Unitarity bound on dark matter in low-temperature reheating scenarios
Nicolás Bernal, Partha Konar, Sudipta Show
Abstract
The model-independent theoretical upper bound on the thermal dark matter (DM) mass can be derived from the maximum inelastic DM cross section featuring the whole observed DM abundance. We deploy partial-wave unitarity of the scattering matrix to derive the maximal thermally averaged cross section for general number-changing processes <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>r</a:mi><a:mo stretchy="false">→</a:mo><a:mn>2</a:mn></a:math> (with <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>r</d:mi><d:mo>≥</d:mo><d:mn>2</d:mn></d:math>), which may involve standard model particles or occur solely within the dark sector. The usual upper limit on the DM mass for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>s</f:mi></f:math>-wave annihilation is around 130 TeV (1 GeV) for <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>r</h:mi><h:mo>=</h:mo><h:mn>2</h:mn></h:math> (3) and only applies in the case of a freeze-out occurring in the standard cosmological scenario. We consider the effects of two nonstandard cosmological evolutions, characterized by low-temperature reheating: (i) a kinationlike scenario and (ii) an early matter-dominated scenario. In the first case, early freeze-out strengthens the unitarity bound to a few TeVs for weakly interacting massive particles (WIMPs); while in the second case, the WIMP DM can be as heavy as <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mo>∼</j:mo><j:msup><j:mn>10</j:mn><j:mn>10</j:mn></j:msup><j:mtext> </j:mtext><j:mtext> </j:mtext><j:mi>GeV</j:mi></j:math> due to a large entropy dilution. Published by the American Physical Society 2024