Ratio of strange to non-strange quark condensates in QCD

Abstract

Laplace transform QCD sum rules for two-point functions related to the strangeness-changing scalar and pseudoscalar Green's functions $\psi(Q^2)$ and $\psi_5(Q^2)$, are used to determine the subtraction constants $\psi(0)$ and $\psi_5(0)$, which fix the ratio $R_{su}\equiv \frac{<\bar{s}s>}{<\bar{u}u>}$. Our results are $\psi(0)= - (1.06 \pm 0.21) \times 10^{-3} {GeV}^4$, $\psi_5(0)= (3.35 \pm 0.25) \times 10^{-3} {GeV}^4$, and $R_{su}\equiv \frac{<\bar{s}s>}{<\bar{u}u>} = 0.5 \pm 0.1$. This implies corrections to kaon-PCAC at the level of 50%, which although large, are not inconsistent with the size of the corrections to Goldberger-Treiman relations in $SU(3)\otimes SU(3)$.