Dark branes for dark matter

We propose a setup for the origin of dark matter based on spacetime with a warped extra dimension and three branes: the Planck brane, the TeV brane, at a (few) TeV scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>ρ</a:mi></a:mrow><a:mrow><a:mi>T</a:mi></a:mrow></a:msub></a:mrow></a:math>, and a dark brane, at a (sub-)GeV scale <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ρ</c:mi><c:mn>1</c:mn></c:msub><c:mo>≲</c:mo><c:mn>100</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mrow><c:mi>GeV</c:mi></c:mrow><c:mo>≪</c:mo><c:msub><c:mi>ρ</c:mi><c:mi>T</c:mi></c:msub></c:math>. The Standard Model (SM) is localized in the TeV brane, thus solving the Higgs hierarchy problem, while the dark matter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>χ</e:mi></e:math>, a Dirac fermion with mass <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>χ</g:mi></g:msub><g:mo>&lt;</g:mo><g:msub><g:mi>ρ</g:mi><g:mn>1</g:mn></g:msub></g:math>, is localized in the dark brane. The radion, with mass <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>m</i:mi><i:mi>r</i:mi></i:msub><i:mo>&lt;</i:mo><i:msub><i:mi>m</i:mi><i:mi>χ</i:mi></i:msub></i:math>, interacts strongly [<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mo>∼</k:mo><k:msub><k:mrow><k:mi>m</k:mi></k:mrow><k:mrow><k:mi>χ</k:mi></k:mrow></k:msub><k:mo>/</k:mo><k:msub><k:mrow><k:mi>ρ</k:mi></k:mrow><k:mrow><k:mn>1</k:mn></k:mrow></k:msub><k:mo>∼</k:mo><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:mn>1</k:mn><k:mo stretchy="false">)</k:mo></k:mrow></k:math>] with dark matter and very weakly (<p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mo>∼</p:mo><p:msub><p:mi>m</p:mi><p:mi>f</p:mi></p:msub><p:msub><p:mi>ρ</p:mi><p:mn>1</p:mn></p:msub><p:mo>/</p:mo><p:msubsup><p:mi>ρ</p:mi><p:mi>T</p:mi><p:mn>2</p:mn></p:msubsup><p:mo>≪</p:mo><p:mn>1</p:mn></p:math>) with the Standard Model matter <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>f</r:mi></r:math>. The generic conflict between the bounds on its detection signatures and its proper relic abundance is avoided as dark matter annihilation is <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>p</t:mi></t:math>-wave suppressed. The former is determined by its very weak interactions with the SM and the latter by its much stronger annihilation into radions. Therefore, there is a vast range in the dark matter’s parameter space where the correct relic abundance is achieved consistently with the existing bounds. Moreover, for the dark brane with <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msub><v:mi>ρ</v:mi><v:mn>1</v:mn></v:msub><v:mo>≲</v:mo><v:mn>3</v:mn><v:mtext> </v:mtext><v:mtext> </v:mtext><v:mi>GeV</v:mi></v:math>, a confinement/deconfinement first order phase transition, where the radion condensates, produces a stochastic gravitational wave background at the nanohertz frequencies, which can be identified with the signal detected by the Pulsar Timing Array (PTA) experiments. In the PTA window, for <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mn>0.15</x:mn><x:mo>≲</x:mo><x:msub><x:mi>m</x:mi><x:mi>χ</x:mi></x:msub><x:mo>≲</x:mo><x:mn>2</x:mn><x:mtext> </x:mtext><x:mtext> </x:mtext><x:mi>GeV</x:mi></x:math> the relic abundance is reproduced and all constraints are satisfied. Published by the American Physical Society 2024