Meson dynamics in the SU3 × SU3 σ model

Lai Him Chan, Louisiana State University
Richard W. Haymaker, Louisiana State University


We present the calculation of phase shifts for the renormalizable SU3 σ model with the symmetry-breaking term LSB=-ε0σ0-ε8σ8. Perturbation theory is carried out to the one-loop approximation and phase shifts are obtained from Padé approximants. We renormalize at physical quantities: masses of π, K, η, η′, decay constant fπ, and the ππ, I=0, l=0 S-wave scattering amplitude near threshold. As a consequence of this choice, perturbation theory is a power series in 1fπ2. A further consequence is that there are low-energy off-mass-shell points where the tree approximation is exact,as we show. The symmetry-breaking picture is that of a nearly SU2 × SU2-invariant Hamiltonian and a nearly SU3-invariant vacuum. The SU3 × SU3 limit is the Goldstone type. The corrections to decay constants and symmetry-breaking parameters are small. We can account for the size of corrections to all quantities of interest in a simple way. We achieve consistency between two measures of SU3-symmetry breaking, i.e., mKmπ and fKfπ. That is, we find fKfπf+(0)=1.34. With the physical value of fπ(=0.095 GeV), and with one free parameter, mσ(tree), we achieve qualitative agreement with experiment for the S-wave nonexotic phase shifts, and the P- and D-wave octet central masses. The exotic S-wave phase shifts are too strongly repulsive and an SU3 27 representation of states occurs in the D wave. SU3 is a good symmetry for the P- and D-wave states in spite of large differences in the thresholds of channels generating them. The magnitude of splitting is quantitatively correct. A novel expression for the unequal-mass box graph is presented. © 1974 The American Physical Society.