Anomalous magnetic and weak magnetic dipole moments of the $$\tau $$ τ lepton in the simplest little Higgs model

Abstract

Abstract We obtain analytical expressions, both in terms of parametric integrals and Passarino–Veltman scalar functions, for the one-loop contributions to the anomalous weak magnetic dipole moment (AWMDM) of a charged lepton in the framework of the simplest little Higgs model (SLHM). Our results are general and can be useful to compute the weak properties of a charged lepton in other extensions of the standard model (SM). As a by-product we obtain generic contributions to the anomalous magnetic dipole moment (AMDM), which agree with previous results. We then study numerically the potential contributions from this model to the $$\tau $$ τ lepton AMDM and AWMDM for values of the parameter space consistent with current experimental data. It is found that they depend mainly on the energy scale f at which the global symmetry is broken and the $$t_{\beta }$$ t β parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the $$\tau $$ τ AMDM is of the order of $$10^{-9}$$ 10 - 9 , the real (imaginary) part of its AWMDM is of the order of $$10^{-9}$$ 10 - 9 ( $$10^{-10}$$ 10 - 10 ). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.