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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 theseamplitudes we used a modified coupled-channel Muskhelischvili-Omn\`esformalism, with the input from the left-hand cuts and the hadronic Omn\`esfunction. The latter were obtained using a data-driven $N/D$ method in whichthe fits were performed to the different sets of experimental data ontwo-photon fusion processes with $\pi\eta$ and $K\bar{K}$ final states. Thisyields the preliminary dispersive estimate$a_\mu^{HLbL}[a_0(980)]_{resc.}=-0.46(2)\times 10^{-11}$.

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