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

TL;DR

This paper derives analytical formulas for the weak magnetic dipole moments of charged leptons in the simplest little Higgs model and numerically assesses their potential experimental detectability, finding they are likely too small for future measurements.

Contribution

It provides the first analytical expressions for the one-loop contributions to lepton weak magnetic moments in the SLHM, applicable to other models, and performs a numerical analysis of the tau lepton's moments.

Findings

Tau lepton AMDM is around 10^{-9}.

Real and imaginary parts of AWMDM are about 10^{-9} and 10^{-10}.

Values are below future experimental sensitivity.

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 $\tau$ 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 $t_\beta$ parameter, whereas there is little sensitivity to a mild change in the values of other parameters of the model. While the $\tau$ AMDM is of the order of $10^{-9}$, the real (imaginary) part of its AWMDM is of the order of $10^{-9}$ ($10^{-10}$). These values seem to be out of the reach of the expected experimental sensitivity of future experiments.