Long-lived sterile neutrino searches at future muon colliders

We explore the potential of studying sterile neutrinos at a future high-energy muon collider, where these particles can generate small active neutrino masses via the seesaw mechanism and exhibit long-lived particle signatures. A Dirac sterile neutrino model with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mrow><a:mi mathvariant="normal">U</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:msub><a:mi>L</a:mi><a:mi>μ</a:mi></a:msub><a:mo>−</a:mo><a:msub><a:mi>L</a:mi><a:mi>τ</a:mi></a:msub></a:mrow></a:msub></a:math> symmetry is introduced, where the heavy right-handed neutrino (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>N</f:mi><f:mi>R</f:mi></f:msub></f:math>) produces tiny active neutrino masses, and the light left-handed neutrino (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>N</h:mi><h:mi>L</h:mi></h:msub></h:math>) naturally behaves as a long-lived particle. The <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mrow><j:mi mathvariant="normal">U</j:mi><j:mo stretchy="false">(</j:mo><j:mn>1</j:mn><j:mo stretchy="false">)</j:mo></j:mrow><j:mrow><j:msub><j:mi>L</j:mi><j:mi>μ</j:mi></j:msub><j:mo>−</j:mo><j:msub><j:mi>L</j:mi><j:mi>τ</j:mi></j:msub></j:mrow></j:msub></j:math> gauge symmetry also enhances sterile neutrino pair production at a future high-energy muon collider. Using the displaced vertex method, the muon collider can search for heavy sterile neutrino, especially for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>m</o:mi><o:mi>L</o:mi></o:msub><o:mo>&gt;</o:mo><o:msub><o:mi>m</o:mi><o:mi>W</o:mi></o:msub></o:math>. We find that a muon collider with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msqrt><q:mi>s</q:mi></q:msqrt><q:mo>=</q:mo><q:mn>3</q:mn><q:mo stretchy="false">(</q:mo><q:mn>10</q:mn><q:mo stretchy="false">)</q:mo><q:mtext> </q:mtext><q:mtext> </q:mtext><q:mi>TeV</q:mi></q:math> and luminosity <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi mathvariant="script">L</u:mi><u:mo>=</u:mo><u:mn>1</u:mn><u:mo stretchy="false">(</u:mo><u:mn>10</u:mn><u:mo stretchy="false">)</u:mo><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mrow><u:msup><u:mrow><u:mi>ab</u:mi></u:mrow><u:mrow><u:mo>−</u:mo><u:mn>1</u:mn></u:mrow></u:msup></u:mrow></u:math> can probe <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>N</z:mi><z:mi>L</z:mi></z:msub></z:math> masses of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>m</bb:mi><bb:mi>L</bb:mi></bb:msub><bb:mo>∈</bb:mo><bb:mo stretchy="false">[</bb:mo><bb:mn>100</bb:mn><bb:mo>,</bb:mo><bb:mn>1500</bb:mn><bb:mo stretchy="false">(</bb:mo><bb:mn>5000</bb:mn><bb:mo stretchy="false">)</bb:mo><bb:mo stretchy="false">]</bb:mo><bb:mtext> </bb:mtext><bb:mtext> </bb:mtext><bb:mi>GeV</bb:mi></bb:math> and mixing angles <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>θ</hb:mi><hb:mrow><hb:mi>ν</hb:mi><hb:mi>L</hb:mi></hb:mrow></hb:msub><hb:mo>∈</hb:mo><hb:mo stretchy="false">[</hb:mo><hb:msup><hb:mn>10</hb:mn><hb:mrow><hb:mo>−</hb:mo><hb:mn>13</hb:mn></hb:mrow></hb:msup><hb:mo>,</hb:mo><hb:msup><hb:mn>10</hb:mn><hb:mrow><hb:mo>−</hb:mo><hb:mn>6</hb:mn></hb:mrow></hb:msup><hb:mo stretchy="false">]</hb:mo></hb:math>.