Nearly perturbative QCD coupling with lattice-motivated zero IR limit (1712.00622v1)

Abstract: 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 $1/Q^{2 n}$, a nonperturbative generalization $A(Q^2)$ of the perturbative QCD running coupling $a(Q^2)$ ($\equiv \alpha_s(Q^2)/\pi$). Recent large volume lattice calculations for these dressing functions strongly indicate that such a generalized coupling goes to zero as $A(Q^2) \sim Q^2$ when the squared momenta $Q^2$ go to zero ($Q^2 \ll 1 \ {\rm GeV}^2$). We construct such a QCD coupling $A(Q^2)$ which fulfills also various other physically motivated conditions. At high momenta it becomes the underlying perturbative coupling $a(Q^2)$ to a very high precision. And at intermediately low momenta $Q^2 \sim 1 \ {\rm GeV}^2$ it gives results consistent with the data of the semihadronic $\tau$ lepton decays as measured by OPAL and ALEPH. The coupling is constructed in a dispersive way, ensuring as a byproduct the holomorphic behavior of $A(Q^2)$ in the complex $Q^2$-plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to $\tau$-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 MSbar coupling (+OPE) approach. The comparison with the experimental V-channel Adler function, related with the $e^+ e^- \to$ hadrons ratio, at low $Q^2 \sim 1 \ {\rm GeV}^2$, also gives results considerably better than with the usual MSbar pQCD+OPE approach.