Lepton pair emission in the top quark decay $t\to b{W}^{+}{\ell }^{-}{\ell }^{+}$

Abstract

The heaviness of the top quark makes its 2-body decay mode $t\to b{W}^{+}$ to be dominant, at such level that hardly any other decay mode reaches a detectable branching ratio (BR) within the SM. Here we study the decay $t\to b{W}^{+}{\ell }^{-}{\ell }^{+}$ ($\ell =e,\mu ,\tau$), which diverges for massless leptons, and it can reach a BR $\sim \mathcal{O}(10^{-5}\sim 10^{-6})$ for reasonable values of the low energy cut in the lepton-pair invariant mass. This rate surpasses 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, the estimate of this channel is relevant because it can mimic the signal arising from the lepton number violating decay $t\to b{W}^{-}{\ell }^{+}{\ell }^{+}$, when the $W$ boson decays into lepton channels.

Comments: 9 pages, 4 figures, v2: comments and references added, matches with version accepted in Phys. Rev. D