Longitudinal short-distance constraints for the hadronic light-by-light contribution to (g − 2)μ with large-Nc Regge models

Abstract

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon (g − 2) µ also mixed-and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π 0 , η, η . Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π 0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by ∆a LSDC µ = 13(6) × 10 −11 . A Anomalous Pseudoscalar-Vector-Vector Coupling 46 B Alternative model for pion, η, and η transition form factors 48 1 Introduction Current Standard Model (SM) evaluations of the anomalous magnetic moment of the muon, a µ = (g − 2) µ /2, differ from the value measured at the Brookhaven National Laboratory [1]a exp µ = 116 592 089(63) × 10 −11 , (1.1) by around 3.5 σ. In the near future, the new Fermilab E989 experiment [2] will be able to reduce the experimental uncertainty by a factor 4, and the E34 experiment at J-PARC [3] will provide an important cross check, see ref.[4] for a comparison of the experimental methods. Therefore, the theoretical calculation of a µ needs to be improved accordingly. The uncertainty of the SM prediction mainly stems from hadronic contributions, such as hadronic vacuum polarization (HVP), see figure 1 (a), and HLbL scattering, see figure 1 (b). Since the HVP contribution can be systematically calculated with a data-driven dispersive approach [5-9], lattice QCD [10][11][12][13][14][15][16], and potentially be accessed independently by the proposed MUonE experiment [17,18], which aims to measure the space-like finestructure constant α(t) in elastic electron-muon scattering, the HLbL contribution may end up dominating the theoretical error. 1 Apart from lattice QCD [27][28][29], recent data-driven approaches towards HLbL scattering are again rooted in dispersion theory, either for the HLbL tensor [30][31][32][33][34][35], the Pauli 1 Note that higher-order insertions of HVP [5,19,20] and HLbL [21] are already under sufficient control, as are hadronic corrections in the anomalou...

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 .…”

“…the result of which is based on [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. As reported in [1], this results in the difference Δa μ ¼ a exp μ − a SM μ ¼ ð27.9 AE 7.6Þ × 10 −10 ; ð1:3Þ…”

Hadronic Vacuum Polarization: (g−2)μ versus Global Electroweak Fits

“…With recent advances in constraining the contribution from hadronic light-by-light scattering (including evaluations [33][34][35]37,38,[55][56][57] based on dispersion relations in analogy to Eq. (1), short-distance constraints [39][40][41], and lattice QCD [36,42]) as well as higher-order hadronic corrections [30,31,43,58], this data-driven determination of HVP has corroborated the ðg − 2Þ μ tension at the level of 3.7σ. Nevertheless, since by far the largest hadronic correction arises from HVP, requirements for the relative precision are extraordinary, with a HVP μ ¼ 693.1ð4.0Þ × 10 −10 [20, [25][26][27][28][29][30] as currently determined from e þ e − → hadrons cross sections corresponding to less than 0.6%.…”

Consistency of hadronic vacuum polarization between lattice QCD and the R ratio

“…For the HLbL contribution, new analytic approaches [39][40][41][42][43] as well as the first ab-initio lattice QCD calculation [32] building on multi-year methodology development [44][45][46][47][48][49] so far show consistent results and rule out the HLbL contribution as an explanation for the current * christoph.lehner@ur.de † ameyer@quark.phy.bnl.gov tension between theory and experiment. For the HVP contribution, however, tensions exist within lattice QCD calculations [50] as well as between lattice QCD calculations and R-ratio results [27,50].…”