It was found many years ago that some terms can be added to a supersymmetric lagrangian that do not respect supersymmetry but still keep the soft ultraviolet behaviour of the theory. These are the soft-breaking terms. They are naturally generated after supersymmetry breaking in general supergravity models and correspond to the following terms

- (i) Scalar masses, implying that the scalars such as squarks,
become usually heavier than the fermions of the same multiplet.
These are terms in the Lagrangian of the form
.
- (ii) Gaugino masses
splitting the gauge
multiplets.
- (iii)Cubic terms. Cubic scalar terms in the potential related
to Yukawa couplings and controlled by arbitrary dimensionfull
coefficients () of order the gravitino mass.
- (iv)The -term. A quadratic term in the potential for the scalars
of the form
where
represent the Higgs fields and
is a constant that gives rise to a term in the original
superpotential
which is allowed by all the
symmetries of the minimal supersymmetric standard model.
Since is a dimensionfull parameter it causes a problem to introduce it
in the supersymmetric Lagrangian since it has to be of the order of
the gravitino mass and there is no reason that a term in the
supersymmetric lagrangian knows the scale of the breaking of
supersymmetry.This is known as the problem and several
solutions have been proposed. Depending on the proposed solution there is
an expression for the parameter after supersymmetry breaking.
In particular, if in eq. (21), it can be seen that
the term is generated after supersymmetry breaking. Some calculations
have shown that there are models for which (for recent discussions see [45,95] ).

In this section we will follow the following strategy.
Treat the supersymmetry breaking mechanism as a black box,
but based on the experience with gaugino condensation,
use that the end result of this mechanism is to induce nonvanishing
values to the auxiliary fields of the moduli or dilaton fields.
Therefore we can parametrize our ignorance of the
particular breaking mechanism by working with general values of these auxiliary fields. Let us for simplicity treat a single modulus field
and the dilaton . But the analysis has been done in more general
cases [96,60,97,98]. We can then write the goldstino field (Goldstone fermion
eaten by the gravitino in the process of supersymmetry breaking) as a linear combination of the fermionic components of and
[98]:

(44) |

(45) |

From this we can extract several conclusions. The dilaton dominated scenario for which , the soft breaking parameters are