Dark sink enhances the direct detection of freeze-in dark matter

We describe a simple dark sector structure which, if present, has implications for the direct detection of dark matter (DM); . A dark sink transports energy density from the DM into light dark-sector states that do not appreciably contribute to the DM density. As an example, we consider a light, neutral fermion <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ψ</a:mi></a:math> which interacts solely with DM <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>χ</c:mi></c:math> via the exchange of a heavy scalar <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Φ</e:mi></e:math>. We illustrate the impact of a dark sink by adding one to a DM freeze-in model in which <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>χ</h:mi></h:math> couples to a light dark photon <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>γ</j:mi><j:mo>′</j:mo></j:msup></j:math> which kinetically mixes with the Standard Model (SM) photon. This freeze-in model (absent the sink) is itself a benchmark for ongoing experiments. In some cases, the literature for this benchmark has contained errors; we correct the predictions and provide them as a public code. We then analyze how the dark sink modifies this benchmark, solving coupled Boltzmann equations for the dark-sector energy density and DM yield. We check the contribution of the dark sink <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>ψ</l:mi></l:math>’s to dark radiation; consistency with existing data limits the maximum attainable cross section. For DM with a mass between <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>MeV</n:mi><n:mo>−</n:mo><n:mi mathvariant="script">O</n:mi><n:mo stretchy="false">(</n:mo><n:mn>10</n:mn><n:mtext> </n:mtext><n:mtext> </n:mtext><n:mi>GeV</n:mi><n:mo stretchy="false">)</n:mo></n:math>, adding the dark sink can increase predictions for the direct detection cross section all the way up to the current limits.