  Using an effective \sigma/f_0(500) resonance, which describes the
\pi\pi-->\pi\pi and \gamma\gamma-->\pi\pi scattering data, we evaluate its
contribution and the ones of the other scalar mesons to the the hadronic
light-by-light (HLbL) scattering component of the anomalous magnetic moment
a_\mu of the muon. We obtain the conservative range of values:
\sum_S~a_\mu^{lbl}\vert_S = -(4.51+- 4.12) 10^{-11}, which is dominated by the
\sigma/f_0(500) contribution ( 50%~98%), and where the large error is due to
the uncertainties on the parametrisation of the form factors. Considering our
new result, we update the sum of the different theoretical contributions to
a_\mu within the standard model, which we then compare to experiment. This
comparison gives (a_\mu^{\rm exp} - a_\mu^{SM})= +(312.1+- 64.3) 10^{-11},
where the theoretical errors from HLbL are dominated by the scalar meson
contributions.
