Two and Three Pseudoscalar Production in $e^{+}e^{-}$ annihilation and their contributions to $(g-2)_{\mu}$

A coherent study of $e^{+}e^{-}$ annihilation into two ($\pi^{+}\pi^{-}$,$K^{+}K^{-}$) and three ($\pi^{+}\pi^{-}\pi^{0},\pi^{+}\pi^{-}\eta$) pseudoscalar meson production is carried out within the framework of resonance chiral theory in energy region $E\lesssim 2 \, \mathrm{GeV}$. The work of {[}L. Y. Dai, J. Portol\'es, and O. Shekhovtsova, Phys. Rev. D 88,056001 (2013){]} is revisited with the latest experimental data and a joint analysis of two pseudoscalar meson production. Hence, we evaluate the lowest order hadronic vacuum polarization contributions of those two and three pseudoscalar processes to the anomalous magnetic moment of the muon. We also estimate some higher-order additions led by the same hadronic vacuum polarization. Combined with the other contributions from the standard model, the theoretical prediction differs still by $(21.6 \pm 7.4)\times 10^{-10}$ (2.9$\sigma$) from the experimental value.