,$$ which is similar to the so-called bilinear RPV scenario [@Hirsch:2000ef]. In addition, the Lagrangian contains various other bilinear terms, generated by ${v_L}_i$ and $v_R$, from the super-covariant derivative: $$\begin{aligned}
    \label{L.n}
    \mathcal{L} \supset
    - \frac{1}{2}{v_L}_i^* \left[ g_2 \left(\sqrt 2 \, e_i \tilde W^+ 
    +  \nu_i \tilde W^0\right) - g_{BL} \nu_i \tilde B' \right]
    -\frac{1}{2} v_R \left[-g_R \nu_3^c \tilde W_R + g_{BL} \nu_3^c \tilde B' \right]+ \text{h.c.}\end{aligned}$$ The results and analysis in the paper will be carried out using the Lagrangian based on Eqs. (\[W.brpv\]) and (\[L.n\]). However, it is worthwhile to note that it is sometimes useful to rotate away the $\epsilon_{i}$ term in favor of the so-called trilinear $R$-parity violating terms. This is true when comparing to given bounds on various low-energy constraints on RPV, such as lepton number violating processes, and it makes approximating decays widths more straightforward. An example of each of these will be given in this section. Rotating $\epsilon_i$ away generates the following terms in the superpotential: $$\label{eq:TRPV}
    W_{TRPV} = \lambda_{ijk} L_i L_j e^c_k + \lambda_{ijk}' Q_i L_j d^c_k,$$ where $\lambda_{ijk}$ is antisymmetric under the interchange of $i$ and $j$.[^4] This is accomplished by considering $H_d$ as a fourth generation lepton. In this case, the 