Abstract
A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to the muon g-2. The latter is dominated by the annihilation channel e+e- -> pi+pi-, for which data are available by scan (CMD-2 and SND) and ISR (KLOE-2008, KLOE-2010 and BaBar) experiments. It is well known that the different data sets are not in satisfactory agreement. In fact it is possible to fix the model parameters without using the pi+pi- data, by using instead the dipion spectra measured in the tau decays together with experimental spectra for the pi0 gamma, eta gamma, pi+pi-pi0, K+K-, K0bar K0 final states supplemented by specific meson decay properties. Among these, the accepted decay width for rho0 -> e+e- and the partial widths and phase information for the omega/phi -> pi+pi- transitions, are considered. It is then shown that, relying on this global data set, the HLS model, appropriately broken, allows to predict accurately the pion form factor up to 1.05 GeV. It is shown that the data samples provided by CMD-2, SND and KLOE-2010 behave consistently with each other and with the other considered data. Consistency problems with the KLOE-2008 and BaBar data samples are substantiated. "All data" global fits are investigated by applying reweighting the conflicting data sets. Constraining to our best fit, the broken HLS model yields a_mu(th) = (11659169.55 [+1.26 -0.59]_phi +[+0.00 -2.00]_tau +/- 5.21_(th))~10**-10 associated with a very good global fit probability. Correspondingly, we find that Delta a_mu=a_mu (exp)- a_mu (th) exhibits a significance ranging between 4.7 and 4.9 sigma.
Highlights
The uncertainty of the Standard Model prediction for aμ is driven by the uncertainty on the leading order (LO) hadronic vacuum polarization (HVP) up to 2 GeV [6, 7]
A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to the muon g − 2
4.3 Isospin breaking effects in the broken HLS model (BHLS) model: comments. It follows from the developments just above that the BHLS model fed with a limited number of accepted values for some Isospin Breaking (IB) pieces of information is able to provide a quite satisfactory prediction for the e+e− → π +π − cross section once the τ spectra are considered
Summary
The uncertainty of the Standard Model prediction for aμ is driven by the uncertainty on the leading order (LO) hadronic vacuum polarization (HVP) up to 2 GeV [6, 7]. The broken HLS model (BHLS) [13]— basically an empty shell—has been fed with all existing data sets for what concerns the annihilation channels π 0γ , ηγ , π +π −π 0, K+K−, K0K0, with the spectra from ALEPH [21], CLEO [22] and BELLE [23] for the τ dipion decay and with the V P γ /P γ γ partial width information extracted from the Review of Particle Properties (RPP) [24] This already represents more than 40 data sets collected by different groups with different detectors; one may consider that the systematics affecting these data sets wash out to a large extent within a global fit framework. The uncertainty on the contribution to aμ of each of the annihilation channels considered was improved by—at least—a factor of 2, compared to the standard estimation method based on the numerical integration of the measured cross sections.
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