Contribution of exclusive $(\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma$ channels to the leading order HVP of the muon $g-2$

TL;DR

This paper calculates the contributions of specific exclusive channels involving neutral mesons and a photon to the muon g-2's leading order hadronic vacuum polarization, highlighting the importance of interference effects and model uncertainties.

Contribution

It introduces a model-independent method using S-matrix formalism to evaluate these channels' contributions, reducing reliance on resonance-background separation.

Findings

Calculated contribution: (1.13 ± 0.13) × 10^{-10} to muon g-2

Uncertainties mainly from vector meson dominance parameters

Emphasizes need for improved experimental data below 2 GeV

Abstract

We evaluate the contributions of $(\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma$ exclusive channels to the dispersion integral of the leading order HVP of the muon anomalous magnetic moment. These channels are included in some way in previous evaluations of the $\pi^0\omega, \eta\omega$ and $\eta\phi$ contributions to $a_{\mu}^{\rm had, LO}$, where the vector resonances (decaying into $\pi^0/\eta+ \gamma$) are assumed to be on-shell. Since the separation of resonance and background contributions in a given observable is, in general, a model-dependent procedure, here we use pseudoscalar mesons and the photon as the $in$ and $out$ states of the $e^+e^- \to (\pi^0\pi^0, \pi^0\eta, \eta\eta)\gamma$ $S$-matrix, such that the cross section contains the interferences among different contributing to the amplitudes. We find $a^{\rm had, LO}_{\mu}(P^0_1P^0_2\gamma)=(1.13\pm 0.13 ) \times 10^{-10}$, where uncertainties stem mainly from vector meson dominance model parameters. Improved experimental studies of these exclusive channels in the whole range below 2 GeV would reduce model-dependency.