Large tau and tau neutrino electric dipole moments in models with vectorlike multiplets

It is shown that the electric dipole moment of the $\tau$ lepton several orders of magnitude larger than predicted by the standard model can be generated from mixings in models with vectorlike mutiplets. The electric dipole moment (EDM) of the $\tau$ lepton arises from loops involving the exchange of the $W$, the charginos, the neutralinos, the sleptons, the mirror leptons, and the mirror sleptons. The EDM of the Dirac $\tau$ neutrino is also computed from loops involving the exchange of the $W$, the charginos, the mirror leptons, and the mirror sleptons. A numerical analysis is presented, and it is shown that the EDMs of the $\tau$ lepton and the $\tau$ neutrino which lie just a couple of orders of magnitude below the sensitivity of the current experiment can be achieved. Thus the predictions of the model are testable in an improved experiment on the EDM of the $\tau$ and the $\tau$ neutrino.

Figure 1

The loop contributions to the electric dipole moment of the $\tau$ via exchange of the $W$ boson and $\tau$ neutrino and mirror neutrino denoted by ${\nu }_j$, via neutralino (${\tilde{\chi }}_i^0$) and sleptons (${\tilde{\tau }}_k$) exchange and via the exchange of charginos (${\tilde{\chi }}_j^{-}$), sneutrinos, and mirror sneutrinos denoted by (${\tilde{\nu }}_k$).

Figure 2

The loop contribution to the electric dipole moment of the $\tau$ neutrino (${\nu }_{\tau }$) via exchange of the $W$ boson and $\tau$ and mirror lepton denoted by ${\tau }_j$, and via exchange of the charginos (${\tilde{\chi }}_j^{+}$), sleptons, and mirror sleptons denoted by (${\tilde{\tau }}_k$).

Figure 3

Left panel: An exhibition of the dependence of $d_{\tau }$ on ${\chi }_3$ when $\tan \beta =10$, $m_N=100$, $|f_3|=50$, $|f_4|=70$, $|f_5|=90$, $m_0=100$, $|A_0|=150$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150$, ${\chi }_4=0.4$, ${\chi }_5=0.6$, ${\alpha }_E=0.5$, ${\alpha }_N=0.8$, and $m_E=300$, 250, 200, 150, 100 (in ascending order at ${\chi }_3=0$). Middle panel: An exhibition of the dependence of $d_{\tau }$ on $|f_3|$ when $\tan \beta =10$, $m_N=120$, $m_E=100$, $|f_4|=80$, $|f_5|=60$, $m_0=150$, $|A_0|=100$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150\mathrm{GeV}{\chi }_4=0.3$, ${\chi }_5=0.7$, ${\alpha }_E=0.4$, ${\alpha }_N=1.0$, ${\alpha }_{\tau }=0$, ${\alpha }_{\nu }=0$, and ${\chi }_3=0.4$, 0.8, 1.2 (in ascending order). Right panel: An exhibition of the dependence of $d_{\tau }$ on ${\alpha }_N$ when $\tan \beta =20$ $m_N=100$, $|f_3|=70$, $|f_4|=50$, $|f_5|=80$, $m_0=120$, $|A_0|=130$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150$, ${\chi }_3=0.5$, ${\chi }_4=0.6$, ${\chi }_5=0.7$, and ${\alpha }_E=0.6$ and $m_E=180$, 130, 80 (in ascending order at ${\alpha }_N=0$). Masses in GeV and angles in rad here and in figures below.

Figure 4

Left panel: An exhibition of the dependence of $d_{\nu }$ on ${\chi }_3$ with the input $\tan \beta =10$, $m_E=120$, $|f_3|=60$, $|f_4|=80$, $|f_5|=100$, $m_0=100$, $|A_0|=170$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150$, ${\chi }_4=0.2$, ${\chi }_5=0.7$, ${\alpha }_E=0.6$, and ${\alpha }_N=0.4$ and $m_N=300$, 250, 200, 150, 100 (in ascending order at ${\chi }_3=0$). Middle panel: An exhibition of the dependence of $d_{\nu }$ on $|f_3|$ with the input $\tan \beta =10$, $m_N=120$, $m_E=100$, $|f_4|=80$, $|f_5|=60$, $m_0=150$, $|A_0|=100$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150\mathrm{GeV}$ and the phases ${\chi }_4=0.3$, ${\chi }_5=0.7$, ${\alpha }_E=0.4$, and ${\alpha }_N=1.0$ and ${\chi }_3=0.4$, 0.8, 1.2 (in ascending order). Right panel: An exhibition of the dependence of $d_{\nu }$ on ${\alpha }_E$ with the input $\tan \beta =20$ $m_E=120$, $|f_3|=80$, $|f_4|=60$, $|f_5|=90$, $m_0=100$, $|A_0|=120$, ${\tilde{m}}_1=50$, ${\tilde{m}}_2=100$, $\mu =150$, ${\chi }_3=0.4$, ${\chi }_4=0.8$, ${\chi }_5=0.7$, and ${\alpha }_N=0.5$ and $m_N=190$, 140, 90 (in ascending order at ${\alpha }_E=0$).