Hadronic light-by-light contribution to the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> from holographic QCD with solved <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:msub><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>A</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> problem
Josef Leutgeb, Jonas Mager, Anton Rebhan
Abstract
We employ the comparatively minimal extension of hard-wall AdS/QCD due to Katz and Schwartz which takes into account the ${\mathrm{U}(1)}_{A}$ anomaly for computing hadronic light-by-light scattering contributions of pseudoscalar and axial-vector mesons to the anomalous magnetic moment of the muon ${a}_{\ensuremath{\mu}}$. By including a gluon condensate as one extra tunable parameter besides those fixed by ${f}_{\ensuremath{\pi}}$ and the pion, kaon, and rho masses, we obtain remarkably accurate fits for $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ masses and their decay rates to photons, leading to ${a}_{\ensuremath{\mu}}$ contributions in complete agreement with the Standard Model result by the Muon $g\ensuremath{-}2$ 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 ${\mathrm{U}(1)}_{A}$ breaking.