Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement

Understand

In order to understand the confining decoupling solution of the Yang-Mills theory in the Landau gauge, we consider the massive Yang-Mills model which is defined by just adding a gluon mass term to the Yang-Mills theory with the Lorentz-covariant gauge fixing term and the associated Faddeev-Popov ghost term.

• First of all, we show that massive Yang-Mills model is obtained as a gauge-fixed version of the gauge-invariantly extended theory which is identified with the gauge-scalar model with a single fixed-modulus scalar field in the fundamental representation of the gauge group.
• This equivalence is obtained through the gauge-independent description of the Brout-Englert-Higgs mechanism proposed recently by one of the authors.
• Then, we reconfirm that the Euclidean gluon and ghost propagators in the Landau gauge obtained by numerical simulations on the lattice are reproduced with good accuracy from the massive Yang-Mills model by taking into account one-loop quantum corrections.