Determination of QCD Condensates Without Hadronic Spectra

Abstract

The bounds on the values of gluon, four-quark and quark-gluon condensates are derived from the requirement of consistency of the sum rules for various correlators of the hybrid current $a_{\mu}=g\bar d\gamma_{\rho}\tilde G_{\rho\mu}u$. The upper bound for the gluon condensate is found to be less then twice its standard value while for the four-quark condensates the violation of factorization by a factor 3-4 is allowed. The value of the quark-gluon condensate is given as a function of $\left<\frac{\alpha_s}{\pi} G^2\right>$ and $\left<(\bar q\Gamma q)^2\right >$ which for the standard values yields $m_0^2=0.63~\mbox{GeV}^2$ . Our procedure of simultaneous solution of a number of sum rules allows the quantitative error analysis and is appropriate for condensate determination also in other cases.