Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory

Abstract

The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared ($Q_i^2$) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three $Q_i^2$ are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small.

53 pages, analytical results as FORM output included as results.txt, some references added, misprints corrected, one figure changed

References in corpus (4)

• Form Factors in the radiative pion decay
• Magnetic susceptibility of QCD matter and its decomposition from the lattice
• Novel patterns for vector mesons from the large-Nc limit
• On some properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon

Cited by in corpus (41)

• The anomalous magnetic moment of the muon in the Standard Model: an update
• Consequences of chirally enhanced explanations of $(g-2{)}_{\mu }$ for $h\to \mu \mu$ and $Z\to \mu \mu$
• Kaon electromagnetic form factors in dispersion theory
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• The two-loop perturbative correction to the (g-2)${}_{\mu }$ HLbL at short distances
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• Unveiling Hidden Physics at the LHC
• The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g-2
• Semileptonic tau decays beyond the Standard Model
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1{)}_A$ problem
• Axial-vector transition form factors and $e^{+}{e}^{-}\to f_1{\pi }^{+}{\pi }^{-}$
• A phenomenological estimate of isospin breaking in hadronic vacuum polarization
• Type-X two Higgs doublet model in light of the muon $\mathbf{g}-2$: confronting Higgs and collider data
• Constraints on the hadronic light-by-light in the Melnikov-Vainshtein regime
• Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• An optimized basis for hadronic light-by-light scattering
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relations for hadronic light-by-light scattering in triangle kinematics
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Mixed leptonic and hadronic corrections to the anomalous magnetic moment of the muon
• 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 $g-2$
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
• Short-distance constraints on the hadronic light-by-light
• Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• 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
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model