| A Global Treatment Of VMD Physics Up To The $\phi$: II. $\tau$ Decay and Hadronic Contributions To $g-2$ (2009) | |||||||||
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| Relying on the Hidden Local Symmetry (HLS) model equipped with a mechanism breaking the U(3)/SU(3)/SU(2) symmetries and generating a dynamical vector meson mixing, it has been shown that a global fit successfully describes the cross sections for the $e^+ e^- \ra \pi^+ \pi^-$, $e^+ e^- \ra (\pi^0/\eta) \gamma$ and $e^+ e^- \ra \pi^0 \pi^+ \pi^-$ annihilation channels. One extends this global fit in order to include also the dipion spectra from the $\tau$ decay, taking into account all reported information on their statistical and systematic errors. It is first shown that all $e^+ e^-$ data collected at Novosibirsk together with the BELLE and CLEO spectra can provide consistent results for $a_\mu(\pi^+ \pi^-)$, the $\pi^+ \pi^-$ loop contribution to the muon $g-2$; the global fit performed under various configurations returns errors reduced compared to existing estimations and very good fit probabilities. Integrated between 0.630 and 0.958 GeV, one finds $a_\mu(\pi^+ \pi^-)= 359.48 \pm 1.04_{exp}$ (in units of $10^{-10}$) with an additional error of $\simeq 1$ unit due to the uncertainty on the BELLE sample absolute scale. Including KLOE data provides a value for $a_\mu(\pi^+ \pi^-)$ consistent with the previous one and an improved accuracy, but a poorer probability. Including ALEPH data also results in degraded fit probabilities but always leads to an estimation for $a_\mu(\pi^+ \pi^-)$ shifted upwards by $\simeq 5$ units. Relying on global fits to the data quoted above, one provides estimates of the $ \pi^+ \pi^-$, $\pi^0\gamma$, $\eta \gamma$ and $\pi^0 \pi^+ \pi^-$ contributions to $a_\mu$ up to 1 GeV, removing only the ALEPH sample. These estimates are based on various global fit configurations, each yielding a good probability.. Comment: 28 pages, 5 figures Correct some misprints and references. Footnote 4 developped | |||||||||
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