Gauge-invariant and infrared-improved variational analysis of the Yang-Mills vacuum wave functional

Abstract

We study a gauge-invariant variational framework for the Yang-Mills vacuum wave functional. Our approach is built on gauge-averaged Gaussian trial functionals which substantially extend previously used trial bases in the infrared by implementing a general low-momentum expansion for the vacuum-field dispersion (which is taken to be analytic at zero momentum). When completed by the perturbative Yang-Mills dispersion at high momenta, this results in a significantly enlarged trial-functional space which incorporates both dynamical mass generation and asymptotic freedom. After casting the dynamics associated with these wave functionals into an effective action for collections of soft vacuum-field orbits, the leading infrared improvements manifest themselves as four-gradient interactions. Those turn out to significantly lower the minimal vacuum energy density, thus indicating a clear overall improvement of the vacuum description. The dimensional transmutation mechanism and the dynamically generated mass scale remain almost quantitatively robust, however, which ensures that our prediction for the gluon condensate is consistent with standard values. Further results include a finite group velocity for the soft gluonic modes due to the higher-gradient corrections and indications for a negative differential color resistance of the Yang-Mills vacuum.