Abstract
We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models. This requires the summation of an infinite tower of axial vector mesons, which is naturally present in holographic QCD models, and indeed takes care of the longitudinal short-distance constraint due to Melnikov and Vainshtein. Numerically the results of simple hard-wall holographic QCD models point to larger contributions from axial vector mesons than assumed previously, while the predicted contributions from pseudo-Goldstone bosons agree nicely with data-driven approaches.
Highlights
We review the recent progress made in using holographic QCD to study hadronic contributions to the anomalous magnetic moment of the muon, in particular the hadronic light-by-light scattering contribution, where the short-distance constraints associated with the axial anomaly are notoriously difficult to satisfy in hadronic models
The White Paper (WP) result (4) instead uses a much smaller estimate based on a Regge model for an infinite tower of pseudoscalar bosons constructed such that the longitudinal short-distance constraint (LSDC) is satisfied [28,29], which was criticized by Melnikov and Vainshtein (MV) in [37]
In order to obtain the hadronic light-by-light scattering (HLBL) contribution to the muon anomalous magnetic moment, the various form factors have to be used for the respective components of the HLBL scattering amplitude analogous to (18) and inserted into the master formula (8)
Summary
We will sketch a derivation of the leading-order behavior of for two different kinematic configurations when the Euclidean momenta Q1,2,3 become very large [11]. The main strategy to derive the LSDC of [11] is to pick q1 − q2 very large and Euclidean and q1 + q2 = −q3 much smaller (but still larger than the QCD scale) This allows one to insert the OPE (9) into the light-by-light scattering tensor (6). In this way the V V A correlator appears in this asymptotic constraint. One-particle intermediate states which are approximately stable show up as poles in the light-by-light scattering amplitude for the right kinematic configurations These are unambiguously defined since they are on-shell only for special kinematics. The infinite tower of axial vector fields will be responsible for contributing non-zero results for the right-hand sides of the LSDCs (11) and (12)
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