Hadronic light-by-light corrections to the muon g-2: The pion-pole contribution

The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the π⁰-γ^*-γ^* transition form factor based on the large-N_C and short-distance properties of QCD. The resulting two-loop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining two-dimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a_μ^LbyL;π0=+5.8(1.0)×10^-10, disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a_μ^LbyL;π0|_VMD=+5.6×10^-10, and differs only by its overall sign from the value obtained by previous authors. The inclusion of the η and η^′ poles gives a total value a_μ^LbyL;PS=+8.3(1.2)×10^-10 for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a_μ and its theoretical counterpart in the standard model.