Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$

Abstract

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 $a_{\mu }^{\mathrm{light}-\mathrm{by}-\mathrm{light}}=(-9.2\pm 3.2)\cdot 10^{-10}$. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon $g-2$ experiment.

Comments: 43 pages, Latex, 4 figures, the analysis of the intermediate and high energy behaviour has been changed completely. New final number is $(-9.2\pm 3.2)\cdot 10^{-10}$