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

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 $f$, $f \geq 5.4$ $TeV$, which in turn induces bounds on the electromagnetic and weak dipole moments of the tau-lepton. Our bounds on the electromagnetic moments are consistent with the bounds obtained by the L3 and OPAL collaborations for the reaction $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}\gamma$. We also obtained bounds on the tau weak dipole moments which are consistent with the bounds obtained recently by the DELPHI and ALEPH collaborations from the reaction $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$.