Precision measurement of the neutral pion lifetime

Lattice QCD Calculation of π^{0}→e^{+}e^{-} Decay

We extend the application of lattice QCD to the two-photon-mediated, order α^{2} rare decay π^{0}→e^{+}e^{-}. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find ReA=18.60(1.19)(1.05)  eV, ImA=32.59(1.50)(1.65)  eV, a more accurate value for the ratio (ReA/ImA)=0.571(10)(4), and a result for the partial width Γ(π^{0}→γγ)=6.60(0.61)(0.67)  eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay K→μ^{+}μ^{-}.

A dispersive analysis of η ' → π + π - γ and η ' → ℓ + ℓ - γ

We present a dispersive representation of the η ' transition form factor that allows one to account, in a consistent way, for the effects of ρ - ω mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on η ' → π + π - γ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor, which suggests a tension in the ρ - ω mixing parameter. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of η ' → ℓ + ℓ - γ , in particular we find the slope parameter b η ' = 1.455 ( 24 ) GeV - 2 . With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the η ' -pole contribution to the anomalous magnetic moment of the muon using experimental input from both η ' decay channels.

Improved Standard-Model Prediction for π^{0}→e^{+}e^{-}

We present an improved standard-model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for π^{0}→γ^{*}γ^{*}, for which we employ a dispersive representation that incorporates both spacelike and timelike data as well as short-distance constraints. The resulting SM branching fraction, Br[π^{0}→e^{+}e^{-}]=6.25(3)×10^{-8}, sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.

Recent progress in hadronic light-by-light scattering

In recent years, significant progress in the calculation of the HLbL contribution to the anomalous magnetic moment of the muon has been achieved both with data-driven methods and in lattice QCD. In these proceedings I will discuss current developments aimed at controlling HLbL scattering at the level of 10%, as required for the final precision of the Fermilab E989 experiment.

The anomalous magnetic moment of the muon: status of lattice QCD calculations

In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about 3.5 σ is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.

Hadronic vacuum polarization and vector-meson resonance parameters from e + e - → π 0 γ

We study the reactione + e - → π 0 γ based on a dispersive representation of the underlyingπ 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of theπ 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We finda μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of ω and ϕ . We observe good agreement with thee + e - → 3 π channel, explaining a previous tension in the ω mass betweenπ 0 γ and 3 π by an unphysical phase in the fit function. Combining both channels we findM ¯ ω = 782.736 ( 24 ) MeV andM ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from theK ¯ K channel, demonstrating consistency with 3 π andπ 0 γ . For the ω mass, our result is consistent but more precise, exacerbating tensions with the ω mass extracted via isospin-breaking effects from the 2 π channel.