  We evaluate systematically some new contributions of the QCD scalar mesons,
including radiative decay-productions, not considered with a better attention
until now in the evaluation of the hadronic contributions to the muon anomaly.
The sum of the scalar contributions to be added to the existing Standard Model
predictions a_mu^{SM} are estimated in units 10^{-10} to be a^{S}_mu= 1.0(0.6)
[TH based]} and 13(11) [ PDG based], where the errors are dominated by the ones
from the experimental widths of these scalar mesons. PDG based results suggest
that the value of a_mu^{SM} and its errors might have been underestimated in
previous works. The inclusion of these new effects leads to a perfect agreement
(< 1.1\sigma) of the measured value a^{exp}_mu and a_mu^{SM} from tau-decay and
implies a (1.5 ~ 3.3) sigma discrepancy between a^{exp}_mu and a_mu^{SM} from
e^+e^- into hadrons data. More refined unbiased estimates of a_mu^{SM} require
improved measurements of the scalar meson masses and widths. The impact of our
results to a_mu^{SM} is summarized in the conclusions.
