Achieving renormalization-scale- and scheme-independence in Pade-related resummation in QCD

Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme parameter $c_2$ is eliminated by a variant of the method of the principle of minimal sensitivity. The subleading parameter $c_3$ in the approximant is then fixed in such a way that the correct known location of the leading infrared renormalon pole is reproduced. Thus, $beta$-functions which go beyond the last perturbatively calculated order in the observable are used. The $\beta$-functions in the approximant are quasianalytically continued by Pade approximants. Two aspects of nonperturbative physics are accounted for in the presented resummation: a mechanism of quasianalytic continuation from the weak- into the strong-coupling regime, and the (approximant-specific) contribution of the leading infrared renormalon. The case of the Bjorken polarized sum rule is considered as a specific example of how the method works.Comment: 14 pages, 2 eps-figures, revtex; presentation clearer and tightened; an inadvertently included obsolete curve in Fig.2 replaced by the new one; all numerical results and conclusions unchanged; to appear in Phys.Lett.

Nearly perturbative QCD coupling with lattice-motivated zero IR limit

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.Comment: 6 pages, 1 figure, presented at EPS-HEP2017 Conference, 5-12 July 2017, Venice, Ital

Non-Compact AdS5AdS_5 Universe with Parallel Positive Tension 3-Branes

We construct the general model with only parallel positive tension 3-branes on $M^4 \times R^1$ and $M^4 \times R^1/Z_2$. The cosmology constant is sectional constant along the fifth dimension. In this general scenario, the 5-dimensional GUT scale on each brane can be indentified as the 5-dimensional Planck scale, but, the 4-dimensional Planck scale is generated from the low 4-dimensional GUT scale exponentially in our world. We also give two simple models to show explicitly how to solve the gauge hierarchy problem.Comment: 9 pages, Latex, minor change and add reference

anQCD: a Mathematica package for calculations in general analytic QCD models

We provide a Mathematica package that evaluates the QCD analytic couplings (in the Euclidean domain) $\mathcal{A}_{\nu}(Q^2)$, which are analytic analogs of the powers $a(Q^2)^{\nu}$ of the underlying perturbative QCD (pQCD) coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2$\delta$anQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings $\mathcal{A}_{\nu}(Q^2)$, in contrast to the corresponding pQCD expressions $a(Q^2)^{\nu}$, reflect correctly the analytic properties of the spacelike observables ${\cal D}(Q^2)$ in the complex $Q^2$ plane as dictated by the general principles of quantum field theory. They are thus more suited for evaluations of such physical quantities, especially at low momenta $|Q^2| \sim 1 \ {\rm GeV}^2$.Comment: v3: 35 pp., 7 figs.; improved programs which work in Mathematica 9 and 10; improved presentation of the text (Sec.2 shorter, Sec.4 enlarged); to appear in Computer Physics Communication

Rotating Dyonic Black Holes in Heterotic String Theory

We study a class of rotating dyonic black holes in the heterotic string theory in four dimension which have left, right independent electric charges but have same magnitude for the left and right magnetic charges. In both left and right sector the electric and the magnetic vectors are orthogonal to each other. The gyromagnetic(electric) ratios are in general found not to have an upper bound.Comment: harvmac, no figures, version appeared in Phys. Lett. B38