Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon

Abstract

A key ingredient in the evaluation of hadronic light-by-light (HLbL) scattering in the anomalous magnetic moment of the muon (g − 2)µ concerns short-distance constraints (SDCs) that follow from QCD by means of the operator product expansion. Here we concentrate on the most important such constraint, in the longitudinal amplitudes, and show that it can be implemented efficiently in terms of a Regge sum over excited pseudoscalar states, constrained by phenomenological input on masses, two-photon couplings, as well as SDCs on HLbL scattering and the pseudoscalar transition form factors (TFFs). Our estimate of the effect of the longitudinal SDCs on the HLbL contribution is: ∆a LSDC µ = 13(6) × 10 −11 . This is significantly smaller than previous estimates, which mostly relied on an ad-hoc modification of the pseudoscalar poles and led to up to a 40% increase with respect to the nominal pseudoscalar-pole contributions, when evaluated with modern input for the relevant TFFs. We also comment on the status of the transversal SDCs and, by matching to perturbative QCD, argue that the corresponding correction will be significantly smaller than its longitudinal counterpart.

Hadronic Vacuum Polarization:(g−2)μversus 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].…”

g−2 of charged leptons, α(MZ2) , and the hyperfine splitting of muonium

“…Those hadronic LbL contributions that have been determined by dispersive techniques are the pseudoscalar poles (π 0 , η; η 0 ) [62][63][64], the pion/kaon-box contributions [9,65] and the S-wave ππ rescattering contributions [65,66]. In addition, a new analysis of (longitudinal) short-distance constraints has very recently become available [67,68], complementing the dispersive determination of the pseudoscalar contributions. The values for these contributions and their counterparts from the "Glasgow consensus" estimate are shown in Table III, where the estimate of determined from e þ e − → hadrons cross section data.…”