In low energy supersymmetry based models, the soft supersymmetry breaking interactions excepting the mass terms are usually considered to be holomorphic functions of fields. While a
superpotential such as that of
MSSM needs to be holomorphic, there is no reason why soft supersymmetry breaking interactions are required to be
holomorphic functions of fields. Of course, an arbitrary nonholomorphic interaction may invite an appearance of quadratic divergence (or hard supersymmetry breaking); however, there are scenarios with no gauge singlet fields where nonholomorphic interactions can as well be of soft supersymmetry breaking type. One may consider a
hidden sector based supersymmetry breaking, with X and \Phi to be
chiral superfields. Then, there exist nonholomorphic
D-term contributions of the forms \frac{1}{M^3} [XX^*\Phi^2\Phi^*]_D and \frac{1}{M^3} [XX^*D^\alpha\Phi D_\alpha\Phi]_D that are soft supersymmetry breaking in nature. The above lead to nonholomorphic trilinear soft terms like \phi^2\phi^* and an explicit
Higgsino soft mass term like \psi \psi in the Lagrangian. The coefficients of both \phi^2\phi^* and \psi \psi terms are proportional to \frac{|F|^2}{M^3} , where |F| is the vacuum expectation value of the
auxiliary field components of X and M is the scale of mediation of supersymmetry breaking. Away from MSSM, there can be higgsino-gaugino interactions like \psi \lambda that are also nonholomorphic in nature. ==References==