  Relying on the Hidden Local Symmetry (HLS) model equipped with a mechanism
breaking the U(3)/SU(3)/SU(2) symmetries and generating a dynamical vector
meson mixing, it has been shown that a global fit successfully describes the
cross sections for the e+ e- -> pi+ pi-, e+ e- -> (pi0/eta) gamma and e+ e- ->
pi0 pi+ pi- annihilation channels. One extends this global fit in order to
include also the dipion spectra from the tau decay, taking into account all
reported information on their statistical and systematic errors. A model
accounting for lineshape distortions of the rho+- spectrum relative to rho0 is
also examined when analyzing the tau data behavior within the global fit
framework. One shows that a successful account for e+ e- annihilation data and
tau spectra can be simultaneously reached. Then, issues related with
non--perturbative hadronic contributions to the muon g-2 are examined in
details. It is shown that all e+ e- data considered together allow for improved
and motivated estimates for the a_mu(pi+ pi-), the pi+ pi- loop contribution to
the muon g-2; for instance, integrated between 0.630 and 0.958 GeV, we find
a_mu(pi+ pi-)= 359.62 +- 1.62 (in units of 10^{-10}), a 40% improvement of the
current uncertainty. The effects of the various tau samples in the context of a
global fit procedure leads to conclude that different lineshape distortions are
revealed by the ALEPH, BELLE and CLEO data samples. Relying on global fits to
the data quoted above, one also provides motivated estimates of the pi+ pi-,
pi0 gamma, eta gamma and pi0 pi+ pi- contributions to a_mu up to 1 GeV with the
smallest possible uncertainties. These estimates are based on various global
fit configurations, each yielding a good probability.
