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We present an up-to-date analysis of muon $g-2$ evaluations in terms ofMellin-Barnes moments as they might be useful for lattice QCD calculations of$a_\mu$. The moments up to 4th order are evaluated directly in terms of$e^+e^-$--annihilation data and improved within the Hidden Local Symmetry (HLS)Model, supplied with appropriate symmetry breaking mechanisms. The modelprovides a reliable Effective Lagrangian (BHLS) estimate of the two-bodychannels plus the $\pi\pi\pi$ channel up to 1.05~GeV, just including the $\phi$resonance. The HLS piece accounts for 80\% of the contribution to $a_\mu$. Themissing pieces are evaluated in the standard way directly in terms of the data.We find that the moment expansion converges well in terms of a few moments. Thetwo types of moments which show up in the Mellin-Barnes representation arecalculated in terms of hadronic cross--section data in the timelike region andin terms of the hadronic vacuum polarization (HVP) function in the spacelikeregion which is accessible to lattice QCD (LQCD). In the Euclidean the firsttype of moments are the usual Taylor coefficients of the HVP and we show thatthe second type of moments may be obtained as integrals over the appropriatelyTaylor truncated HVP function. Specific results for the isovector part of$a_\mu^{\rm had}$ are determined by means of HLS model predictions in closerelation to $\tau$--decay spectra.

A BHLS model based moment analysis of muon g-2, and its use for lattice QCD evaluations of $a_\mu^{\rm had}$