Pseudoscalar-pole contributions to the muon $g-2$ at the physical point

TL;DR

This paper computes the transition form factors for neutral pseudoscalar mesons using lattice QCD to improve estimates of their contributions to the muon g-2, achieving results consistent with previous studies and providing new data for the pion and eta mesons.

Contribution

The study presents the first lattice QCD calculation of pseudoscalar transition form factors at the physical point, enhancing the precision of muon g-2 hadronic light-by-light contributions.

Findings

Pion g-2 contribution estimate with <10% uncertainty.

Consistent results with previous lattice and data-driven methods.

Preliminary eta meson contribution from a single lattice spacing.

Abstract

Pseudoscalar-pole diagrams are an important component of estimates of the hadronic light-by-light (HLbL) contribution to the muon $g-2$. We report on our computation of the transition form factors $\mathcal{F}_{P \rightarrow \gamma^* \gamma^*}$ for the neutral pseudoscalar mesons $P=\pi^0$ and $\eta$. The calculation is performed using twisted-mass lattice QCD with physical quark masses. On the lattice, we have access to a broad range of (space-like) photon four-momenta and therefore produce form factor data complementary to the experimentally accessible single-virtual direction, which directly leads to an estimate of the pion- and $\eta$-pole components of the muon $g-2$. For the pion, our result for the $g-2$ contribution in the continuum is comparable with previous lattice and data-driven determinations, with combined relative uncertainties below $10\%$. For the $\eta$ meson, we report on a preliminary determination from a single lattice spacing.