Inverting the Supersymmetric Standard Model Spectrum: from Physical to Lagrangian Ino Parameters

We examine the possibility of recovering the supersymmetric (and soft supersymmetry breaking) Lagrangian parameters as direct {\em analytical} expressions of appropriate physical masses, for the unconstrained (but CP and R-parity conserving) minimal supersymmetric standard model. We concentrate mainly on the algebraically non-trivial "inversion" for the ino parameters, and obtain, for given values of $\tan\beta$, simple analytical expressions for the $\mu$, $M_1$ and $M_2$ parameters in terms of three arbitrary input physical masses, namely either two chargino and one neutralino masses, or alternatively one chargino and two neutralino masses. We illustrate and discuss in detail the possible occurrence of ambiguities in this reconstruction. The dependence of the resulting ino Lagrangian parameters upon physical masses is illustrated, and some simple generic behaviour uncovered in this way. We finally briefly sketch generalizing such an inversion to the full set of MSSM Lagrangian parameters.