On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$

Abstract

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.

arXiv comment22 pages, 10 figures. One added figure (Fig. 10) and improvements in Figs. 7,8 and 9. This version matches the published one

References in corpus (58)

• Gauge Theory Correlators from Non-Critical String Theory
• Low energy hadron physics in holographic QCD
• QCD and a Holographic Model of Hadrons
• The Muon g-2
• Chiral symmetry breaking from five dimensional spaces
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Complete Tenth-Order QED Contribution to the Muon g-2
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• The electroweak contributions to (g-2)_μ after the Higgs boson mass measurement
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Dispersion relation for hadronic light-by-light scattering: pion pole
• Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
• Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks
• Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution
• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• Hadronic light-by-light scattering contribution to the muon g-2: an effective field theory approach
• Dispersion relation for hadronic light-by-light scattering: theoretical foundations
• Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$
• Towards a data-driven analysis of hadronic light-by-light scattering
• Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $g-2$
• Single meson contributions to the muon's anomalous magnetic moment
• Dispersive approach to hadronic light-by-light scattering
• Interpolating between low and high energy QCD via a 5D Yang-Mills model
• Comment on the Pion Pole Part of the Light-by-Light Contribution to the Muon $g-2$
• Hadronic Contributions to the Muon $g-2$ and Low-Energy QCD
• Hadronic Light-by-Light Contribution to the Muon $g-2$
• Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• Hadronic Light-by-light Scattering Effect on Muon g-2
• Hadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange
• Hadronic Light-by-light Scattering Contribution to Muon $g-2$
• Perturbative and nonperturbative renormalization of anomalous quark triangles
• Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass
• Anomalous magnetic moment of the muon in a dispersive approach
• Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• New nonrenormalization theorems for anomalous three point functions
• Using infinite volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment
• Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon
• Hadronic Contributions to the Muon Anomaly in the Constituent Chiral Quark Model
• The hadronic light by light contribution to the $(g-2{)}_{\mu }$ with holographic models of QCD
• Pion in the Holographic Model with 5D Yang-Mills Fields
• Effective Action and Holography in 5D Gauge Theories
• Pseudo scalar contributions to light-by-light correction of muon g-2 in AdS/QCD
• Contribution of neutral pseudoscalar mesons to $a_{\mu }^{HLbL}$ within a Schwinger-Dyson equations approach to QCD
• Pseudoscalar pole light-by-light contributions to the muon $(g-2)$ in Resonance Chiral Theory
• Generic dijet soft functions at two-loop order: correlated emissions
• The hadronic light-by-light contribution to the muon's anomalous magnetic moment
• Exact Equivalence of the D=4 Gauged Wess-Zumino-Witten Term and the D=5 Yang-Mills Chern-Simons Term
• Constraints on the $\eta {\eta }^{\prime }$ decay rate of a scalar glueball from gauge/gravity duality
• Theta dependence in Holographic QCD
• Pseudoscalar transition form factors and the hadronic light-by-light contribution to the anomalous magnetic moment of the muon from holographic QCD
• Analytic Approaches to Kaon Physics
• Hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• On dispersion relations and hadronic light-by-light scattering contribution to the muon anomalous magnetic moment

Cited by in corpus (44)

• The anomalous magnetic moment of the muon in the Standard Model
• Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
• The anomalous magnetic moment of the muon in the Standard Model: an update
• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• A dispersive estimate of scalar contributions to hadronic light-by-light scattering
• The two-loop perturbative correction to the (g-2)${}_{\mu }$ HLbL at short distances
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
• The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g-2
• Effects of Longitudinal Short-Distance Constraints on the Hadronic Light-by-Light Contribution to the Muon $g-2$
• Axial-vector transition form factors and $e^{+}{e}^{-}\to f_1{\pi }^{+}{\pi }^{-}$
• 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
• On some properties of the fourth-rank hadronic vacuum polarization tensor and the anomalous magnetic moment of the muon
• An optimized basis for hadronic light-by-light scattering
• Dispersion relation for hadronic light-by-light scattering: subleading contributions
• Dispersion relations for hadronic light-by-light scattering in triangle kinematics
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Dispersion relation for hadronic light-by-light scattering: $\eta$ and ${\eta }^{\prime }$ poles
• Dispersion relations for the hadronic VVA correlator
• Holographic QCD and the muon anomalous magnetic moment
• Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
• Central exclusive diffractive production of axial-vector $f_1(1285)$ and $f_1(1420)$ mesons in proton-proton collisions
• Precision evaluation of the $\eta$- and ${\eta }^{\prime }$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
• 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
• Improved evaluation of the electroweak contribution to muon $g-2$
• Axial-vector exchange contribution to the Hyperfine Splitting
• The light-by-light contribution to the muon anomalous magnetic moment from the axial-vector mesons exchanges within the nonlocal quark model
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Production of axial-vector mesons at $e^{+}{e}^{-}$ collisions with double-tagging as a way to constrain the axial meson LbL contribution to muon g-2 and/or hyperfine splitting of muonic hydrogen
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Exclusive $f_1(1285)$ meson production for energy ranges available at the GSI-FAIR with HADES and PANDA
• ${\pi }^0,\eta ,{\eta }^{\prime }$ two-photon transition form factors in the holographic soft-wall model and contributions to $(g-2{)}_{\mu }$
• Constituent quark axial current couplings to light vector mesons in the vacuum and with a weak magnetic field
• Hadronic vacuum polarization contribution to the muon $g-2$ in holographic QCD
• Hadronic Light by Light Corrections to the Muon Anomalous Magnetic Moment
• Perturbative QCD below charm threshold: theory and tensions with $e^{+}{e}^{-}$ data
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains
• New high-statistics measurement of the ${\pi }^0\to e^{+}{e}^{-}\gamma$ Dalitz decay at the Mainz Microtron
• From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models