model gauge interactions only [374, 379–381, 398]. As a result the soft terms in the MSSM arise through ordinary gauge interactions. There will still be gravitational communication, but it is a weak effect. The simplest example is a messenger sector with a pair of SU (2) doublet chiral fields l, ¯ l and a pair of SU (3) triplet fields q, ¯ q , which couple to a singlet field z with Yukawa couplings λ$_{2}$, λ$_{3}$ , respectively. The superpotential is given by The singlet acquires a non-zero VEV and a non-zero F-term 〈 F$_{z}$ 〉 . This can be accomplished either substituting z into an O’Raifeartaigh type model [379, 398], or by a dynamical mech- anism [374, 380]. One may parameterize SUSY breaking in a superpotential W$_{break}$ by 〈 ∂W$_{break}$/∂z 〉 = −〈 F ∗ z 〉 . As a consequence, the messenger fermions acquire masses and a scalar potential with 〈 ∂W$_{mess}$/∂z 〉 = 0. SUSY breaking is then mediated to the observable fields by one-loop corrections, which generate masses for the MSSM gauginos [374]. The q, ¯ q messenger loop diagrams provide masses to the gluino and the bino, while l, ¯ l messenger loop diagrams provide masses to the wino and the bino, i.e., M$_{a}$$_{=1}$$_{,}$$_{2}$$_{,}$$_{3}$ = ( α$_{a}$/ 4 π )Λ, where Λ = 〈 F$_{z}$ 〉 / 〈 z 〉 . For squarks and sleptons the leading term comes from two-loop diagrams, e.g. m 2 φ ∝ α $^{2}$. The A -terms get negligible contribution at two-loop order compared to the gaugino masses, they come with an extra suppression of α/ 4 π compared with the gaugino mass, therefore a$_{u}$ = a$_{d}$ = a$_{e}$ = 0 is a good approximation. The Yukawa couplings at the electroweak scale are generated by evolving the RG equations. One can estimate [374, 380] the soft SUSY breaking masses to be of order If M$_{s}$ ∼ 〈 z 〉 and √ 〈 F 〉 are comparable mass scales, then the SUSY breaking can take place at about √ 〈 F 〉 ∼ 10 4 − 10 6 GeV. In gauge mediated SUSY breaking the gravitino could be the LSP, and the next-to-LSP In gauge mediated SUSY breaking the gravitino could be the LSP, and the next-to-LSP (NLSP) could be either stau, bino-like neutralino. The NLSP decay into gravitino could be very long ranging from seconds to years, the decay process: ˜ τ → τ ˜ G is governed by the gravitational coupling. The decay of long lived staus are constrained by the BBN. W$_{mess}$ = λ$_{2}$zl ¯ l + λ$_{3}$zq ¯ q . (112) m$_{soft}$ ∼ α$_{a}$ 4 π 〈 F 〉 M$_{s}$ . (113) 53