Neutralino projector formalism for complex supersymmetry parameters

We present a new formalism describing neutralino physics in the context of the minimal supersymmetric standard model (MSSM), where $\mathrm{CP}$ violation induced by complex ${M}_{1}$ and $\ensuremath{\mu}$ parameters is allowed. The formalism is based on the construction of neutralino projectors, and can be directly generalized to nonminimal supersymmetric (SUSY) models involving any number of neutralinos. It extends a previous work applied to the real SUSY parameter case. In the MSSM, the method allows us to describe all physical observables related to a specific neutralino in terms of its $\mathrm{CP}$ eigenphase and three complex numbers called its ``reduced projector elements.'' As an example, $\ensuremath{\sigma}{(e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{i}^{0}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{j}^{0})$ is presented in this language. As the experimental knowledge on the neutralino-chargino sectors is accumulated, the problem of extracting the various SUSY parameters will arise. Motivated by this, we consider various scenarios concerning the quantities that could be measured first. Analytical disentangled expressions determining the related SUSY parameters from them are then derived, which emphasize the efficiency of the formalism.