Chiral symmetry breaking in QCD; Mesons as spin waves

The strong chiral symmetry breaking in Wilson's lattice version of QCD is discussed and interpreted as a necessary manifestation of the triangle anomaly. At strong coupling the effective hamiltonian acting in the s-wave hadron sector is found to describe a generalized antiferromagnet which is analyzed with the $\text{1}\text{2}\text{S}\text{(= 1/N, N = N}{}_{\mathrm{<mtext>color</mtext>}}\text{)}$ expansion known in the theory of magnetism. Mesons emerge as spin waves: pseudoscalars as Nambu-Goldstone bosons, vectors as “dormant” Goldstone bosons. Current and dynamical quark masses are identified, such that m_P² ∫ m(cur), m_v≈2m(cur) + m(fyn)], and a fit to the particle spectrum gives m(dyn) = 390 MeV, m_u,d(cur) = 5.4 MeV, m_s(cur) = 140 MeV, m_c(cur) = 1.07 GeV. Static baryons emerge with a mass m_B = Nm(dyn) + m(cur)] + a contribution which is argued to vanish in the continuum limit. Vector and axial vector currents are defined on the lattice and studied at strong coupling. The relations $\text{1 =}\text{3}\text{5}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{γ}{}_{\mathrm{?}}\text{(f}{}_{\mathrm{\pi }}\text{/m}{}_{\mathrm{?}}\text{)(Z}{}_{\mathrm{\pi }}\text{/Z}{}_{\mathrm{?}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, Z_π/Z_? = 3.0 are found to agree with experiment. The resolution of the U(1) problem at strong coupling is discussed.