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.

26 pages

References in corpus (5)

• Muon g-2: Review of Theory and Experiment
• Towards a data-driven analysis of hadronic light-by-light scattering
• The Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment: Where do we stand?
• 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

Cited by in corpus (8)

• 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
• The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD
• Strange and charm HVP contributions to the muon ($g-2)$ including QED corrections with twisted-mass fermions
• 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
• Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization
• Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel