Eur. Phys. J. C (2013) 73: 2453
https://doi.org/10.1140/epjc/s10052-013-2453-3

Regular Article - Experimental Physics

An update of the HLS estimate of the muon g−2

¹ LPNHE des Universités Paris VI et Paris VII, IN2P3/CNRS, 75252, Paris, France
² Institut für Physik, Humboldt–Universität zu Berlin, Newtonstrasse 15, 12489, Berlin, Germany
³ Deutsches Elektronen–Synchrotron (DESY), Platanenallee 6, 15738, Zeuthen, Germany

^* e-mail: benayoun@in2p3.fr

Received: 26 October 2012
Revised: 29 April 2013
Published online: 5 June 2013

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 ⁻→π ⁺ π ⁻, for which data are available by scan (CMD-2 & SND) and ISR (KLOE-2008, KLOE-2010 & 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 π ⁺ π ⁻ data, by using instead the dipion spectra measured in the τ-decays together with experimental spectra for the π ⁰ γ, ηγ, π ⁺ π ⁻ π ⁰, K ⁺ K ⁻, final states, supplemented by specific meson decay properties. Among these, the accepted decay width for ρ ⁰→e ⁺ e ⁻ and the partial widths and phase information for the ω/ϕ→π ⁺ π ⁻ 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 below 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_µ^th = (11 659 169.55+[_−0.59^+1.26]_φ+[_−2.00^+0.00]_τ±5.21_th)10⁻¹⁰ associated with a very good global fit probability. Correspondingly, we find that Δa_µ = Δa_µ^exp−a_µ^th exhibits a significance ranging between 4.7 and 4.9σ.