Muon $$g-2$$ 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 (Broken Hidden Local Symmetry, BHLS) which encompasses a large number of processes within a unified framework. Based on it, a global fit procedure allows for a simultaneous description of the e⁺ e⁻ annihilation into six final states— π ⁺π ⁻ , π ⁰γ , η γ , π ⁺π ⁻π ⁰ , K⁺K⁻ , KL KS —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 aμ^th of these annihilation channels over the range of validity of the HLS model (up to 1.05 GeV) is found much improved in comparison to the standard approach of integrating the measured spectra directly. However, because most spectra for the annihilation process e⁺e⁻ → π ⁺π ⁻ undergo overall scale uncertainties which dominate the other sources, one may suspect some bias in the dipion contribution to aμ^th , which could question the reliability of the global fit method. However, an iterated global fit algorithm, shown to lead to unbiased results by a Monte Carlo study, is defined and applied successfully to the e⁺e⁻ → π ⁺π ⁻ data samples from CMD2, SND, KLOE, BaBar, and BESSIII. The iterated fit solution is shown to further improve the prediction for aμ , which we find to deviate from its experimental value above the 4σ level. The contribution to aμ of the π ⁺π ⁻ intermediate state up to 1.05 GeV has 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.