Comprehensive study of WIMP models explaining the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>F</mml:mi> <mml:mi>e</mml:mi> <mml:mi>r</mml:mi> <mml:mi>m</mml:mi> <mml:mi>i</mml:mi> </mml:math> -LAT Galactic Cent

The Galactic Center excess (GCE) of GeV <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>γ</a:mi> </a:math> rays may hint at dark matter (DM), yet its origin remains debated. Motivated by this, we survey weakly interacting massive particle (WIMP) models that can fit the GCE while satisfying relic-density, direct-detection (DD), and indirect-detection (ID) bounds. We group candidates into (Higgs portals; simplified scalar/vector mediators), [ <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:msub> <c:mo stretchy="false">)</c:mo> <c:mrow> <c:msub> <c:mi>L</c:mi> <c:mi>i</c:mi> </c:msub> <c:mo>−</c:mo> <c:msub> <c:mi>L</c:mi> <c:mi>j</c:mi> </c:msub> </c:mrow> </c:msub> </c:math> ], and [ <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>U</g:mi> <g:mo stretchy="false">(</g:mo> <g:mn>1</g:mn> <g:msub> <g:mo stretchy="false">)</g:mo> <g:mrow> <g:mi>B</g:mi> <g:mo>−</g:mo> <g:mi>L</g:mi> </g:mrow> </g:msub> </g:math> , <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>Z</k:mi> </k:math> -portal] classes. Across all cases, present DD and dwarf-spheroidal <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>γ</m:mi> </m:math> -ray limits exclude wide regions, leaving mainly narrow with <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>m</o:mi> <o:mrow> <o:mi>DM</o:mi> </o:mrow> </o:msub> <o:mo>≃</o:mo> <o:msub> <o:mi>m</o:mi> <o:mrow> <o:mi>med</o:mi> </o:mrow> </o:msub> <o:mo>/</o:mo> <o:mn>2</o:mn> </o:math> and portal couplings <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mo>≪</q:mo> <q:mn>1</q:mn> </q:math> . In hadronic setups, scalar and vector Higgs portals survive only in a thin strip near <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>m</s:mi> <s:mi>h</s:mi> </s:msub> <s:mo>/</s:mo> <s:mn>2</s:mn> <s:mo>≃</s:mo> <s:mn>62.5</s:mn> <s:mtext> </s:mtext> <s:mtext> </s:mtext> <s:mi>GeV</s:mi> </s:math> with portal couplings <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo>∼</u:mo> <u:msup> <u:mn>10</u:mn> <u:mrow> <u:mo>−</u:mo> <u:mn>4</u:mn> </u:mrow> </u:msup> </u:math> , while the Dirac Higgs and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>Z</w:mi> </w:math> portals are essentially excluded. The UV-complete vector Higgs portal retains resonant bands whose viable portal strength depends on the mixing angle. Simplified scalars allow small windows for complex-scalar or vector DM; Dirac DM is strongly disfavored, whereas a pseudoscalar with Dirac DM remains viable over a broader parameter range. For a simplified <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msup> <y:mi>Z</y:mi> <y:mo>′</y:mo> </y:msup> </y:math> mediator, a pure vector coupling leaves only a marginal region, while pure axial is excluded by DD/ID bounds. In leptonic scenarios, inverse-Compton emission is essential: <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>L</ab:mi> <ab:mi>μ</ab:mi> </ab:msub> <ab:mo>−</ab:mo> <ab:msub> <ab:mi>L</ab:mi> <ab:mi>e</ab:mi> </ab:msub> </ab:math> (and, to a lesser extent, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>B</cb:mi> <cb:mo>−</cb:mo> <cb:mi>L</cb:mi> </cb:math> ) fits the GCE with near-thermal cross sections, while <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>L</eb:mi> <eb:mi>μ</eb:mi> </eb:msub> <eb:mo>−</eb:mo> <eb:msub> <eb:mi>L</eb:mi> <eb:mi>τ</eb:mi> </eb:msub> </eb:math> is disfavored. Overall, viable WIMP explanations are , with leptophilic vectors and pseudoscalar portals emerging as the most robust options.