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] $^{30}$. 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. 2. Soft SUSY breaking Lagrangian The most general soft SUSY breaking terms in the MSSM Lagrangian can be written as (see e.g. [31, 32]) 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 30 Symmetries with the property that fields within the same supermultiplet have different transformations are called R symmetries; they do not commute with SUSY. Continuous U (1) R symmetries are often employed in inflationary model-building literature. Under this symmetry a general chiral superfield transforms as Φ → e $^{iRα}$Φ, and in order to keep the theory R-invariant, the superpotential must have R = 2. 31 Within global SUSY there exists a mass formula Str M 2 ≡ ∑ 1 j $_{=0}$( − 1) $^{j}$tr M 2 j , which prevents all the squarks and sleptons to have masses larger than those of quarks and leptons. This constraints on SUSY breaking scenarios in the global case, but by introducing SUGRA the above relationship will be modified. 49 L soft = − 1 2 ( M$_{λ}$λ $^{a}$λa + c . c . ) − ( m $^{2}$) i $_{j}$φ j ∗$_{φ}$$_{i}$ − ( 1 2 b$_{ij}$φ$_{i}$φ$_{j}$ + 1 6 a $^{ijk}$φ$_{i}$ φ$_{j}$φ$_{k}$ + c . c . ) , (107) 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