R - parity violation : Hide & Seek

We point out that, if R-parity is broken spontaneously, the neutralino can decay to the final state majoron plus neutrino, which from the experimental point of view is indistinguishable from the standard missing momentum signal of supersymmetry. We identify the regions of parameter space where this decay mode is dominant and show that they are independent of R-parity conserving SUSY parameters. Thus, (a) only very weak limits on R-parity violating couplings can be derived from the observation of missing momentum events and (b) at future collider experiments huge statistics might be necessary to establish that R-parity indeed is broken. Parameter combinations which give calculated relic neutralino density larger than the measured dark matter density in case of conserved R-parity are valid points in this scenario and their phenomenology at the LHC deserves to be studied. Is R-parity broken? Undoubtedly, a definite, affirmative answer to this question would have profound implications for both, particle physics and cosmology. Low-energy precision data can be used to derive limits on R-parity violating (R p /) couplings [1], but experimental proof that R-parity indeed is broken can only come from the observation of a decaying lightest supersymmetric particle (LSP) at a future collider experiment. In this paper we present and discuss a scenario with spontaneously broken R-parity where the model can be easily confused with the usual Minimal Supersymmetric Standard Model (MSSM) with conserved R-parity despite the fact that the LSP decays within a typical detector of present and future high energy experiments. We concentrate here on neutral LSPs as this is the case which has been studied mostly by experimental groups. However, in principle the LSP could be charged and quasi-stable on collider time scales and, thus, be observable. Suppose supersymmetric particles exist with masses, such that they can be produced at the LHC. To obtain evidence that the LSP decays, at least the following two conditions need to be met: (i) The decay length should not be (much) larger than the size of a typical detector. And, (ii) a minimum percentage of LSP decays, the exact number depending on