Using an effective sigma/f_0(500) resonance, which describes the pipi-->pipi and gammagamma-->pipi 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.
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