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

TL;DR

This paper develops a dispersive method to estimate the contribution of the $a_0(980)$ resonance to the muon's anomalous magnetic moment, improving precision over previous narrow resonance models.

Contribution

It introduces a novel dispersive approach using a modified coupled-channel Muskhelishvili-Omnes formalism with data-driven inputs for the $a_0(980)$ contribution to $(g-2)_$, enhancing accuracy.

Findings

Dispersive estimate for $a_0(980)$ contribution: $-0.43(1)(2) imes 10^{-11}$.

Order of magnitude improvement over narrow resonance approximation.

Method provides a more precise theoretical input for $(g-2)_$ calculations.

Abstract

A dispersive implementation of the $a_0(980)$ resonance to $(g-2)_\mu$ requires the knowledge of the double-virtual $S$-wave $\gamma^*\gamma^*\to\pi\eta/ K K(I=1)$ 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 $K K$ 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.