Towards a Theory of Soft Terms for the Supersymmetric Standard Model

Abstract

We perform a systematic analysis of the soft supersymmetry-breaking terms arising from four-dimensional strings. The analysis does not assume any specific supersymmetry-breaking mechanism but provides a means of parametrizing our ignorance in a way consistent with some known properties of four-dimensional strings. We introduce a {\it goldstino angle} parameter $\theta $ which says where the source of supersymmetry-breaking resides, either predominantly in the dilaton sector ($sin \theta =1$ limit) or in the rest of the chiral fieds, notably the moduli ($sin\theta =0$ limit). All formulae for soft parameters take particularly simple forms when written in terms of this angle. The $sin\theta =1$ limit is (up to small corrections) universal. As $sin\theta $ decreases, the model dependence increases and the resulting soft terms may or may not be universal, depending on the model. General expressions for the soft terms as functions of $\theta$ for generic four-dimensional strings are provided. For each {\it given} string model, one trades the four soft parameters ($M,m,A,B$) of the minimal supersymmetric standard model by the two parameters $m_{3/2}$ (gravitino mass) and $sin\theta $. The role of complex phases and the associated constraints from limits on the electric dipole moment of the neutron are discussed. It is also emphasized the importance of treating the problem of the cosmological constant in a self-consistent manner.