Pion light-by-light contributions to the muon $g-2$

Abstract

This paper contains some new results on the hadronic light-by-light contribution (HLbL) to the muon $g-2$. The first part argues that we can expect large effects from disconnected diagrams in present and future calculations by lattice QCD of HLbL. The argument is based on the dominance of pseudo-scalar meson exchange. In the second part, we revisit the pion loop HLbL contribution to the muon anomalous magnetic moment. We study it in the framework of some models studied earlier, pure pion loop, full VMD and hidden local symmetry for inclusion of vector mesons. In addition we study possible ways to include the axial-vector meson. The main part of the work is a detailed study of how the different momentum regions contribute. We derive a short distance constraint on the ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \pi$ amplitude and use this as a constraint on the models used for the pion loop. As a byproduct we present the general result for integration using the Gegenbauer polynomial method.

arXiv comment26 pages

References in corpus (23)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• The Muon g-2
• Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.7 ppm
• Muon g-2: Review of Theory and Experiment
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$
• Towards a data-driven analysis of hadronic light-by-light scattering
• Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g-2$
• Dispersive approach to hadronic light-by-light scattering
• Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon $g-2$
• Hadronic Contributions to the Muon $g-2$ and Low-Energy QCD
• Hadronic Light-by-Light Contribution to the Muon $g-2$
• Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment
• Hadronic Light-by-light Scattering Effect on Muon g-2
• The Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment: Where do we stand?
• QCD Short-distance Constraints and Hadronic Approximations
• Lattice QCD calculation of hadronic light-by-light scattering
• Measurement of the charged-pion polarisability
• A fresh look at hadronic light-by-light scattering in the muon g-2 with the Dyson-Schwinger approach
• The Muon Anomalous Magnetic Moment and the Pion Polarizability
• Hadronic light-by-light contribution to $a_{\mu }$: extended Nambu-Jona-Lasinio, chiral quark models and chiral Lagrangians
• The hadronic light-by-light contribution to the muon anomalous magnetic moment and renormalization group for EFT

Cited by in corpus (24)

• The anomalous magnetic moment of the muon in the Standard Model
• 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
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD: a complete calculation
• Lattice QCD and the anomalous magnetic moment of the muon
• The light-quark contribution to the leading HVP term of the muon $g-2$ from twisted-mass fermions
• The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD
• The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g-2
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• Contribution of neutral pseudoscalar mesons to $a_{\mu }^{HLbL}$ within a Schwinger-Dyson equations approach to QCD
• Pseudoscalar pole light-by-light contributions to the muon $(g-2)$ in Resonance Chiral Theory
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
• Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD with SU(3) flavor symmetry
• Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization
• Hadronic light-by-light scattering contribution to the muon g-2 on the lattice
• Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel
• On the Hadronic light-by-light contribution to the muon $g-2$
• Light-by-light forward scattering amplitudes in Lattice QCD