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The heaviness of the top quark makes its 2-body decay mode $t \to bW^+$ to bedominant, at such level that hardly any other decay mode reaches a detectablebranching ratio (BR) within the SM. Here we study the decay $t \tobW^+\ell^-\ell^+$ ($\ell=e, \mu, \tau$), which diverges for massless leptons,and it can reach a BR $\sim \mathcal{O}(10^{-5}\sim 10^{-6})$ for reasonablevalues of the low energy cut in the lepton-pair invariant mass. This ratesurpasses almost any other rare decays such as $t \to cX$ ($X=\gamma,Z,g,H,W^+W^-$), and thus offers the possibility of being detectable. Furthermore, theestimate of this channel is relevant because it can mimic the signal arisingfrom the lepton number violating decay $t\to bW^-\ell^+\ell^+$, when the $W$boson decays into lepton channels.

Lepton pair emission in the top quark decay $t \to bW^+\ell^-\ell^+$