  In this paper, we study the processes of $e^{+}e^{-}$ annihilation into two
body final states, either two pseudoscalar mesons or one meson with a photon.
The hadronic vacuum polarization form factors are calculated within the
framework of resonance chiral theory in the energy region of $E \lesssim 2$
GeV, with final state interactions taken into account. A joint analysis on the
processes of $e^{+}e^{-} \rightarrow \pi^{+}\pi^{-}$, $K^{+}K^{-}$,
$K_{L}^{0}K_{S}^{0}$, $\pi^{0}\gamma$, and $\eta\gamma$ has been performed, and
the latest experimental data are included. Based on the vacuum polarization
form factors of these processes, we estimate their contributions to the lowest
order of anomalous magnetic moment of the muon, $(g-2)_\mu$. Combined with
other contributions from hadronic vacuum polarization and other interactions
from the standard model, the discrepancy between theoretical prediction and
experimental measurement is $\Delta a_{\mu}=(24.1\pm5.4)\times 10^{-10}$, i.e.,
4.5$\sigma$.
