Constraining light dark matter and mediator with <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

We study the decay of <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:math> meson into <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>K</c:mi><c:mo>+</c:mo></c:msup></c:math> plus a light mediator <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ϕ</e:mi></e:math>, which subsequently decays into a dark matter pair, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mover accent="true"><g:mi>χ</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>χ</g:mi></g:math>. Integrating constraints from DM relic density, direct detection, collider data and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>B</k:mi></k:math>-physics, alongside the recently reported results form Belle II experiment, we analyze the couplings between the mediator, standard model fermions, and the dark matter particles. Our results indicate that if the decay process <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>ϕ</m:mi><m:mo stretchy="false">→</m:mo><m:mover accent="true"><m:mi>χ</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>χ</m:mi></m:math> is kinematically allowed, i.e., <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>m</r:mi><r:mi>ϕ</r:mi></r:msub><r:mo>&gt;</r:mo><r:mn>2</r:mn><r:msub><r:mi>m</r:mi><r:mi>χ</r:mi></r:msub></r:math>, then the mediator mass must be constrained within <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mrow><t:mn>0.35</t:mn><t:mtext> </t:mtext><t:mtext> </t:mtext><t:mi>GeV</t:mi><t:mo>≲</t:mo><t:msub><t:mi>m</t:mi><t:mi>ϕ</t:mi></t:msub><t:mo>≲</t:mo><t:mn>3</t:mn><t:mtext> </t:mtext><t:mtext> </t:mtext><t:mi>GeV</t:mi></t:mrow></t:math>. Conversely, if <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msub><v:mi>m</v:mi><v:mi>ϕ</v:mi></v:msub><v:mo>&lt;</v:mo><v:mn>2</v:mn><v:msub><v:mi>m</v:mi><v:mi>χ</v:mi></v:msub></v:math>, the mediator <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msub><x:mi>m</x:mi><x:mi>ϕ</x:mi></x:msub></x:math> is long-lived relative to the detector size, and the only allowed decay channel is <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>ϕ</z:mi><z:mo stretchy="false">→</z:mo><z:msup><z:mi>e</z:mi><z:mo>+</z:mo></z:msup><z:msup><z:mi>e</z:mi><z:mo>−</z:mo></z:msup></z:math>. Published by the American Physical Society 2024