Sensitivity Estimates on the Electromagnetic Dipole Moments of the τ-Lepton at Future e+e− Linear Colliders

We estimate bounds on the prediction for the anomalous magnetic and electric dipole moments of the tau-lepton through the process e+e−→(Zi)→τ+τ−γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$e^{+}e^{-} \rightarrow (Z_{i}) \to \tau ^{+} \tau ^{-}\gamma $\end{document}, Zi = 1,2,3 within the context of a SU(4)L × U(1)X electroweak model, framed into the capabilities at the future International Linear Collider (ILC) and the Compact Linear Collider (CLIC). We assume center-of-mass energies and luminosities for the ILC of s=0.250−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt {s}=0.250-1$\end{document} TeV and L=10−1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathscr{L}}= 10-1000$\end{document}fb− 1, while for the CLIC of s=0.380−3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt {s}=0.380-3$\end{document} TeV and L=100−5000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathscr{L}}= 100-5000$\end{document}fb− 1. With these energies and luminosities the ILC and CLIC can measure the electromagnetic dipole moments of the τ-lepton aτ and dτ with a sensitivity of the order O(10−3−10−1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {O} (10^{-3}-10^{-1})$\end{document} and O(10−17)(ecm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {O}(10^{-17})(\text {ecm})$\end{document} at 95% C.L..