Nearly perturbative lattice-motivated QCD coupling with zero IR limit

Abstract

The product of the gluon dressing function and the square of the ghost\ndressing function in the Landau gauge can be regarded to represent, apart from\nthe inverse power corrections 1/Q^{2n}, a nonperturbative generalization A(Q^2)\nof the perturbative QCD running coupling a(Q^2)=alpha_s(Q^2)/pi. Recent large\nvolume lattice calculations for these dressing functions indicate that the\ncoupling defined in such a way goes to zero as A(Q^2)~Q^2 when the squared\nmomenta Q^2 go to zero (Q^2<<1 GeV^2). In this work we construct such a QCD\ncoupling A(Q^2) which fulfills also various other physically motivated\nconditions. At high momenta it becomes the underlying perturbative coupling\na(Q^2) to a very high precision. And at intermediate low squared momenta Q^2~1\nGeV^2 it gives results consistent with the data of the semihadronic tau lepton\ndecays as measured by OPAL and ALEPH. The coupling is constructed in a\ndispersive way, resulting as a byproduct in the holomorphic behavior of A(Q^2)\nin the complex Q^2-plane which reflects the holomorphic behavior of the\nspacelike QCD observables. Application of the Borel sum rules to tau-decay V+A\nspectral functions allows us to obtain values for the gluon (dimension-4)\ncondensate and the dimension-6 condensate, which reproduce the measured OPAL\nand ALEPH data to a significantly better precision than the perturbative MSbar\ncoupling approach.\n