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From the total cross section for the reaction $e^+e^-\to \tau^+\tau^-\gamma$at the $Z_1$ pole and in the framework of a simplest little Higgs model (SLHM),we get a limit on the characteristic energy scale of the model $f$, $f \geq5.4$ $TeV$, which in turn induces bounds on the electromagnetic and weak dipolemoments of the tau-lepton. Our bounds on the electromagnetic moments areconsistent with the bounds obtained by the L3 and OPAL collaborations for thereaction $e^+e^-\to \tau^+\tau^-\gamma$. We also obtained bounds on the tauweak dipole moments which are consistent with the bounds obtained recently bythe DELPHI and ALEPH collaborations from the reaction $e^+e^-\to \tau^+\tau^-$.

Bounding the electromagnetic and weak dipole moments of the tau-lepton in a simplest little Higgs model