Analysis of the Neutralino System in Supersymmetric Theories

Charginos $\tilde{\chi}^\pm$ and neutralinos $\tilde{\chi}^0$ in supersymmetric theories can be produced copiously at $e^+e^-$ colliders and their properties can be measured with high accuracy. Consecutively to the chargino system, in which the SU(2) gaugino parameter $M_2$, the higgsino mass parameter $\mu$ and $\tan\beta$ can be determined, the remaining fundamental supersymmetry parameter in the gaugino/higgsino sector of the minimal supersymmetric extension of the Standard Model, the U(1) gaugino mass $M_1$, can be analyzed in the neutralino system, including its modulus and its phase in CP-noninvariant theories. The CP properties of the neutralino system are characterized by unitarity quadrangles. Analytical solutions for the neutralino mass eigenvalues and for the mixing matrix are presented for CP-noninvariant theories in general. They can be written in compact form for large supersymmetric mass parameters. The closure of the neutralino and chargino systems can be studied by exploiting sum rules for the pair-production processes in $e^+e^-$ collisions. Thus the picture of the non-colored gaugino and higgsino complex in supersymmetric theories can comprehensively be reconstructed in these experiments.