The product of the gluon dressing function and the square of the ghost dressing function in the Landau gauge can be regarded to represent, apart from the inverse power corrections , a nonperturbative generalization of the perturbative QCD running coupling ( ). Recent large volume lattice calculations for these dressing functions indicate that the coupling defined in such a way goes to zero as when the squared momenta Q2 go to zero ( ). In this work we construct such a QCD coupling which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling to a very high precision. And at intermediate low squared momenta it gives results consistent with the data of the semihadronic τ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of in the complex Q2 -plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ -decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative coupling approach.
16 May 2013 in Journal of Physics A: Mathematical and Theoretical