Abelian dominance and quark confinement in Yang-Mills theories. II. Oblique confinement and eta' mass

Making a working hypothesis of Abelian dominance at a long-distance scale, we analyze the U(1) problem as well as the confinement problem in the SU(N) Yang-Mills theory with the vacuum angle theta. We show that quarks are confined only when theta/2π is a rational number such that theta/2πnot =(1+nN)/mN, n and m being integers. We also calculate a correlation function of the topological charge density Q(x) = (16π2)-1TrF/sub munu/F(/sub munu/(x) at theta = 0. We derive that ∫d4x = N2/128π4(N-1)(α')2, where α' denotes the Regge slope of mesons. This formula yields approx.(150 MeV)4 in case of SU(3), which gives rise to a mass approx.550 MeV to the eta' meson through a chiral anomaly in QCD with massless quarks. This numerical result would explain the eta' mass reasonably well in the approximation where pions are massless Goldstone bosons