On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$

Abstract

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.

22 pages, 10 figures. One added figure (Fig. 10) and improvements in Figs. 7,8 and 9. This version matches the published one

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• Holographic QCD and the muon anomalous magnetic moment
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• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
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• Axial-vector exchange contribution to the Hyperfine Splitting
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
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• ${\pi }^0,\eta ,{\eta }^{\prime }$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2{)}_{\mu }$
• Exclusive $f_1(1285)$ meson production for energy ranges available at the GSI-FAIR with HADES and PANDA
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• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
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• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
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• New high-statistics measurement of the ${\pi }^0\to e^{+}{e}^{-}\gamma$ Dalitz decay at the Mainz Microtron
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models
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• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains