Search for a Dark Higgs Boson Produced in Association with Inelastic Dark Matter at the Belle II Experiment

Inelastic dark matter models that have two dark matter particles and a massive dark photon can reproduce the observed relic dark matter density without violating cosmological limits. The mass splitting between the two dark matter particles <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>χ</a:mi><a:mn>1</a:mn></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>χ</c:mi><c:mn>2</c:mn></c:msub></c:math>, with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>m</e:mi><e:mo stretchy="false">(</e:mo><e:msub><e:mi>χ</e:mi><e:mn>2</e:mn></e:msub><e:mo stretchy="false">)</e:mo><e:mo>></e:mo><e:mi>m</e:mi><e:mo stretchy="false">(</e:mo><e:msub><e:mi>χ</e:mi><e:mn>1</e:mn></e:msub><e:mo stretchy="false">)</e:mo></e:math>, is induced by a dark Higgs field and a corresponding dark Higgs boson <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>h</k:mi><k:mo>′</k:mo></k:msup></k:math>. We present a search for dark matter in events with two vertices, at least one of which must be displaced from the interaction region, and missing energy. Using a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>365</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:msup><m:mi>fb</m:mi><m:mrow><m:mo>−</m:mo><m:mn>1</m:mn></m:mrow></m:msup></m:math> data sample collected at Belle II, which operates at the SuperKEKB <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>e</o:mi><o:mo>+</o:mo></o:msup><o:msup><o:mi>e</o:mi><o:mo>−</o:mo></o:msup></o:math> collider, we observe no evidence for a signal. We set upper limits on the product of the production cross section <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>σ</q:mi><q:mrow><q:mo stretchy="false">(</q:mo><q:mrow><q:msup><q:mi>e</q:mi><q:mo>+</q:mo></q:msup><q:msup><q:mi>e</q:mi><q:mo>−</q:mo></q:msup></q:mrow><q:mo stretchy="false">→</q:mo><q:msup><q:mi>h</q:mi><q:mo>′</q:mo></q:msup><q:msub><q:mi>χ</q:mi><q:mn>1</q:mn></q:msub><q:msub><q:mi>χ</q:mi><q:mn>2</q:mn></q:msub><q:mo stretchy="false">)</q:mo></q:mrow></q:math>, and the product of branching fractions <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi mathvariant="script">B</v:mi><v:mrow><v:mo stretchy="false">(</v:mo><v:msub><v:mi>χ</v:mi><v:mn>2</v:mn></v:msub><v:mo stretchy="false">→</v:mo><v:msub><v:mi>χ</v:mi><v:mn>1</v:mn></v:msub><v:msup><v:mi>e</v:mi><v:mo>+</v:mo></v:msup><v:msup><v:mi>e</v:mi><v:mo>−</v:mo></v:msup><v:mo stretchy="false">)</v:mo></v:mrow><v:mo>×</v:mo><v:mi mathvariant="script">B</v:mi><v:mrow><v:mo stretchy="false">(</v:mo><v:msup><v:mi>h</v:mi><v:mo>′</v:mo></v:msup><v:mo stretchy="false">→</v:mo><v:msup><v:mi>x</v:mi><v:mo>+</v:mo></v:msup><v:msup><v:mi>x</v:mi><v:mo>−</v:mo></v:msup><v:mo stretchy="false">)</v:mo></v:mrow></v:math>, where <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msup><fb:mi>x</fb:mi><fb:mo>+</fb:mo></fb:msup><fb:msup><fb:mi>x</fb:mi><fb:mo>−</fb:mo></fb:msup></fb:math> indicates <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msup><hb:mi>μ</hb:mi><hb:mo>+</hb:mo></hb:msup><hb:msup><hb:mi>μ</hb:mi><hb:mo>−</hb:mo></hb:msup><hb:mo>,</hb:mo><hb:msup><hb:mi>π</hb:mi><hb:mo>+</hb:mo></hb:msup><hb:msup><hb:mi>π</hb:mi><hb:mo>−</hb:mo></hb:msup></hb:math>, or <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msup><jb:mi>K</jb:mi><jb:mo>+</jb:mo></jb:msup><jb:msup><jb:mi>K</jb:mi><jb:mo>−</jb:mo></jb:msup></jb:math>, as functions of <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msup><lb:mi>h</lb:mi><lb:mo>′</lb:mo></lb:msup></lb:math> mass and lifetime at the level of <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msup><nb:mn>10</nb:mn><nb:mrow><nb:mo>−</nb:mo><nb:mn>1</nb:mn></nb:mrow></nb:msup><nb:mtext> </nb:mtext><nb:mtext> </nb:mtext><nb:mi>fb</nb:mi></nb:math>. We set model-dependent upper limits on the dark Higgs mixing angle at the level of <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msup><pb:mn>10</pb:mn><pb:mrow><pb:mo>−</pb:mo><pb:mn>5</pb:mn></pb:mrow></pb:msup></pb:math> and on the dark photon kinetic mixing parameter at the level of <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msup><rb:mn>10</rb:mn><rb:mrow><rb:mo>−</rb:mo><rb:mn>3</rb:mn></rb:mrow></rb:msup></rb:math>. This is the first search for dark Higgs bosons in association with inelastic dark matter.