Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1{)}_A$ problem

Abstract

We employ the comparatively minimal extension of hard-wall AdS/QCD due to Katz and Schwartz which takes into account the U(1)${}_A$ anomaly for computing hadronic light-by-light scattering contributions of pseudoscalar and axial vector mesons to the anomalous magnetic moment of the muon $a_{\mu }$. By including a gluon condensate as one extra tunable parameter besides those fixed by $f_{\pi }$ and the pion, kaon, and rho masses, we obtain remarkably accurate fits for $\eta$ and ${\eta }^{\prime }$ masses and their decay rates to photons, leading to $a_{\mu }$ contributions in complete agreement with the Standard Model result by the Muon $g-2$ Theory Initiative. Turning to the less well understood axial vector contributions, we update our previous predictions obtained in flavor-symmetric hard-wall AdS/QCD models without U(1)${}_A$ breaking.

Comments: REVTEX, 13 pages, 4 figures, 4 tables; v2: slight extensions and updates of numerical results, minor additions, references added