of local composite operators $A_n$ of degree $n=2p$ and $2p+1$ in the scalar fields ($p=1,2$) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the $p=2$ operators into polynomials in $p=1$ operators. No sizable signal in any $A_n$ correlation can be attributed to $1/n$ times a Debye screening length associated with $n$ elementary fields. These results are quantitatively consistent with the picture of scalar ``matter'' fields confined within colourless boundstates whose residual ``strong'' interactions are very weak.