Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

Abstract

The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the ${\pi }^2$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polarization function and in the studies of the renormalization scale setting in the relevant physical observables.

12 pages

References in corpus (15)

• Hadronic Z- and tau-Decays in Order alpha_s^4
• The five-loop beta function of Yang-Mills theory with fermions
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• A new approach to evaluate the leading hadronic corrections to the muon g-2
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• The Determination of alpha_s from Tau Decays Revisited
• On the running coupling constant in QCD
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Measurements of the cross sections for $e^{+}{e}^{-}\to \mathrm{hadrons}$ at 3.650, 3.6648, 3.773 GeV and the branching fraction for $\psi (3770)\to \mathrm{non}-D\bar{D}$
• Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative
• The Compact Linear Collider (CLIC) - Project Implementation Plan
• Muon-electron scattering at NNLO: the hadronic corrections
• Hadronic vacuum polarization function within dispersive approach to QCD
• Detector Technologies for CLIC
• Electron-positron annihilation into hadrons at the higher-loop levels

Cited by in corpus (5)

• 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
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Novel Method to Reliably Determine the QCD Coupling from $R_{\mathrm{uds}}$ Measurements and its effects to Muon $g-2$ and $\alpha (M_Z^2)$ within the Tau-Charm Energy Region
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling