Estimate of $\langle \bar q q \bar q q \rangle$ from the V-A Current-Current Correlator

In QCD, the difference of the current-current correlators for vector and axial vector currents, in a color singlet and flavor non-singlet channel, is zero to all orders in perturbation theory if the quarks are massless. As an example of the efficiency of this so-called V-A correlator in probing nonperturbative phenomena, its leading ultraviolet term is proportional to the scalar 4-quark condensate $\langle \bar q q \bar q q \rangle$. This condensate is a key ingredient in QCD sum rule analyses of hadronic properties and, in the absence of independent information, it is often assumed that vacuum saturation holds, namely $\langle \bar q q \bar q q \rangle \approx \langle \bar q q \rangle^2$. We describe here an independent estimate based upon direct evaluation of the current-current correlators within a ladder-rainbow truncated model of QCD. Our results indicate that $\langle \bar q q \bar q q \rangle$ is significantly larger than what vacuum saturation would suggest.