Hadronic light-by-light scattering contribution to muong−2

The hadronic light-by-light scattering contribution to muon $g-2\mathrm{}$ is examined based on the low energy effective theories of QCD, the Nambu-Jona-Lasinio model, and hidden local symmetry approach, supplemented by general information concerning the asymptotic behavior of QCD. Our result is -52×${10}^{-11\mathrm{}}$ with an uncertainty of ±18×${10}^{-11\mathrm{}}$, which includes our best estimate of the model dependence. This is within the expected measurement uncertainty of 40×${10}^{-11\mathrm{}}$ in the forthcoming experiment at Brookhaven National Laboratory. Our result removes one of the main theoretical obstacles in verifying the existence of the weak contribution to the muon $g-2\mathrm{}$.