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Abstract
We discuss how holographic models of QCD are used to study the the hadronic light-by-light (HLbL) scattering amplitude contribution to the muon anomalous magnetic moment. After a brief description of the various models, we focus on a particular one, introduced by Hirn and Sanz, emphasizing the role it assigns to the pion, and the vector and-axial vector resonances. We review how the parameters of the model are fixed by imposing condition on the low energy and the deep Euclidean limit of two-point correlators of QCD vector and axial vector currents. We then focus on the evaluation of the three-point axial-vector-vector current correlator and the pion anomalous transition form factor to be used in the one-pion exchange HLbL diagram and study its asymptotic properties. Finally, we present preliminary results on the four vector current correlator that defines the Hadronic Light-by-Light tensor. We find that axial-vector resonances play an important rule in recovering the correct asymptotic behaviour predicted by QCD at large Euclidean momenta.
Highlights
The present experimental value for the anomalous magnetic moment of the muon, aμ = (g − 2)μ/2, is given by aEμXP = 11659209.1(5.4)(3.3) × 10−10 [1], where statistical errors are the largest source of uncertainties
We shall focus on the HW2 model proposed by Hirn and Sanz (HS), [20], and analyze twothree- and four point functions which are relevant for the evaluation of the hadronic Light-by-Light contribution to (g − 2)μ
We have illustrated the main ingredients of one particular model, introduced by Hirn and Sanz, and shown how one can evaluate the one-pion exchange contribution, by mean of the expression of the pion transition form factor provided by the model
Summary
Depending on few independent parameters, they produce surprisingly good results at low energy, with predictions comparable with those of Chiral Lagrangians, and vector meson dominance It is clear, that HQCD models are not aimed at producing accurate physics predictions, but rather to get hints in the study of QCD phenomena , which could be suggestive for more sound attempts, e.g. lattice calculations. In Sect., we shall focus on the evaluation of AVV three-point axial-vector-vector current correlator, in order to extract the pion TFF to be used in the one-pion exchange HLbL diagram and we study its asymptotic properties.
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