Soft SUSY breaking

• Gaugino mass
• Scalar masses
• Scalar trilinear interactions ("A-terms")

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.[2] 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.[3] One may consider a hidden sector based supersymmetry breaking, with ${\displaystyle X}$ and ${\displaystyle \Phi }$ to be chiral superfields. Then, there exist nonholomorphic ${\displaystyle D}$-term contributions of the forms ${\displaystyle {\frac {1}{M^{3}}}[XX^{*}\Phi ^{2}\Phi ^{*}]_{D}~and~{\frac {1}{M^{3}}}[XX^{*}D^{\alpha }\Phi D_{\alpha }\Phi ]_{D}}$ that are soft supersymmetry breaking in nature. The above lead to nonholomorphic trilinear soft terms like ${\displaystyle \phi ^{2}\phi ^{*}}$ and an explicit Higgsino soft mass term like ${\displaystyle \psi \psi }$ in the Lagrangian. The coefficients of both ${\displaystyle \phi ^{2}\phi ^{*}}$ and ${\displaystyle \psi \psi }$ terms are proportional to ${\displaystyle {\frac {|F|^{2}}{M^{3}}}}$, where ${\displaystyle |F|}$ is the vacuum expectation value of the auxiliary field components of ${\displaystyle X}$ and ${\displaystyle M}$is the scale of mediation of supersymmetry breaking. Away from MSSM, there can be higgsino-gaugino interactions like ${\displaystyle \psi \lambda }$ that are also nonholomorphic in nature.