Strong-coupling calculations of the hadron spectrum of quantum chromodynamics

Abstract

We present calculations of the low-energy mass spectrum and matrix elements of quantum chromodynamics. We employ an isospin doublet of massless quarks and analyze the theory from the strong-coupling limit using a particularly simple lattice Hamiltonian. In the strong-coupling limit the vacuum state has exact local color symmetry, but spontaneously breaks those elements of chiral symmetry which are present in the lattice Hamiltonian. Expansions for masses ($\pi ,\rho ,\omega ,\sigma ,A_1,B,f,$ and nucleon) and matrix elements $g_A$ in the reciprocal coupling constant are analytically continued to the continuum limit using Padé approximants. The results are in surprisingly good agreement with experiment except for the pion mass. This single failure is traced to the lack of full chiral symmetry in the theory for large lattice spacing and the lack of significant spin-spin forces in low orders of strong-coupling perturbation theory. Higher-order calculations should resolve this problem, but a more realistic Hamiltonian suggested by renormalization-group analyses also looks promising.