Gauge-mediated SUSY Breaking with a Gluino LSP

In gauge-mediated SUSY breaking models, messengers transmit SUSY breaking from a partially hidden sector to the standard model sector via common standard model gauge interactions. The minimal set of messengers has quantum numbers of a 5 + 5̄ of SU(5); identical to the quantum numbers of the minimal Higgs sector of an SU(5) GUT. We show in a simple model with messenger masses of order the GUT scale that Higgs messenger mixing quite naturally leads to a low energy MSSM with gluinos as the lightest supersymmetric particles [LSP]. We study the phenomenological consequences of such a model. 1 Gauge-mediated SUSY Breaking Gauge-mediated SUSY breaking [GMSB] models [1, 2] solve the problem of flavor changing neutral currents inherent in the MSSM [3, 4]. Consider for the purposes of this short paper, flavor changing processes of charged leptons. Supersymmetric charged lepton mass terms are of the form ē me e where e (ē) represents 3 families of left-handed (right-handed) fermions and their scalar partners and me is a complex 3 x 3 mass matrix. In addition, scalars necessarily have soft SUSY breaking mass terms given by ẽ∗ m ẽ ẽ + ̃̄e ∗ m ̃̄e ̃̄e where ẽ ( ̃̄e) represents the left-handed (right-handed) sleptons and m ẽ (m 2 ̃̄e) is an hermitian 3 x 3 mass squared matrix. One may always diagonalize the supersymmetric mass term me by a simultaneous rotation of the charged lepton and slepton fields. This rotation however will not, in general, diagonalize m ẽ ,m 2 ̃̄e, unless they are proportional to the identity matrix. Note, off diagonal slepton masses lead to flavor violating processes such as μ → eγ, μ → 3e, μ → e conversion, etc. In GMSB, SUSY breaking occurs in an almost hidden sector of the theory due to the expectation value FX , the F component of a superfield X. Moreover, standard model [SM] squarks, sleptons and gauginos do not couple directly to X. Hence they do not obtain SUSY breaking masses at tree level. The states which couple directly to X are the messengers of SUSY breaking. They carry SM gauge interactions, but otherwise do not couple to squarks and sleptons directly. Thus SUSY breaking enters the SM sector at one loop to gauginos and at two loops to squarks and sleptons. These SUSY breaking effects are dimensionally of order Λ ≡ FX/M where M is the messenger mass. Moreover, they are determined by gauge quantum numbers; thus, for example, the matrices m ẽ, m 2 ̃̄e are proportional to the identity matrix at M . As a result individual lepton number is conserved. Hence processes such as μ → eγ are forbidden. Our discussion ignored the possibility of new flavor violating interactions due to physics at the GUT scale, MG. These interactions can only enter through loops containing GUT mass states, hence they generate off diagonal mass squared terms suppressed by factors of (M/MG) .