The two-loop perturbative correction to the (g-2)${}_{\mu }$ HLbL at short distances

Abstract

The short-distance behaviour of the hadronic light-by-light (HLbL) contribution to $(g-2{)}_{\mu }$ has recently been studied by means of an operator product expansion in a background electromagnetic field. The leading term in this expansion has been shown to be given by the massless quark loop, and the non-perturbative corrections are numerically very suppressed. Here, we calculate the perturbative QCD correction to the massless quark loop. The correction is found to be fairly small compared to the quark loop as far as we study energy scales where the perturbative running for the QCD coupling is well-defined, i.e.~for scales $\mu \gtrsim 1\mathrm{GeV}$. This should allow to reduce the large systematic uncertainty associated to high-multiplicity hadronic states.

arXiv comment28 pages, the expressions and the many expansions that are too long are included in the supplementary files. Minor misprints corrected, short discussion about the MV limit and explicit expressions at the symmetric point added

References in corpus (50)

• The anomalous magnetic moment of the muon in the Standard Model
• FLAG Review 2019
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Complete Tenth-Order QED Contribution to the Muon g-2
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• Two-pion contribution to hadronic vacuum polarization
• The electroweak contributions to (g-2)_μ after the Higgs boson mass measurement
• Remarks on higher-order hadronic corrections to the muon g-2
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Three-pion contribution to hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: pion pole
• Kira - A Feynman Integral Reduction Program
• Pseudoscalar-pole contribution to the $(g_{\mu }-2)$: a rational approach
• Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
• Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks
• Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$
• Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g-2$
• Single meson contributions to the muon's anomalous magnetic moment
• Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon $g-2$
• Hadronic Light-by-Light Contribution to the Muon $g-2$
• Light-by-light scattering sum rules in light of new data
• Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• Kaon-box contribution to the anomalous magnetic moment of the muon
• Scalar Meson Contributions to a_μfrom Hadronic Light-by-Light Scattering
• New results for two-loop off-shell three-point diagrams
• Three-mass triangle integrals and single-valued polylogarithms
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon
• On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$
• Asymptotic behavior of meson transition form factors
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Hadronic light-by-light scattering in the muon g-2: a Dyson-Schwinger equation approach
• Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
• Hadronic Contributions to the Muon Anomaly in the Constituent Chiral Quark Model
• Heavy mass expansion, light-by-light scattering and the anomalous magnetic moment of the muon
• Effects of Longitudinal Short-Distance Constraints on the Hadronic Light-by-Light Contribution to the Muon $g-2$
• Hadronic light-by-light scattering contribution to the muon magnetic anomaly: constituent quark loops and QCD effects
• On some properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon
• Dynamical quark loop light-by-light contribution to muon g-2 within the nonlocal chiral quark model
• Ballpark prediction for the hadronic light-by-light contribution to the muon (g-2)_μ

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• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
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• Axial-vector transition form factors and $e^{+}{e}^{-}\to f_1{\pi }^{+}{\pi }^{-}$
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1{)}_A$ problem
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• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
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• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$
• Improved evaluation of the electroweak contribution to muon $g-2$
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Hadronic vacuum polarization contribution to the muon $g-2$ in holographic QCD
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
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• Short-distance constraints on the hadronic light-by-light
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains
• New high-statistics measurement of the ${\pi }^0\to e^{+}{e}^{-}\gamma$ Dalitz decay at the Mainz Microtron
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$