Hadronic Light-by-Light Scattering Effect on Muong−2

The hadronic light-by-light scattering contribution to muon $g-2\mathrm{}$ is examined using low energy effective theories of QCD, the Nambu–Jona-Lasinio model, and hidden local chiral symmetry, as guides. Our result is $-36\mathrm{}\times {10}^{-11\mathrm{}}$ with an uncertainty of $\pm 16\times {10}^{-11\mathrm{}}$, which includes our best estimate of model dependence. This is within the expected measurement uncertainty of $40\times {10}^{-11\mathrm{}}$ 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 $g-2\mathrm{}$.