Hunting for hypercharge anapole dark matter in all spin scenarios

We conduct a combined analysis to investigate dark matter (DM) with hypercharge anapole moments, focusing on scenarios where Majorana DM particles with spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math>, 1, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>3</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math>, and 2 interact exclusively with Standard Model particles through <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi mathvariant="normal">U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mo stretchy="false">)</e:mo></e:mrow><e:mi>Y</e:mi></e:msub></e:mrow></e:math> hypercharge anapole terms for the first time. For completeness, we construct general effective U(1) gauge-invariant three-point vertices. These enable the generation of hypercharge gauge-invariant interaction vertices for both a virtual photon <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>γ</j:mi></j:math> and a virtual <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>Z</l:mi></l:math> boson with two identical massive Majorana particles of any nonzero spin <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>s</n:mi></n:math>, after the spontaneous breaking of electroweak gauge symmetry. For complementarity, we adopt effective operators tailored to each dark matter spin allowing crossing symmetry. We calculate the relic abundance, analyze current constraints and future sensitivities from dark matter direct detection and collider experiments, and apply the conceptual naive perturbativity bound. Our estimations based on a generalized vertex calculation demonstrate that the scenario with a higher-spin DM is more stringently constrained than a lower-spin DM, primarily due to the reduced annihilation cross section and/or the enhanced rate of LHC monojet events. As a remarkable outcome, the spin-2 anapole DM scenario is almost entirely excluded, while the high-luminosity LHC exhibits high sensitivities in probing spin-1 and -<p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mn>3</p:mn><p:mo>/</p:mo><p:mn>2</p:mn></p:mrow></p:math> scenarios, except for a tiny parameter range of DM mass around 1 TeV. A significant portion of the remaining parameter space in the spin-<r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>1</r:mn><r:mo>/</r:mo><r:mn>2</r:mn></r:mrow></r:math> DM scenario can be explored through upcoming Xenon experiments, with more than 20 ton-yr exposure equivalent to approximately 5 years of running the XENONnT experiment.