The role of vector meson dominance and running masses in the hadronic contributions to the muon $g-2$

TL;DR

This paper investigates the impact of vector meson dominance and running masses on the hadronic contributions to the muon g-2, emphasizing the importance of momentum-dependent vertex functions in accurate calculations.

Contribution

It provides a detailed Dyson-Schwinger approach to the quark loop contributions, comparing it with hadronic models like ENJL, highlighting the significance of momentum dependence.

Findings

Momentum dependence significantly affects the hadronic light-by-light contribution.

Transverse quark-photon-vertex parts do not suppress the contribution as in ENJL.

Realistic vertex dressings alter the impact of vector meson dominance models.

Abstract

We summarize our recent results for the quark loop part of the light-by-light scattering contribution as well as the hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon. In particular we focus on the role played by the momentum dependence of the quark- and quark-photon vertex dressing functions. We give a detailed comparison of the Dyson-Schwinger description of this contribution to the corresponding picture emerging from hadronic models in particular the extended Nambu--Jona-Lasonio model (ENJL). We find that the details of the momentum dependence are important on a quantitative level. Especially the transverse parts of the quark-photon-vertex, which serve as a dynamical extension of simple vector meson dominance models, do not yield the large suppression of the light-by-light contribution found in the ENJL model if realistic dressings are taken into account.