Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment reexamined

We discuss the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}$, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50% increase in the central value of $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}$, compared to commonly accepted estimates (see, e.g., [M. Davier, S. Eidelman, A. Hocker, and Z. Zhang, Eur. Phys. J. C 31, 503 (2003).]). The hadronic light-by-light scattering contribution becomes $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}=136(25)\times {10}^{-11}$, thereby shifting the standard model prediction closer to the experimental value.