Grand unified theory framework for accidental composite dark matter

We study and classify <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>S</a:mi><a:mi>U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>5</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math>-grand unified theory (GUT) completions of accidental composite dark matter models. These theories postulate new vectorlike confining dark color dynamics and give an accidentally stable baryonic dark matter candidate. In realistic theories, dark fermion <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>5</e:mn><e:mo stretchy="false">)</e:mo></e:math> irreps split into light dark quarks, whose bound states include the dark matter, and their much heavier GUT partners. A simple analysis shows that such a mass hierarchy requires a fine-tuning of parameters and thus implies a naturalness problem. We select theories requiring that all dangerous metastable states decay before the onset of nucleosynthesis through higher-dimensional operators generated at the GUT scale or at the mass scale of dark quark GUT partners. Demanding Standard Model gauge coupling unification puts severe constraints on the landscape of viable theories. Under the assumption of an approximately degenerate spectrum of dark quark GUT partners, we find that only one model gives precision unification.