Resonant ALP-portal dark matter annihilation as a solution to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:mo stretchy="false">→</mml:mo> <mml:msup> <

The Belle II collaboration recently reported a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>2.7</a:mn> <a:mi>σ</a:mi> </a:math> excess in the rare decay <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>B</c:mi> <c:mo>±</c:mo> </c:msup> <c:mo stretchy="false">→</c:mo> <c:msup> <c:mi>K</c:mi> <c:mo>±</c:mo> </c:msup> <c:mi>ν</c:mi> <c:mover accent="true"> <c:mi>ν</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> </c:math> , potentially signaling new physics. We propose an axionlike particle (ALP)-portal dark matter (DM) framework to explain this anomaly while satisfying the observed DM relic abundance. By invoking a resonant annihilation mechanism ( <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>m</h:mi> <h:mi>a</h:mi> </h:msub> <h:mo>∼</h:mo> <h:mn>2</h:mn> <h:msub> <h:mi>m</h:mi> <h:mi>χ</h:mi> </h:msub> </h:math> ), we demonstrate that the ALP-mediated interactions between the Standard Model and DM sectors simultaneously account for the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msup> <j:mi>B</j:mi> <j:mo>±</j:mo> </j:msup> <j:mo stretchy="false">→</j:mo> <j:msup> <j:mi>K</j:mi> <j:mo>±</j:mo> </j:msup> <j:mi>ν</j:mi> <j:mover accent="true"> <j:mi>ν</j:mi> <j:mo stretchy="false">¯</j:mo> </j:mover> </j:math> anomaly and thermal freeze-out dynamics. Two distinct scenarios—long-lived ALPs decaying outside detectors (displaced diphotons) and ALPs decaying invisibly to DM pairs (missing energy)—are examined. While the displaced diphotons scenario is excluded by kaon decay bounds ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msup> <o:mi>K</o:mi> <o:mo>±</o:mo> </o:msup> <o:mo stretchy="false">→</o:mo> <o:msup> <o:mi>π</o:mi> <o:mo>±</o:mo> </o:msup> <o:mo>+</o:mo> <o:mrow> <o:mi>inv</o:mi> </o:mrow> </o:math> .), the invisible decay channel remains unconstrained and aligns with Belle II’s missing energy signature. Using the coupled Boltzmann equation formalism, we rigorously incorporate early kinetic decoupling effects, revealing deviations up to a factor of 20 from traditional relic density predictions in resonance regions. For the missing energy scenario, the viable parameter space features ALP–Standard Model (SM) and ALP-DM couplings: <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:msub> <r:mrow> <r:mi>g</r:mi> </r:mrow> <r:mrow> <r:mi>a</r:mi> <r:mi>W</r:mi> <r:mi>W</r:mi> </r:mrow> </r:msub> <r:mo stretchy="false">(</r:mo> <r:msub> <r:mrow> <r:mi>g</r:mi> </r:mrow> <r:mrow> <r:mi>a</r:mi> <r:mi>γ</r:mi> <r:mi>γ</r:mi> </r:mrow> </r:msub> <r:mo stretchy="false">)</r:mo> <r:mo>∈</r:mo> <r:mspace linebreak="goodbreak"/> <r:mo stretchy="false">(</r:mo> <r:mn>7.13</r:mn> <r:mo>×</r:mo> <r:msup> <r:mrow> <r:mn>10</r:mn> </r:mrow> <r:mrow> <r:mo>−</r:mo> <r:mn>5</r:mn> </r:mrow> </r:msup> <r:mi>–</r:mi> <r:mn>9.60</r:mn> <r:mo>×</r:mo> <r:msup> <r:mrow> <r:mn>10</r:mn> </r:mrow> <r:mrow> <r:mo>−</r:mo> <r:mn>5</r:mn> </r:mrow> </r:msup> <r:mo stretchy="false">)</r:mo> <r:mtext> </r:mtext> <r:mtext> </r:mtext> <r:msup> <r:mrow> <r:mi>GeV</r:mi> </r:mrow> <r:mrow> <r:mo>−</r:mo> <r:mn>1</r:mn> </r:mrow> </r:msup> </r:mrow> </r:math> (from <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msup> <y:mi>B</y:mi> <y:mo>±</y:mo> </y:msup> <y:mo stretchy="false">→</y:mo> <y:msup> <y:mi>K</y:mi> <y:mo>±</y:mo> </y:msup> <y:mi>a</y:mi> </y:math> ) and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mrow> <bb:msub> <bb:mrow> <bb:mi>g</bb:mi> </bb:mrow> <bb:mrow> <bb:mi>a</bb:mi> <bb:mi>χ</bb:mi> <bb:mi>χ</bb:mi> </bb:mrow> </bb:msub> <bb:mo>∈</bb:mo> <bb:mo stretchy="false">(</bb:mo> <bb:mn>7.12</bb:mn> <bb:mo>×</bb:mo> <bb:msup> <bb:mrow> <bb:mn>10</bb:mn> </bb:mrow> <bb:mrow> <bb:mo>−</bb:mo> <bb:mn>5</bb:mn> </bb:mrow> </bb:msup> <bb:mi>–</bb:mi> <bb:mn>7.73</bb:mn> <bb:mo>×</bb:mo> <bb:msup> <bb:mrow> <bb:mn>10</bb:mn> </bb:mrow> <bb:mrow> <bb:mo>−</bb:mo> <bb:mn>3</bb:mn> </bb:mrow> </bb:msup> <bb:mo stretchy="false">)</bb:mo> <bb:mtext> </bb:mtext> <bb:mtext> </bb:mtext> <bb:msup> <bb:mrow> <bb:mi>GeV</bb:mi> </bb:mrow> <bb:mrow> <bb:mo>−</bb:mo> <bb:mn>1</bb:mn> </bb:mrow> </bb:msup> </bb:mrow> </bb:math> (for resonant annihilation), accommodating ALP masses <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>m</fb:mi> <fb:mi>a</fb:mi> </fb:msub> <fb:mo>∈</fb:mo> <fb:mo stretchy="false">(</fb:mo> <fb:mn>0.6</fb:mn> <fb:mo>,</fb:mo> <fb:mn>4.8</fb:mn> <fb:mo stretchy="false">)</fb:mo> <fb:mtext> </fb:mtext> <fb:mtext> </fb:mtext> <fb:mi>GeV</fb:mi> </fb:math> . Therefore, this work establishes the ALP portal as a viable bridge between the <jb:math xmlns:jb="http://www.w