Abstract
Estimating the contribution from axial-vector intermediate states to hadronic light-by-light scattering requires input on their transition form factors (TFFs). Due to the Landau–Yang theorem, any experiment sensitive to these TFFs needs to involve at least one virtual photon, which complicates their measurement. Phenomenologically, the situation is best for the f1(1285) resonance, for which information is available from e+e− → e+e−f1, f1 → 4π, f1 → ργ, f1 → ϕγ, and f1 → e+e−. We provide a comprehensive analysis of the f1 TFFs in the framework of vector meson dominance, including short-distance constraints, to determine to which extent the three independent TFFs can be constrained from the available experimental input — a prerequisite for improved calculations of the axial-vector contribution to hadronic light-by-light scattering. In particular, we focus on the process f1 → e+e−, evidence for which has been reported recently by SND for the first time, and discuss the impact that future improved measurements will have on the determination of the f1 TFFs.
Highlights
We provide a comprehensive analysis of the f1 transition form factors (TFFs) in the framework of vector meson dominance, including short-distance constraints, to determine to which extent the three independent TFFs can be constrained from the available experimental input — a prerequisite for improved calculations of the axial-vector contribution to hadronic light-by-light scattering
While at present the uncertainty is dominated by hadronic vacuum polarization, with an emerging tension between the determination from e+e− data [9, 14,15,16,17,18,19,20] and lattice QCD [9, 39,40,41,42,43,44,45,46,47,48], see refs. [49,50,51,52], the ultimate precision expected from the Fermilab [53] and J-PARC [54] experiments demands that the second-most-uncertain contribution, hadronic light-by-light (HLbL) scattering, be further improved
We performed a comprehensive analysis of the TFFs of the axial-vector resonance f1(1285), motivated by its contribution to HLbL scattering in the anomalous magnetic moment of the muon
Summary
The matrix element for the decay of an axial-vector meson into two virtual photons, A(P, λA) → γ∗(q1, λ1)γ∗(q2, λ2), is given by [80]. In deriving these relations, the axial-vector meson is treated as an asymptotic state in the narrow-width approximation; the electromagnetic quark current is given by jeμm(x) = q(x)Qγμq(x), q(x) = (u(x), d(x), s(x)) ,
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