Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model

Abstract

We use the Wentzel-Kramers-Brillouin (WKB) approximation to uncover divergences and instances of non-commuting limits in a large class of holographic soft-wall models. We show that the infinite sum over single resonance contributions for a variety of observables involving the Chern-Simons term, such as the vector-vector-axial (VVA) correlator or the hadronic light-by-light tensor, does not converge. These divergences can in some cases (such as the VVA correlator) be traced back to non-commuting limits and avoided by working directly in the 5-dimensional setup with bulk-to-boundary propagators. However, the hadronic light-by-light scattering tensor also diverges in the 5-dimensional formulation with corresponding Green functions, preventing a correct implementation of the Melnikov-Vainshtein short-distance constraint and even leading to an infinite contribution to the muon $g-2$. We also discuss modifications of the standard soft-wall model that are able to resolve this issue.

REVTeX, 28 pages, 8 figures, 3 tables, v2: references and one appendix on WSS model added, v3 (published version): minor typos corrected

References in corpus (26)

• Linear Confinement and AdS/QCD
• Exploring improved holographic theories for QCD: Part II
• Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
• Chiral symmetry breaking as open string tachyon condensation
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Dynamical Soft-Wall AdS/QCD
• Highly Excited Mesons, Linear Regge Trajectories and the Pattern of the Chiral Symmetry Realization
• An AdS/QCD model from tachyon condensation: II
• Pion Form Factor in Improved Holographic QCD Backgrounds
• An AdS/QCD model from Sen's tachyon action
• Asymptotic behavior of meson transition form factors
• Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
• The hadronic light by light contribution to the $(g-2{)}_{\mu }$ with holographic models of QCD
• Anomalous Form Factor of the Neutral Pion in Extended AdS/QCD Model with Chern-Simons Term
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with solved $U(1{)}_A$ problem
• Hadronic light-by-light contribution to the muon $g-2$ from holographic QCD with massive pions
• The dynamical holographic QCD method for hadron physics and QCD matter
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relations for the hadronic VVA correlator
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Spontaneous chiral symmetry breaking in holographic soft wall models
• Scalar resonances in the hadronic light-by-light contribution to the muon $(g-2)$
• Hadronic light-by-light scattering contributions to $(g-2{)}_{\mu }$ from axial-vector and tensor mesons in the holographic soft-wall model
• The V-QCD baryon : numerical solution and baryon spectrum
• Tachyon-dependent Chern-Simons terms and the V-QCD Baryon
• ${\pi }^0,\eta ,{\eta }^{\prime }$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2{)}_{\mu }$