Towards OPE based local quark-hadron duality: Light-quark channels

Abstract

Various light-quark channel current-current correlators are subjected to the concept of a non-perturbative component of coarse graining in operator product expansions introduced in a parallel work. This procedure allows for low-energy structure of the OPE-derived spectral function. With naive vacuum saturation for 4 quark operators and using lattice data for the gauge invariant scalar quark correlator the results are far off the experimentally measured behavior. However, using the correlation length of the gauge invariant vector quark correlator, which is about 10 times smaller than the scalar one, the qualitative results are rather realistic. Namely, the input of information on the mass of the lowest resonance in one channel yields the corresponding masses within acceptable errors in other channels. Still, the shapes of the calculated spectral functions are considerably deformed as compared to experiment. This may be a consequence of vacuum saturation and the truncation at a mass dimension which is below the critical dimension from which on the asymptotic expansion does not approximate anymore. To improve on this high-resolution lattice information on gauge invariant $n>2$ point correlators would be needed. Motivated by the small effective correlation length in the 4 quark contributions the relevance of the approach for heavy quark physics, in particular in the calculation of nonleptonic, inclusive $ΔΓ$, is discussed.