Visible Supersymmetry Breaking and an Invisible Higgs

If there are multiple hidden sectors which independently break supersymmetry, then the spectrum will contain multiple goldstini. In this paper, we explore the possibility that the visible sector might also break supersymmetry, giving rise to an additional pseudo-goldstino. By the standard lore, visible sector supersymmetry breaking is phenomenologically excluded by the supertrace sum rule, but this sum rule is relaxed with multiple supersymmetry breaking. However, we find that visible sector supersymmetry breaking is still phenomenologically disfavored, not because of a sum rule, but because the visible sector pseudo-goldstino is generically overproduced in the early universe. A way to avoid this cosmological bound is to ensure that an R symmetry is preserved in the visible sector up to supergravity effects. A key expectation of this R-symmetric case is that the Higgs boson will dominantly decay invisibly at the LHC.