Closed-loop corrections to the SU3 x SU3 sigma model: one- and two-point functions

We present the calculation of one-loop corrections to the one- and two-point functions in the renormalizable SU₃ σ model with a symmetry-breaking term $L_{SB}={ϵ}_0{\sigma }_0+{ϵ}_8{\sigma }_8$. We renormalized at the masses of π, K, η, η′, σ, and $f_{\pi }$. The second-order corrections are found to be small compared to tree-approximation values. The measure of octet breaking, $b=\frac{〈{\sigma }_8〉}{\sqrt{2}〈{\sigma }_0〉}$, changes less than 5%. The value of $a=\frac{{ϵ}_8}{\sqrt{2}{ϵ}_0}$ is insignificantly changed. The scalar-meson masses are shifted by less than 10%, with the exception of the σ′. The widths are large, with the exception of the ${\pi }_N$. We calculate corrections to $\frac{f_K}{f_{\pi }}$, the wave-function renormalization constants, mixing angles, and the renormalized π and K propagators at q²=0.