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.

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

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• Hadronic contributions to $(g-2)$ of the leptons and to the effective fine structure constant $\alpha (M_Z^2)$
• Electroweak Fermion-loop Contributions to the Muon Anomalous Magnetic Moment
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• Hadronic Light-by-Light Contribution to the Muon $g-2$
• Hadronic Light-by-light Scattering Effect on Muon g-2
• Two--Loop Electroweak Corrections to the Muon g-2: a new class of Hadronic Contributions
• Hadronic Light-by-light Scattering Contribution to Muon $g-2$
• The $B_K$ Parameter in the $1/N_c$ Expansion
• The asymptotic behaviour of the ${\pi }^0$ ${\gamma }^{\ast }$ ${\gamma }^{\ast }$ vertex
• Three-loop QED Vacuum Polarization and the Four--loop Muon Anomalous Magnetic Moment
• Hadronic light-by-light scattering contribution to the muon g-2

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