Scalar-mediated inelastic dark matter as a solution to small-scale structure anomalies

We propose a novel self-interacting dark matter (SIDM) model mediated by a light leptophilic scalar boson to solve long-standing small-scale structure problems within the Lambda cold dark matter ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>CDM</a:mi> </a:math> ) framework. Small-scale anomalies such as the core-cusp problem challenge the traditional CDM framework. Therefore, we introduce a scalar-mediated SIDM model as an alternative to CDM that naturally addresses these problems. It also exhibits <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>p</d:mi> </d:math> -wave-suppressed annihilation and avoids constraints from the cosmic microwave background. In our model, we assume pseudo-Dirac dark matter with a small mass splitting of order <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mn>10</f:mn> <f:mn>2</f:mn> </f:msup> <f:mtext> </f:mtext> <f:mtext> </f:mtext> <f:mi>eV</f:mi> </f:math> to ensure kinematic scattering suppression in satellites. We also introduce a dimension-five transition magnetic dipole operator to satisfy big bang nucleosynthesis requirements. It allows the decay <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>χ</h:mi> <h:mn>2</h:mn> </h:msub> <h:mo stretchy="false">→</h:mo> <h:msub> <h:mi>χ</h:mi> <h:mn>1</h:mn> </h:msub> <h:mi>γ</h:mi> </h:math> , so the excited-state abundance is primarily depleted by exothermic self-interactions ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>χ</k:mi> <k:mn>2</k:mn> </k:msub> <k:msub> <k:mi>χ</k:mi> <k:mn>2</k:mn> </k:msub> <k:mo stretchy="false">→</k:mo> <k:msub> <k:mi>χ</k:mi> <k:mn>1</k:mn> </k:msub> <k:msub> <k:mi>χ</k:mi> <k:mn>1</k:mn> </k:msub> </k:math> ) in the early Universe. This ensures that the excited-state population is negligible for structure formation at the dipole scale <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi mathvariant="normal">Λ</n:mi> <n:mi>eff</n:mi> </n:msub> <n:mo>≳</n:mo> <n:msup> <n:mn>10</n:mn> <n:mn>7</n:mn> </n:msup> <n:mtext> </n:mtext> <n:mtext> </n:mtext> <n:mi>GeV</n:mi> </n:math> . The model is made inelastic by a dark discrete <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi mathvariant="double-struck">Z</q:mi> <q:mn>2</q:mn> </q:msub> </q:math> symmetry that prevents tree-level elastic scattering. Treating the scattering dynamics nonperturbatively in a Schrödinger framework yields a relatively small residual resonant benchmark window ( <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msub> <t:mi>m</t:mi> <t:mi>χ</t:mi> </t:msub> <t:mo>≈</t:mo> <t:mn>40</t:mn> <t:mtext> </t:mtext> <t:mtext> </t:mtext> <t:mi>GeV</t:mi> </t:math> , <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi mathvariant="normal">Δ</v:mi> <v:mi>m</v:mi> <v:mo>≈</v:mo> <v:mn>100</v:mn> <v:mtext> </v:mtext> <v:mtext> </v:mtext> <v:mi>eV</v:mi> </v:math> , <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>m</y:mi> <y:mi>ϕ</y:mi> </y:msub> <y:mo>≈</y:mo> <y:mn>20</y:mn> <y:mtext> </y:mtext> <y:mtext> </y:mtext> <y:mi>MeV</y:mi> </y:math> ). In such a system, the kinematic threshold minimizes interactions in ultrafaint Milky Way satellites, while resonant effects produce large cross sections, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mrow> <ab:mi>σ</ab:mi> <ab:mo>/</ab:mo> <ab:mi>m</ab:mi> <ab:mo>∼</ab:mo> <ab:mi mathvariant="script">O</ab:mi> <ab:mo stretchy="false">(</ab:mo> <ab:mn>10</ab:mn> <ab:mo stretchy="false">)</ab:mo> </ab:mrow> <ab:mtext> </ab:mtext> <ab:mtext> </ab:mtext> <ab:msup> <ab:mrow> <ab:mi>cm</ab:mi> </ab:mrow> <ab:mrow> <ab:mn>2</ab:mn> </ab:mrow> </ab:msup> <ab:mo>/</ab:mo> <ab:mi mathvariant="normal">g</ab:mi> </ab:math> , in field dwarf galaxies. Current direct-detection prospects are weak, and the leptophilic scalar mediator keeps the model away from existing nuclear recoil constraints. However, the low-threshold dipole operator provides a potential discovery channel for future xenon-based experiments.