Limits on Split Supersymmetry from Gluino Cosmology

TL;DR

The work investigates how cosmological constraints on long-lived gluinos in split supersymmetry bound the SUSY-breaking scale $m_S$. By solving the Boltzmann equation for gluino annihilation across the pre- and post-QCD regimes and evaluating perturbative and non-perturbative cross sections—inclining toward Sommerfeld-enhanced and unitarity-limited scenarios—the authors derive gluino lifetimes that would preserve standard cosmology. Big Bang Nucleosynthesis provides the strongest bound for TeV-scale gluinos, requiring $\tau_{\tilde{g}} \lesssim 100$ s and $m_S \lesssim 10^9$ GeV; lighter gluinos face gamma-ray and CMB constraints allowing longer lifetimes up to $\sim 10^6$ years and $m_S \lesssim 10^{11}$ GeV. Collider data (e.g., the LHC) could further constrain or measure the gluino lifetime, linking cosmology with particle physics scales. Overall, the paper establishes a robust, cosmology-driven upper limit on the SUSY-breaking scale in split supersymmetry via gluino cosmology.

Abstract

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 Li-6. This sets an upper limit on the supersymmetry breaking scale of 10^9 GeV.

Figures (2)

• Figure 1: Gluino abundance per co-moving 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 Eqn. \ref{['Eqn: Enhanced']}. 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 Eqn. \ref{['Eqn: Enhanced']} 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.