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

Abstract

A dispersive implementation of the $a_0(980)$ resonance to $(g-2{)}_{\mu }$ requires the knowledge of the double-virtual $S$-wave ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \eta /K{\bar{K}}_{I=1}$ amplitudes. To obtain these amplitudes we used a modified coupled-channel Muskhelischvili-Omnès formalism, with the input from the left-hand cuts and the hadronic Omnès 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 $a_{\mu }^{HLbL}[a_0(980){]}_{resc.}=-0.46(2)\times 10^{-11}$.

Comments: 4 pages, 2 figures, Proceedings of 17th International Workshop on Meson Physics (MESON2023), 22nd - 27th June, 2023