Recent <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><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mi>ν</mml:mi><m

The Belle II collaboration recently announced that they observed the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>B</a:mi><a:mo>+</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msup><a:mi>K</a:mi><a:mo>+</a:mo></a:msup><a:mi>ν</a:mi><a:mover accent="true"><a:mi>ν</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> decay process for the first time. However, their result encounters a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mn>2.7</f:mn><f:mi>σ</f:mi></f:mrow></f:math> deviation from the Standard Model (SM) calculation. Additionally, Fermilab released new data on muon <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>g</h:mi><h:mo>−</h:mo><h:mn>2</h:mn></h:math> away from the SM expectation with <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mn>5.1</j:mn><j:mi>σ</j:mi></j:math>. In this paper, we study the simplest UV-complete <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mi mathvariant="normal">U</l:mi><l:mo stretchy="false">(</l:mo><l:mn>1</l:mn><l:msub><l:mrow><l:mo stretchy="false">)</l:mo></l:mrow><l:mrow><l:msub><l:mrow><l:mi mathvariant="sans-serif">L</l:mi></l:mrow><l:mrow><l:mi>μ</l:mi></l:mrow></l:msub><l:mo>−</l:mo><l:msub><l:mrow><l:mi mathvariant="sans-serif">L</l:mi></l:mrow><l:mrow><l:mi>τ</l:mi></l:mrow></l:msub></l:mrow></l:msub></l:mrow></l:math>-charged complex scalar dark matter (DM) model. Thanks to the existence of light dark Higgs boson and light dark photon, we can explain the observed relic density of DM and resolve the results reported by both Belle II and Fermilab experiments simultaneously. As a by-product, the Hubble tension can be alleviated by taking <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi mathvariant="normal">Δ</s:mi><s:msub><s:mrow><s:mi>N</s:mi></s:mrow><s:mrow><s:mi mathvariant="sans-serif">eff</s:mi></s:mrow></s:msub><s:mo>≃</s:mo><s:mn>0.3</s:mn></s:mrow></s:math> induced by the light dark photon, which could be tested by CMB stage-4 and new NA64 experimental data in the near future. In addition, our light DM mass is highly testified by future data released by Belle II and CMB stage-4.