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.

arXiv comment12 pages

References in corpus (40)

• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• Five-Loop Running of the QCD coupling constant
• Future Physics Programme of BESIII
• Hadronic Z- and tau-Decays in Order alpha_s^4
• The five-loop beta function of Yang-Mills theory with fermions
• Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications
• The Physics of Hadronic Tau Decays
• Measurements of the Cross Section for e+e- -> hadrons at Center-of-Mass Energies from 2 to 5 GeV
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Measuring the leading hadronic contribution to the muon g-2 via $\mu e$ scattering
• Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays
• 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
• Measurement of the Total Cross Section for Hadronic Production by e+e- Annihilation at Energies between 2.6-5 Gev
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Determination of the $\psi (3770)$, $\psi (4040)$, $\psi (4160)$ and $\psi (4415)$ resonance parameters
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• An updated determination of α_s from 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 $\psi (3770)\to \mathrm{non}-D\bar{D}$
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the planar graphs
• $R$ value measurements for $e^{+}{e}^{-}$ annihilation at 2.60, 3.07 and 3.65 GeV
• The Compact Linear Collider (CLIC) - Project Implementation Plan
• A new determination of α_s from hadronic τ decays
• Hadronic corrections to $\mu$-$e$ scattering at NNLO with space-like data
• Muon-electron scattering at NNLO: the hadronic corrections
• R(s) and hadronic tau-Decays in Order alpha_s^4: technical aspects
• Measurement of $R_{\text{uds}}$ and $R$ between 3.12 and 3.72 GeV at the KEDR detector
• Precise measurement of $R_{\text{uds}}$ and $R$ between 1.84 and 3.72 GeV at the KEDR detector
• Hadronic vacuum polarization function within dispersive approach to QCD
• Measurement of $R$ between 1.84 and 3.05 GeV at the KEDR detector
• Muon-electron scattering at NLO
• Detector Technologies for CLIC
• Electron-positron annihilation into hadrons at the higher-loop levels
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Gauge coupling unification in SO(32) heterotic string theory with magnetic fluxes

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