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

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

1994-08-15

arxiv.org/abs/hep-th/9408081v1

Phys.Rev. D52 (1995) 3719-3734

Physics

High Energy Physics

High Energy Physics - Theory

37 pages, (1 Figure available upon request), preprint LA-UR-94-2727, PUPT-1492

Scientific paper

10.1103/PhysRevD.52.3719

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 ${\alpha\over \pi}= 0.008 Gev^4$.

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