A dispersive estimate of the $a_0(980)$ contribution to hadronic light-by-light scattering in $(g-2)_\mu$

TL;DR

This paper develops a dispersive approach to quantify the $a_0(980)$ resonance's contribution to the muon's anomalous magnetic moment, using a coupled-channel formalism and experimental data-driven methods.

Contribution

It introduces a modified coupled-channel Muskhelischvili-Omnès formalism with a data-driven $N/D$ method to estimate the $a_0(980)$ contribution to $(g-2)_$.

Findings

Preliminary dispersive estimate of the $a_0(980)$ contribution: -0.46(2) x 10^{-11}

Uses a data-driven $N/D$ method for hadronic Omnès functions

Employs a modified coupled-channel Muskhelischvili-Omnès formalism

Abstract

A dispersive implementation of the $a_0(980)$ resonance to $(g-2)_\mu$ requires the knowledge of the double-virtual $S$-wave $\gamma^*\gamma^*\to\pi\eta / K\bar{K}_{I=1}$ amplitudes. To obtain these amplitudes we used a modified coupled-channel Muskhelischvili-Omn\`es formalism, with the input from the left-hand cuts and the hadronic Omn\`es function. The latter were obtained using a data-driven $N/D$ method in which the fits were performed to the different sets of experimental data on two-photon fusion processes with $\pi\eta$ and $K\bar{K}$ final states. This yields the preliminary dispersive estimate $a_\mu^{HLbL}[a_0(980)]_{resc.}=-0.46(2)\times 10^{-11}$.