Holographic QCD and the muon anomalous magnetic moment

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.

Self-Interactions, Self-Energy and the Electromagnetic Contribution to the Anomalous <em>g</em>-Factor

“…where for the self-Coulomb energy term we get Σ q = a e γ e m q c 2 and for the effective rest mass we have M q = m q (1 + a e ). Here, γ e is a constant, with β e = α for all q, obtained by solving Equations ( 20) and (21), see Section 3.1. We would like to point out once more that within the considered mathematical framework if ∄e, then ∄a e , the transformations given in Equation ( 25) are no longer applicable and the particle can be at rest with respect to any observer.…”

“…Determining with high accuracy the dynamics of the two remaining massive leptons carrying elementary charge, the muon and tau, is an active field of research. The muon's anomalous magnetic moment [14,15] is still puzzling the community aiming to reduce the gap between theory and experiment [16][17][18][19][20][21][22], recently known to be of about 0.58%. On the other hand, having a very short lifetime and being the massive among all leptons, measuring and predicting tau anomalous magnetic moment is a challenging task requiring great efforts [23][24][25][26][27][28][29].…”

Hadronic contributions to the muon g − 2 in holographic QCD

“…[4] for g 5 = 2π (OPE fit, blue) and the reduced value (red) corresponding to a fit of F ρ . (Taken from [41]) modified by gluonic corrections of the order of 10% [35,36], while hQCD models with a simple AdS 5 background approach the asymptotic limit somewhat too quickly. Similar corrections but with opposite sign appear in the vector correlator appearing in HVP.…”

Muon g-2: Theory overview

“…The present precision requirements made it necessary to go beyond this model. Different attempts in this direction have been made recently: in our group we considered a tower of excited pseudoscalars to satisfy the longitudinal SDC [28,65], whereas two different groups have addressed both the transverse as well as the longitudinal SDC by considering a tower of axial resonances within a model of holographic QCD [66][67][68]. While it is clear that the axials have to play a prominent role in satisfying the SDC because the contribution of excited pseudoscalars vanishes in the chiral limit, pseudoscalars have the unique advantage that for them the ambiguities mentioned above are absent.…”