Limits on split supersymmetry from gluino cosmology

An upper limit on the masses of scalar superpartners in split supersymmetry is found by considering cosmological constraints on long-lived gluinos. Over most of parameter space, the most stringent constraint comes from big bang nucleosynthesis. A TeV-mass gluino must have a lifetime of less than 100 seconds to avoid altering the abundances of D and ${}^6\mathrm{L}\mathrm{i}$. This sets an upper limit on the supersymmetry breaking scale $m_S$ of ${10}^9$ GeV.

Figure 1

Gluino abundance per comoving volume as a function of mass. Three curves are shown. In the first (solid), the annihilation cross section is assumed to be simply given by the perturbative cross section of Eq. (3). The other curves correspond to a cross section that saturates $s$-wave (dashed) and $s$-wave plus $p$-wave unitarity (dot-dashed).

Figure 2

Limits on the supersymmetry breaking scale, $m_S$, as a function of the gluino mass, $m_{\tilde{g}}$. The bounds are derived assuming a perturbative cross section in Eq. (3) for temperatures greater than the QCD phase transition, $T>200$ MeV. For $T<200$ MeV, we assume that the annihilation cross section saturates $s$-wave unitarity. Also shown (dashed) are the limits in the case where the annihilation cross section saturated $s$-wave plus $p$-wave unitarity. The shaded regions are excluded. The lower edge of the BBN curve arises from the requirement that the $D/H$ ratio remained undisturbed, and corresponds to a lifetime of approximately 100 seconds.