New limits from lepton flavour violating processes on the Littlest Higgs model with T-parity

We study lepton flavor violation (LFV) within the Littlest Higgs Model with T parity (LHT) realizing an inverse seesaw (ISS) mechanism of type I. In this scenario there appear new $\mathcal{O}$(TeV) Majorana neutrinos, driving LFV. We are analyzing the heavy Majorana neutrinos effects on LFV processes: $\ell \to \ell' \gamma$, $Z \to \bar{\ell}\ell'$, $L \to 3 \ell$ decays and $\mu \to e$ conversion in nuclei but we emphasize Type III decay channel of $L \to 3 \ell$ which are known as "wrong-sign": $\ell \rightarrow \ell' \ell'' \Bar{\ell}'''$ satisfying $\ell \neq \ell' = \ell'' \neq \ell'''$, since these processes vanish in the traditional LHT. First, we get values to $| \theta_{ej} \theta^{\dagger}_{\mu j}|$, $| \theta_{ej} \theta^{\dagger}_{\tau j}|$, and $| \theta_{\mu j} \theta^{\dagger}_{\tau j}|$ through $\ell \to \ell' \gamma$. With aid of these limits for mixing matrices, we can demonstrate that results for branching ratios of wrong sign processes yield within one order of magnitude below present bounds. We do not expect large correlations among the two wrong-sign decay modes. Also, we see that the mean values of heavy Majorana neutrino masses for all LFV processes are quasi-degenerate around 4 TeV.