Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$

Abstract

We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime $|Q^2|\lesssim 1{\mathrm{GeV}}^2$, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here in the evaluation of the quantities related with the semihadronic (strangeless) $\tau$-decay spectral functions, including Borel-Laplace sum rules in the (V+A)-channel. The analysis is then extended to the evaluation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, $a_{\mu }^{\mathrm{had}(1)}$, where we include in the Adler function the V-channel higher-twist OPE terms which are regulated in the infrared (IR) by mass parameters which are expected to be $\lesssim 1$ GeV. The correct value of $a_{\mu }^{\mathrm{had}(1)}$ can be reproduced with the mentioned IR-regulating mass parameters if the value of the condensate $⟨O_4{⟩}_{\mathrm{V}+\mathrm{A}}$ is positive (and thus the gluon condensate value is positive). This restriction and the requirement of the acceptable quality of the fits to the various mentioned sum rules then lead us to the restriction $0.1171<{\alpha }_s(M_Z^2;\overline{MS})<0.1180$.

33 pages, 10 figures; v4: minor corrections in the references; version to appear in J.Phys.G

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Cited by in corpus (9)

• QCD Running Couplings and Effective Charges
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Fractional Analytic QCD beyond Leading Order
• Fractional Analytic QCD beyond Leading Order in timelike region
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Towards unifying perturbative and Holographic Light-Front QCD via holomorphic coupling
• Renormalon-based resummation for spacelike and timelike QCD quantities whose perturbation expansion has general form