Abstract
We extend our previous calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment in holographic QCD to models with finite quark masses and a tower of massive pions. Analysing the role of the latter in the Wess-Zumino-Witten action, we show that the Melnikov-Vainshtein short-distance constraint is satisfied solely by the summation of contributions from the infinite tower of axial vector meson contributions. There is also an enhancement of the asymptotic behavior of pseudoscalar contributions when their infinite tower of excitations is summed, but this leads only to subleading contributions for the short-distance constraints on light-by-light scattering. We also refine our numerical evaluations, particularly in the pion and $a_1$ sector, which corroborates our previous findings of contributions from axial vector mesons that are significantly larger than those adopted for the effects of axials and short-distance constraints in the recent White Paper on the Standard Model prediction for $(g-2)_\mu$.
Highlights
The Muon g − 2 Collaboration at Fermilab [1] has confirmed the long-standing discrepancy between the E821/BNL measurement [2] of the anomalous magnetic moment of the muon [3] and the Standard Model prediction, which according to the white paper (WP) of the Muon g − 2 Theory Initiative [4] is below the combined experimental value by an amount of Δaμ 1⁄4 Δðg − 2Þμ=2 1⁄4 251ð59Þ × 10−11
We find that in holographic models of QCD (hQCD), there is a certain enhancement of the asymptotic behavior when summing the infinite tower of pseudoscalars compared to the behavior of individual contributions, but within the allowed range of parameters of hQCD this is insufficient to let pseudoscalars contribute to the leading terms of the longitudinal short-distance constraints (SDCs); the latter are determined by the infinite tower of axial-vector mesons alone, in agreement with the expectation expressed in Ref. [35]
II, we review hQCD with an anti–de Sitter (AdS) background that is cut off by a hard wall, and where in addition to flavor gauge fields, a bifundamental scalar bulk field encodes the chiral condensates with or without finite quark masses
Summary
The Muon g − 2 Collaboration at Fermilab [1] has confirmed the long-standing discrepancy between the E821/BNL measurement [2] of the anomalous magnetic moment of the muon [3] and the Standard Model prediction, which according to the white paper (WP) of the Muon g − 2 Theory Initiative [4] is below the combined experimental value by an amount of Δaμ 1⁄4 Δðg − 2Þμ=2 1⁄4 251ð59Þ × 10−11. [24,25], which is compatible with known experimental constraints This model was, not meant primarily as a phenomenological model for estimating the contributions of excited pseudoscalars, but rather as a model for estimating the effects of the longitudinal SDCs, which according to the hQCD models are instead provided by the axial-vector mesons. As far as these effects are concerned, our present results are not far above the estimates obtained in Refs. As shown in Appendix A, all these models lead to a Gell-Mann–Oakes–Renner (GOR) relation in the limit of small quark masses—to wit, f2πm2π 1⁄4 2αMqΣ for Mq ≪ Σz20 ∝ Σ=m2ρ; ð8Þ where α 1⁄4 1 for the standard choice M2X 1⁄4 −3, and 0 < α < 2 for the admissible generalizations [51] −4 < M2X < 0
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