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

Abstract

A dispersive implementation of the $a_0(980)$ resonance to $(g-2{)}_{\mu }$ requires the knowledge of the double-virtual $S$-wave ${\gamma }^{\ast }{\gamma }^{\ast }\to \pi \eta /KK(I=1)$ amplitudes. To obtain these amplitudes, we used a modified coupled-channel Muskhelishvili-Omnes formalism, with input from the left-hand cuts and the hadronic Omnes matrix. The latter was derived using a data-driven N/D method, where the hadronic left-hand cuts were approximated via a conformal expansion. Due to the absence of direct hadronic data in the $\pi \eta$ channel, the expansion coefficients were fitted to various experimental data sets on two-photon fusion processes with $\pi \eta$ and $KK$ final states. The resulting dispersive estimate for the $a_0(980)$ contribution to $(g-2{)}_{\mu }$ is $a_{\mu }^{HLbL}[a_0(980){]}_{resc.}=-0.43(1)(2)\times 10^{-11}$, which presents an order of magnitude improvement in precision over the narrow resonance approximation.

12 pages, 6 figures, accepted to PRD