4.8.1 R-violating top quark decays

In the minimal supersymmetric model (MSSM), R-parity violation can induce exotic top decays. As an example, we examine the feasibility of detecting B violating R-parity interactions (i.e. $\lambda^{''}$ couplings only) in top production and decay in e⁺e^- collisions at $\sqrt{s}= 500~GeV$. Unlike the case of a hadron collider, where B violating couplings lead to new $\overline{t}t$ production mechanisms, at an e⁺e^- collider the effect of B violating couplings has no effect on top pair production. We thus focus on exotic top decay modes induced by B violating couplings. Furthermore, we assume that the decay of either the t or the $\overline{t}$ proceeds via the R-parity Violating interactions; one quark thus decays via Standard Model channels. With the restriction to B-Violating couplings only, the possible exotic decay modes are

 

$$t\to \tilde{\bar d_i} \bar d_j,~\tilde{\bar{d}}_j \bar{d}_i \to \bar d_i \bar d_j \tilde \chi^0_1$$ (4.46)

Among the decay modes which are relatively easy to detect are those induced by $\lambda^{''}_{3j3}$. To keep the analysis simple we assume that either one, but not both, of the tri-linear coupling just mentioned takes a non-vanishing value. In our analysis we focus on the case of where $\lambda''_{313}$ is non-vanishing. As shown in eq.(4.49), the decay $t\to \bar b \bar d \tilde \chi^0_1$ can proceed through exchange of a sbottom ($\tilde b$) or a down squark ($\tilde d$). Since among the down-type squarks the sbottom is most likely to be significantly lighter than others, we assume the channel of exchanging a sbottom gives the dominant contribution. Since only a light sbottom is meaningful to our analysis, the dominant decay mode of the sbottom is $\tilde b\to b \tilde \chi^0_1$. The charged current decay mode $\tilde b\to t \tilde \chi^+_1$ is kinematically forbidden for a light sbottom in our analysis. We do not consider the strong decay mode $\tilde b\to b \tilde g$ since the gluino $\tilde g$ is likely to be heavy. Note that the LSP ( $\tilde{\chi}^0_1$) is no longer stable when R-parity is violated. In case just one R-violating top quark coupling does not vanish, the lifetime of the LSP will be very long, depending on the coupling and the masses of squarks involved in the LSP decay chain. So we assume the LSP decays outside the detector.