content_image/373809.jpg
with P$_{R}$ = +1 for the SM particles and the Higgs bosons, while P$_{R}$ = − 1 for all the sleptons, squarks, gauginos, and Higgsinos. Here s is spin of the particle. Besides forbidding B and L violation from the renormalizable interactions, R -parity has interesting phenomenological and cosmological consequences. The lightest sparticle with P$_{R}$ = − 1, the LSP, must be absolutely stable. If electrically neutral, the LSP is a natural candidate for cold dark matter [367, 368] $^{30}$. 

## 2. Soft SUSY breaking Lagrangian 

In the MSSM there are several proposals for SUSY breaking, which we shall discuss below. However most of the time it is not important to know the exact mechanism of low energy SUSY breaking. This ignorance of the origin of SUSY breaking can always be hidden by simply writing down explicitly the soft breaking terms. 

The most general soft SUSY breaking terms in the MSSM Lagrangian can be written as (see e.g. [31, 32]) 

<img src='content_image/373809.jpg'>

where M$_{λ}$ is the common gaugino mass ( m $^{2}$) j i ∼ m 2 0 ∼ ( O (100)GeV) 2 are 3 × 3 matrices deter- mining the masses for squarks and sleptons, denoted as m 2 $_{Q}$, m 2 $_{u}$, m 2 $_{d}$, m 2 $_{L}$, m 2 $_{e}$, m 2 $_{H$_{u}$}$, m 2 $_{H$_{d}$}$, b ∼ m 2 0 ∼ ( O (100)) 2 GeV $^{2}$; b$_{ij}$ is the mass term for the combination H$_{u}$H$_{d}$ ; and finally, a ijk are complex 3 × 3 matrices in the family space which yield the A -terms a$_{u}$, a$_{d}$, a$_{e}$ ∼ m$_{0}$ ∼ O (100) GeV. There are a total of 105 new entries in the MSSM Lagrangian which have no counterpart in the SM. However the arbitrariness in the parameters can be partly re- moved by the experimental constraints on flavor changing neutral currents (FCNC) and CP violation [369] 31 

There are a number of possibilities for the origin of SUSY breaking [31, 32, 35]. Fayet- Iliopoulos mechanism [370] provides SUSY breaking by virtue of a non-zero D -term but 

