Superconnections in AdS/QCD and the hadronic light-by-light contribution to the muon g−2

Abstract

In this paper, we consider hard-wall anti–de Sitter/quantum chromodynamics (AdS/QCD) models extended by a string-theory inspired Chern-Simons action in terms of a superconnection involving a bifundamental scalar field which corresponds to the open-string tachyon of brane-antibrane configurations and which is naturally identified with the holographic dual of the quark condensate in chiral symmetry breaking. This realizes both the axial and chiral anomalies of QCD with a Witten-Veneziano mechanism for the 𝜂′ mass in addition to current quark masses, but somewhat differently than in the Katz-Schwartz AdS/QCD model used previously by us to evaluate pseudoscalar and axial vector transition form factors and their contribution to the hadronic light-by-light (HLBL) piece of the muon 𝑔−2. Compared to the Katz-Schwartz model, we obtain a significantly more realistic description of axial-vector mesons with regard to 𝑓₁−𝑓′₁ mixing and equivalent photon rates. Moreover, predictions of the 𝑓₁→𝑒⁺⁢𝑒⁻ branching ratios are found to be in line with a recent phenomenological study. However, pseudoscalar transition form factors compare less well with experiment; in particular the 𝜋⁰ transition form factor turns out to be overestimated at moderate nonzero virtuality. For the combined HLBL contribution to the muon 𝑔−2 from the towers of axial vector mesons and excited pseudoscalars we obtain, however, a result very close to that of the Katz-Schwartz model.