Pion electromagnetic form factor at high precision with implications to aμππ and the onset of perturbative QCD

Abstract

We extend recently developed methods used for determining the electromagnetic charge radius and a ππ µ to obtain a determination of the electromagnetic form factor of the pion, F V π (t), in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, with the inclusion of precise inputs from both timelike and spacelike regions. On the unitarity cut, below the first inelastic threshold, we use the precisely known phase of the form factor, known from ππ elastic scattering via the Fermi-Watson theorem, and above the inelastic threshold a conservative integral condition on the modulus. We also use as input the experimental values of the modulus at several energies in the elastic region, where the data from e + e − → π + π − and τ hadronic decays are mutually consistent, as well as the most recent measurements at spacelike momenta. The experimental uncertainties are implemented by Monte Carlo simulations. At spacelike values Q 2 = −t > 0 near the origin, our predictions are consistent and significantly more precise than the recent QCD lattice calculations. The determinations at larger Q 2 confirm the late onset of perturbative QCD for exclusive quantities. From the predictions of |F V π (t)| 2 on the timelike axis below 0.63 GeV, we obtain the hadronic vacuum polarization (HPV) contribution to the muon anomaly, a ππ µ | ≤0.63 GeV = (132.97 ± 0.70) × 10 −10 , using input from both e + e − annihilation and τ decay, and a ππ µ | ≤0.63 GeV = (132.91 ± 0.76) × 10 −10 using only e + e − input. Our determinations can be readily extended to obtain such contributions in any interval of interest lying between 2mπ and 0.63 GeV.PACS numbers:

Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon

“…. 0.3 GeV 2 , our results furthermore agree very well with recent results from dispersion theory [70,72] with discrepancies smaller than the experimental error bars in this momentum region.…”

Two-pion contributions to the muon g – 2

“…The energy regions in the second block are provided to facilitate comparison with [13] and the results of the direct integration [33]. Our result agrees with the combination of e + e − data sets from [13,56], a ππ µ | ≤0.63 GeV = 132.9(8) × 10 −10 , which provides another important cross check given several conceptual differences compared to our study.…”

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

“…[1], also reflected in the slight decrease in the global χ Although the results of this work are obtained from directly integrating the combined data, detailed analyses employing constraints based on analyticity and unitarity have been performed in Refs. [33][34][35][36][37]. These additional constraints have the potential to improve the determination of the two-pion cross section and to possibly reduce the error, especially at low energies where limited data are available.…”