Total cross section for electron-positron annihilation and hadronic contribution to the muon magnetic moment

A class of rigorous inequalities are derived for the integrated cross section for e-e+ annihilation into hadrons through one photon. They involve the p-wave ππ cross section and a slope of the electromagnetic form factor of the pion. A lower bound on the hadronic contribution to the muon magnetic moment is estimated in terms of the electromagnetic charge radius rπ. The bound is twice as large as the ρ-meson dominance value if rπ=0.86 F as indicated by old data, but no meaningful result is obtained if one substitutes the values for rπ obtained in a new experiment. The inequalities can also be used to test various predictions concerning the asymptotic behavior of the e-e+ annihilation cross section. A slowly decreasing behavior is favored over a rapidly decreasing one like σe+e-(t)t-3, but more accurate data are needed to draw a definite conclusion.