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 $⟨\frac{{\alpha }_s}{\pi }{G}^2⟩$ and $⟨(\bar{q}\Gamma q{)}^2⟩$ 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.

Latex file, 9 pages, 4 figures available on request from [email protected] INFN-FE 07-94