Abstract
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 \$\pi^+ \pi^-\$, \$\pi^0
\gamma\$, \$\gamma\$, \$\pi^+ \pi^- \pi^0\$, \$K^+ K^-\$, \$K\_l K\_s\$ and includes
the dipion spectrum in the \tau 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^- \pi^+ \pi^-\$ 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^- \pi^+ \pi^-\$ data samples from CMD2, SND, KLOE (including the
latest sample) and BaBar. The iterated fit solution is shown to be further
improved and leads to a value for \$a\_\mu\$ different from \$a\_exp\$ above the
4 \$\sigma\$ level. The contribution of the \$\pi^+ \pi^-\$ 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. The main issue raised in this study and the kind of solution
proposed may be of concern for other data driven methods when the data samples
are dominated by global normalization uncertainties.
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