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 $SU(3)\otimes SU(3)$.

Comments: Latex file, 14 pages including 3 figures