  Previous studies have shown that the Hidden Local Symmetry (HLS) Model,
supplied with appropriate symmetry breaking, provides an Effective Lagrangian
(BHLS) able to encompass a large number of processes within a unified
framework. A global fit provides a simultaneous description of the $e^+ e^-$
annihilation into $\pi^+\pi^-$, $\pi^0\gamma$, $\eta \gamma$,
$\pi^+\pi^-\pi^0$, $K^+K^-$, $K_L K_S$, the dipion spectrum in the $\tau$ decay
and other light meson partial widths. Additional breaking schemes extend its
scope to spacelike processes within a new framework (BHLS$_2$). The
phenomenology previously explored with BHLS is revisited in the BHLS$_2$
context with emphasis on the $\Phi$ mass region. It is shown that BHLS$_2$
addresses the close spacelike region covered by NA7 and Fermilab data; also,the
Lattice QCD pion form factor is accurately predicted by BHLS$_2$ using fits to
annihilation data only. These channels contribution to $a_\mu$ over the range
of validity of BHLS$_2$ is shown to strongly reduce the former BHLS
systematics. The uncertainty on $a_\mu^{\rm th}(\sqrt{s}< 1.05$ GeV) is much
improved compared to standard approaches relying on direct integration methods
of measured spectra. Using the BHLS$_2$ results, the leading order HVP
contribution to the muon anomalous moment is $a_\mu^{HVP-LO}= 686.65 \pm 3.01
+(+1.16,-0.75)_{syst.}$ in units of $10^{-10}$. Using a conservative estimate
for the light--by--light contribution, our evaluation is $a_\mu^{\rm th}=\left
[11\,659\,175.96 \pm 4.17 +(+1.16,-0.75)_{syst.}\right]\times 10^{-10}$. The
$\rho^0\gamma$ mixing in dispersive and LQCD approaches is discussed and may
amount to a shift $\delta a_\mu[\pi\pi]_{\rho\gamma} = +(3.10\pm0.31)\times
10^{-10}$ at LO+NLO, presently treated as additional systematics. Taking this
shift into account, $a_\mu^{\rm th}-a_\mu^{\rm BNL}$ exhibits a significance
not smaller than $3.8 \sigma$.
