Hadronic light-by-light scattering in the muon g-2: impact of proposed measurements of the (pi^0 -> gamma gamma) decay width and the (gamma^* gamma -> pi^0) transition form factor with the KLOE-2 experiment

The calculation of the hadronic light-by-light scattering contribution to the muon g-2 currently relies entirely on models. Measurements of the form factors which describe the interactions of hadrons with photons can help to constrain the models and reduce the uncertainty in a_{mu}(had. LbyL) = (116 pm 40) x 10^{-11}. In the dominant pion-exchange contribution, the form factor F_{{pi^0}^*gamma^*gamma^*}((q_1 + q_2)^2, q_1^2, q_2^2) with an off-shell pion enters. In general, measurements of the transition form factor F(Q^2) = F_{{pi^0}^*gamma^*gamma^*}(m_{pi}^2, -Q^2, 0) are only sensitive to a subset of the model parameters. Thus, having a good description for F(Q^2) is only necessary, not sufficient, to determine a_{mu}(LbyL; pi^0). Simulations have shown that measurements at KLOE-2 should be able to determine the (pi^0 -> gamma gamma) decay width to 1% statistical precision and the transition form factor for small space-like momenta, 0.01 GeV^2 < Q^2 < 0.1 GeV^2, to 6% precision. In the two-loop integral for the pion-exchange contribution the relevant regions of momenta are in the range 0 - 1.5 GeV. With the (pi^0 -> gamma gamma) decay width from the PDG [PrimEx] and current data for the transition form factor, the error on a_{mu}(LbyL; pi^0) is (pm 4 x 10^{-11}) [pm 2 x 10^{-11}], not taking into account the uncertainty related to the off-shellness of the pion. Including the simulated KLOE-2 data reduces the error to (pm (0.7 - 1.1) x 10^{-11}). For models like VMD, which have only few parameters that are completely determined by measurements of F(Q^2), this represents the total error. But maybe such models are too simplistic. In other models, e.g. those based on large-N_c QCD, parameters describing the off-shell pion dominate the uncertainty in a_{mu; large-N_c}(LbyL; pi^0) = (72 pm 12) x 10^{-11}.