Abstract
A very simple variational approach to pure SU($N$) Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at $T_c\approx 250$ MeV for $N=3$) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.
Highlights
In the last decades the dynamics of QCD has been under intensive theoretical study, aimed at understanding the properties of matter under the extreme conditions reached by heavy-ion collisions
The main difficulty of handling the gap equation has always been the regularization of the diverging integral JðmÞ and its physical meaning
We have shown that, by dimensional regularization in d > 4, the Gaussian effective potential (GEP) provides a reasonable account of the general features of Yang-Mills theory
Summary
In the last decades the dynamics of QCD has been under intensive theoretical study, aimed at understanding the properties of matter under the extreme conditions reached by heavy-ion collisions.
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