A variational approach to the QCD wave functional:Dynamical mass generation and confinement

TL;DR

This paper introduces a gauge-invariant variational approach to SU(N) Yang Mills theory in 3+1 dimensions, revealing a dynamically generated mass scale related to confinement and QCD scale, with concrete estimates of vacuum condensates.

Contribution

It develops a novel gauge-invariant variational method that predicts dynamical mass generation and confinement in Yang Mills theory, connecting nonperturbative effects to QCD parameters.

Findings

Energy minimized at nonperturbative scale M

Dynamical mass M related to Λ_QCD

Estimated vacuum condensate value

Abstract

We perform a variational calculation in the SU(N) Yang Mills theory in 3+1 dimensions. Our trial variational states are explicitly gauge invariant, and reduce to simple Gaussian states in the zero coupling limit. Our main result is that the energy is minimized for the value of the variational parameter away form the perturbative value. The best variational state is therefore characterized by a dynamically generated mass scale $M$. This scale is related to the perturbative scale $\Lambda_{QCD}$ by the following relation: $\alpha_{QCD}(M)={\pi\over 4}{1\over N}$. Taking the one loop QCD $\beta$- function and $\Lambda_{QCD}=150 Mev$ we find (for N=3) the vacuum condensate ${\alpha\over \pi}<F^2>= 0.008 Gev^4$.