The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops

Abstract

In this paper we compute the four-loop corrections to the QED photon self-energy Pi(Q^2) in the two limits of q=0 and Q^2->infinity. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell(OS) and MSbar scheme. Using these relations and results of Baikov et al. [1] we construct the momentum dependent part of Pi(Q^2,m,alpha) at large Q^2 at five loops in both MSbar and OS schemes. As a direct consequence we arrive at the full result for the QED beta-function in the OS scheme at five loops. These results are applied, in turn, to analytically evaluate a class of asymptotic contributions to the muon anomaly at five and six loops.

25 pages, 6 figures; v2: final published version

References in corpus (36)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• The Muon g-2
• New features of FORM
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Complete Tenth-Order QED Contribution to the Muon g-2
• The three loop relation between the \bar {MS} and the pole quark masses
• The analytical value of the electron (g-2) at order alpha^3 in QED
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• The Tenth-Order QED Contribution to the Lepton g-2: Evaluation of Dominant ${\alpha }^5$ Terms of Muon g-2
• Four-Loop Singlet Contribution to the $\rho$ Parameter
• High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles
• High-precision e-expansions of massive four-loop vacuum bubbles
• A practical criterion of irreducibility of multi--loop Feynman integrals
• Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• Muon Anomaly from Lepton Vacuum Polarization and The Mellin--Barnes Representation
• The muon anomalous magnetic moment in QED: three-loop electron and tau contributions
• Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2
• Calculating four-loop tadpoles with one non-zero mass
• Analytical and Numerical Contributions of Some Tenth-Order Graphs Containing Vacuum Polarization Insertions to the Muon (G-2) in QED
• Tenth-Order Lepton Anomalous Magnetic Moment -- Second-Order Vertex Containing Two Vacuum Polarization Subdiagrams, One Within the Other
• Heavy-quark QCD vacuum polarisation function: analytical results at four loops
• Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2
• Tuning FORM with large calculations
• Heavy-quark vacuum polarization: first two moments of the O(alphas^3 nf^2) contribution
• Extension of the functionality of the symbolic program FORM by external software
• Hypergeometric representation of a four-loop vacuum bubble
• New Results in Four and Five Loop QED calculations
• The Comments on QED Contributions to $(g-2{)}_{\mu }$

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