Confinement from a massive scalar in QCD

A model is introduced with a massive scalar coupling to the Yang–Mills term in four–dimensional gauge theory. It is shown that the resulting potential of colour sources consists of a short range Coulomb interaction and a long range confining part. Far away from the source the scalar vanishes $\sim r^{-1}$ while the potential diverges linearly $\sim r$. Up to an $N_c$–dependent factor of order 1 the tension parameter in the model is $gmf$, where $m$ denotes the mass of the scalar and $f$ is a coupling scale entering the scalar–gluon coupling.