Color ferromagnetic vacuum states in QCD and two-loop energy densities: Bounds on MIT bag constant in relation to QCD Λ

Abstract

We obtain two-loop energy densities of color ferromagnetic states, which are identified with the QCD ground state, using the β-function calculated to the two-loop approximation and the exact formula for the energy density of such a state. This is used to derive bounds on the MIT bag constant correcting our previous bound in the one-loop approximation. For a constant field color ferromagnetic ansatz state we obtain the bound on the QCD scale parameter Λ P⩽0.88 GeV when B 1 4 =0.145 GeV . The correction by going from one loop to two loops is only of the order of 20%. Correcting for instanton effects we obtain Λ P⩽0.46 GeV. Our ϑ 3 vacuum ansatz with two-loop and instanton corrections gives Λ P⩽0.16 GeV. We stress that the ”perturbative vacuum“, which is identified with the inside bag state, is a somewhat ill-defined concept due to a path dependence in the integral giving the energy density.