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 $ψ(Q^2)$ and $ψ_5(Q^2)$, are used to determine the subtraction constants $ψ(0)$ and $ψ_5(0)$, which fix the ratio $R_{su}\equiv \frac{<\bar{s}s>}{<\bar{u}u>}$. Our results are $ψ(0)= - (1.06 \pm 0.21) \times 10^{-3} {GeV}^4$, $ψ_5(0)= (3.35 \pm 0.25) \times 10^{-3} {GeV}^4$, 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 $SU(3)\otimes SU(3)$.