Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment

Abstract

In this work we study the axial contributions to the hadronic light-by-light piece of the muon anomalous magnetic moment using the framework of resonance chiral theory. As a result, we obtain a HLbL;A µ = 0.8 +3.5 −0.8 · 10 −11 , that might suggest a smaller value than most recent calculations, underlining the need of future work along this direction. In particular, we find that our results depend critically on the asymptotic behavior of the form factors, and as such, emphasizes the relevance of future experiments for large photon virtualities. In addition, we present general results regarding the involved axial form factors description, comprehensively examining (and relating) the current approaches, that shall be of general interest. 1 arXiv:1910.02881v2 [hep-ph] 9 Dec 2019 1.2 Axial-vector contributions to the muon anomalous magnetic moment Although the Landau-Yang theorem [64,65] forbids the annihilation of a spin-one particle into a pair of real photons, axial-vector exchange contributions to the HLbL piece of a µ are still possible, since at least one photon is off-shell in both axial-γ * -γ * vertices in such a contribution. Still, the Landau-Yang theorem imposes non-trivial requirements on the symmetry structure of the involved form factors, as we will see.Early estimates of the corresponding contributions were carried out both in the extended Nambu-Jona-Lasino model by Bijnens, and by Hayakawa, Kinoshita and Sanda using Hidden Local Symmetry Lagrangians [38,39]. The first group obtained a HLbL;A µ = (2.5 ± 1.0) · 10 −11 , which includes the ballpark value 1.7 · 10 −11 , given by the second group. Melnikov and Vainshtein [45] derived operator product expansion (OPE) constraints on the hadronic light-by-light (HLbL) tensor and built a model where these were saturated by dropping 2 This arises from a SM µ = 1.16591783(35) [15], a SM µ = 1.16591820.4(35.6) [16], a SM µ = 1.16591830(48) [15]. 3 Remarkable progress in the evaluation of the HLbL part of aµ on the lattice has been achieved recently [60-62], as well (see Ref.[63] for a review on this topic).

Muon g−2 and Δα connection

“…In recent years, major progress has been made in determining the hadronic light-by-light (LbL) contribution, a had;LbL μ , from dispersive approaches and from LQCD. The latest datadriven and dispersive hadronic LbL results [26][27][28][29][30][31]33,[47][48][49][50][51][52][53][54][55][56][57] and first complete LQCD evaluation [32] confirm the previously accepted model-based "Glasgow consensus" result [58], thereby eliminating the hadronic LbL sector as the source of the muon g − 2 discrepancy. This leaves the hadronic vacuum polarization (VP) contributions, a had;VP μ , as the remaining SM candidate to explain Δa μ .…”

Axial-vector and pseudoscalar mesons in the hadronic light-by-light contribution to the muon ( g−2 )

“…We emphasize that the axial-vector contributions are the result of resumming full towers of states, with the first state shown as representative. A comparison of these numbers with the contributions of the lowest-lying axial-vector mesons reported in [8,[68][69][70] is therefore not meaningful. We also note that our prescription to satisfy the anomaly implies that the f 1 and f à 1 towers of states have the same flavor structure as η and η 0 , which is not phenomenologically favored.…”

Electron and muon g−2 anomalies in general flavor conserving two-Higgs-doublet models

“…(6) to the mass eigenstates in Eq. (15). The alignment limit, in which h has the same couplings of the SM Higgs, corresponds to s αβ → 1.…”

“…Another well known and long standing anomaly concerns the anomalous magnetic moment of the muon [9][10][11][12][13][14][15],…”