Instanton correction to some vacuum energy densities and the bag constant

Earlier calculations of a lower bound for the M.I.T. bag constant B are corrected for an effect due to instanton tunneling. This is done by taking into account a non-perturbative correction to the renormalization groups β-function defined in the Savvidy renormalization scheme. From this β-function one can obtain the energy density in the presence of a constant magnetic field. This is then used for estimating the energy density in a vacuum ansatz state and thereby also a bound on the bag constant B. Formulated as a bound on the Q.C.D. scale parameter Λsub(p) in the propagator renormalization scheme and taking Bsup(1/4) = 145 MeV the authors obtain Λsub(p) <= 0.27 GeV. Taking into account excitation of the Nielsen-Olesen unstable mode in the way that was described earlier, one gets instead Λsub(p) <= 0.11 GeV. (Auth.)