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

TL;DR

This paper presents new insights into the hadronic light-by-light contribution to the muon g-2, emphasizing the importance of disconnected diagrams and analyzing the pion loop contribution through various models and constraints.

Contribution

It introduces a detailed analysis of pion loop contributions to muon g-2, including model comparisons and a new short-distance constraint on the amplitude.

Findings

Disconnected diagrams have significant effects in lattice QCD calculations.

Different models show varying contributions to the pion loop part.

A new short-distance constraint on the $ o o o$ amplitude was derived.

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 $\gamma^*\gamma^*\to\pi\pi$ 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.