Dibaryons cannot be the dark matter

The hypothetical $SU(3)$ flavor-singlet dibaryon state $S$ with strangeness $-2$ has been discussed as a dark-matter candidate capable of explaining the curious 5-to-1 ratio of the mass density of dark matter to that of baryons. We study the early-universe production of dibaryons and find that irrespective of the hadron abundances produced by the QCD quark/hadron transition, rapid particle reactions thermalized the $S$ abundance, and it tracked equilibrium until it “froze out” at a tiny value. For the plausible range of dibaryon masses (1860–1890 MeV) and generous assumptions about its interaction cross sections, $S$’s account for at most ${10}^{-11}$ of the baryon number and, thus, cannot be the dark matter. Although it is not the dark matter, if the $S$ exists, it might be an interesting relic.

Figure 1

The BSE baryon fractions for the $\{N,\mathrm{\Lambda },S\}$ system as a function of temperature for $m_S=1875\mathrm{MeV}$.

Figure 2

The ratio of the reaction rate ${\mathrm{\Gamma }}_{\mathrm{\Lambda }\mathrm{\Lambda }\to S\pi \pi }$ to the expansion rate $H$. Shortly after the QCD transition, the ratio is extremely high, ensuring BSE and a small value for $S$ fraction, and around 8 MeV the ratio is unity and the $S$ abundance freezes out. Shown in the inset are the relative rates for $S$ production through all exothermic processes, i.e., $\mathrm{\Lambda }\mathrm{\Lambda }$, $\mathrm{\Sigma }\mathrm{\Sigma }$, $\mathrm{\Sigma }\mathrm{\Xi }$, $\mathrm{\Lambda }\mathrm{\Sigma }$, $\mathrm{\Lambda }\mathrm{\Xi }$ and $\mathrm{\Xi }N$ in the initial state. At high temperature, when ${\mathrm{\Gamma }}_S/H$ is extremely large, all three processes are important, and, at freeze-out, the $\mathrm{\Lambda }\mathrm{\Lambda }$ process dominates.

Figure 3

Results of integrating the $\{N,\mathrm{\Lambda },S\}$ network for the baryon fraction carried by the $S$ species; $m_S=1875\mathrm{MeV}$ and ${\sigma }_0=1/m_{\pi }^2\simeq 20\mathrm{mb}$. Note that freeze occurs at a temperature consistent with Fig. 2.

Figure 4

The final baryon fraction carried by $S$’s as a function of ${\sigma }_0$ for the mass range of interest.