Chiral vacuum effects in a topological bag model of the light baryons

We study the effects of a hedgehog pion configuration, π(β) = f_πr̂_βsin 0, on the vacuum fluctuations of confined quarks in a two-phase model of the light baryons, at the one-loop level. We explicitly construct the confined chiral propagator for a two-flavor massless Dirac field. By using the Debye expansion, we show that the chiral Casimir energy ΔE(0) = E(0) - E(0) diverges logarithmicallly ΔE(θ)∼- 2 15πRsin² θInτ + 1 4πR [θ²-sin²θ 6.644+sin⁴θ0.482], while the normal flux of the vacuum axial currect diverges both linearly and logarithmically ∫ d²s_βrⁱ_βr_β^a〈J_5i^a(β)〉 = sin2θ 2πR 1 τtan^-1 4 τ + dE dθ + 31 120πRsin2θwhere τ → 0+ is a cut-off parameter. The character of the divergences is examined and various subtraction procedures analyzed. The chiral vacuum effects on the fermion condensate are investigated, and their relevance to a bag model of the QCD vacuum discussed.