Hunting physics beyond the standard model with unusual $W^\pm$ and $Z$ decays

Nonstandard on-shell decays of $W^\pm$ and $Z$ bosons are possible within the framework of extended supersymmetric models, i.e., with singlet states and/or new couplings compared to the minimal supersymmetric standard model. These modes are typically encountered in regions of the parameter space with light singlet-like scalars, pseudoscalars, and neutralinos. In this letter we emphasize how these states can lead to novel signals at colliders from $Z$- or $W^\pm$-boson decays with prompt or displaced multileptons/tau jets/jets/photons in the final states. These new modes would give distinct evidence of new physics even when direct searches remain unsuccessful. We discuss the possibilities of probing these new signals using the existing LHC run-I data set. We also address the same in the context of the LHC run-II, as well as for the future colliders. We exemplify our observations with the "$\mu$ from $\nu$" supersymmetric standard model, where three generations of right-handed neutrino superfields are used to solve shortcomings of the minimal supersymmetric standard model. We also extend our discussion for other variants of supersymmetric models that can accommodate similar signatures.