Study of electron-positron annihilation into $K\bar{K}\pi$ within resonance chiral theory

Abstract

In this paper, a coherent study of the $e^{+}{e}^{-}$ annihilation into $K^{+}{K}^{-}{\pi }^0$, $K_S^0{K}_L^0{\pi }^0$ and $K_S^0{K}^{\pm }{\pi }^{\mp }$ is carried out within the framework of resonance chiral theory. The amplitudes are fixed by fitting to the experimental cross-section and invariant mass spectrum. With these amplitudes, one can calculate the hadronic vacuum polarization form factors of these processes. The leading order contributions of $\sigma (e^{+}{e}^{-}\to K\bar{K}\pi )$ to the anomalous magnetic moment of the muon, $(g-2{)}_{\mu }$, is obtained as $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}(e^{+}{e}^{-}\to K\bar{K}\pi )=(3.178\pm 0.071)\times 10^{-10}$ up to $E_{\mathrm{cm}}=2.3$ GeV.

Comments: 14 pages, 2 figures, to be the same as the published version