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Muon g-2 estimates : Can one trust Effective Lagrangians and global fits ?

Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) which encompasses a large number of processes within a unified framework; a global fit procedure allows for a simultaneous description of the e+ e- annihilation into the 6 final states $π^+ π^-$, $π^0 γ$, $ηγ$, $π^+ π^- π^0$, $K^+ K^-$, $K_l K_s$ and includes the dipion spectrum in the τ decay and some more light meson decay partial widths. The contribution to the muon anomalous magnetic moment $a_{th}$ of these annihilation channels over the range of validity of the HLS model (up to 1.05 GeV) is found much improved compared to its partner derived from integrating the measured spectra directly. However, most spectra for the process $e^+ e^- \to π^+ π^-$ undergo overall scale uncertainties which dominate the other sources, and one may suspect some bias in the dipion contribution to $a_{th}$. However, an iterated fit algorithm, shown to lead to unbiased results by a Monte Carlo study, is defined and applied succesfully to the $e^+ e^- \to π^+ π^-$ data samples from CMD2, SND, KLOE, BaBar and BESSIII. The iterated fit solution is shown to be further improved and leads to a value for $a_μ$ different from $a_{exp}$ above the 4 $σ$ level. The contribution of the $π^+ π^-$ intermediate state up to 1.05 GeV to $a_{th}$ derived from the iterated fit benefits from an uncertainty about 3 times smaller than the corresponding usual estimate. Therefore, global fit techniques are shown to work and lead to improved unbiased results.