Analysis of the hadronic light-by-light contributions to the muon g - 2

We calculate the hadronic light-by-light contributions to the muon g - 2. We use both 1/ N_c and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the 1/ N_c expansion low energy contributions using the Extended Nambu-Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon g - 2 are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon g - 2 is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is a_μ^{light-by-light} = (-9.2 ± 3.2) × 10 ^-1. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon g - 2 experiment.