Testing tree level TeV scale seesaw scenarios in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi><mml:mi>TRISTAN</mml:mi></mml:math>

We investigate TeV scale seesaw scenarios at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>μ</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>μ</c:mi><c:mo>+</c:mo></c:msup></c:math> colliders in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>μ</e:mi><e:mi>TRISTAN</e:mi></e:math> (Transposable Ring Intersecting STorage Accelerator in Nippon) experiment. In a minimal type I seesaw scenario, we consider two generations of Standard Model (SM) singlet heavy Majorana–type right-handed neutrinos, which couple with SM-gauge bosons through light-heavy neutrino mixing. We discuss the prospects of probing heavy neutrinos via the processes such as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>μ</g:mi><g:mo>+</g:mo></g:msup><g:msup><g:mi>e</g:mi><g:mo>−</g:mo></g:msup><g:mo stretchy="false">→</g:mo><g:mi>ν</g:mi><g:msub><g:mi>N</g:mi><g:mi>i</g:mi></g:msub><g:mo stretchy="false">→</g:mo><g:msup><g:mi>e</g:mi><g:mo>+</g:mo></g:msup><g:mi>j</g:mi><g:mi>j</g:mi><g:mi>ν</g:mi></g:math> or <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>μ</k:mi><k:mo>−</k:mo></k:msup><k:mi>j</k:mi><k:mi>j</k:mi><k:mi>ν</k:mi></k:math> for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msqrt><m:mi>s</m:mi></m:msqrt><m:mo>=</m:mo><m:mn>346</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>GeV</m:mi></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mn>1</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:msup><o:mrow><o:mi>ab</o:mi></o:mrow><o:mrow><o:mo>−</o:mo><o:mn>1</o:mn></o:mrow></o:msup></o:mrow></o:math> luminosity. Studying these process, we estimate limits on the light-heavy neutrino mixing angles as a function of heavy neutrino mass, which could be 2 orders of magnitude stronger than electroweak precision data. Further, we study the effect of a doubly charged scalar boson <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">(</q:mo><q:msup><q:mi>H</q:mi><q:mrow><q:mo>+</q:mo><q:mo>+</q:mo></q:mrow></q:msup><q:mo stretchy="false">)</q:mo></q:math> from the type II seesaw scenario in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>μ</u:mi><u:mo>+</u:mo></u:msup><u:msup><u:mi>μ</u:mi><u:mo>+</u:mo></u:msup></u:math> collision at <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msqrt><w:mi>s</w:mi></w:msqrt><w:mo>=</w:mo><w:mn>2</w:mn><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>TeV</w:mi></w:math>. In this case, we consider <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>μ</y:mi><y:mo>+</y:mo></y:msup><y:msup><y:mi>μ</y:mi><y:mo>+</y:mo></y:msup><y:mo stretchy="false">→</y:mo><y:msubsup><y:mo>ℓ</y:mo><y:mi>i</y:mi><y:mo>+</y:mo></y:msubsup><y:msubsup><y:mo>ℓ</y:mo><y:mi>j</y:mi><y:mo>+</y:mo></y:msubsup></y:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msup><bb:mi>μ</bb:mi><bb:mo>+</bb:mo></bb:msup><bb:msup><bb:mi>μ</bb:mi><bb:mo>+</bb:mo></bb:msup><bb:mo stretchy="false">→</bb:mo><bb:msup><bb:mi>H</bb:mi><bb:mrow><bb:mo>+</bb:mo><bb:mo>+</bb:mo></bb:mrow></bb:msup><bb:mi>Z</bb:mi><bb:mo>/</bb:mo><bb:mi>γ</bb:mi></bb:math> processes followed by the same-sign dilepton decay of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>H</eb:mi><eb:mrow><eb:mo>+</eb:mo><eb:mo>+</eb:mo></eb:mrow></eb:msup></eb:math>. We find that events involving <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>e</gb:mi><gb:mo>+</gb:mo></gb:msup><gb:msup><gb:mi>e</gb:mi><gb:mo>+</gb:mo></gb:msup></gb:math> among these final states can probe the neutrino mass ordering in the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>μ</ib:mi><ib:mi>TRISTAN</ib:mi></ib:math> experiment at <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mrow><kb:mn>5</kb:mn><kb:mi>σ</kb:mi></kb:mrow></kb:math> significance. In addition, we study the production of positively charged triplet fermions in <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>μ</mb:mi><mb:mi>TRISTAN</mb:mi></mb:math> following the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msup><ob:mi>μ</ob:mi><ob:mo>+</ob:mo></ob:msup><ob:msup><ob:mi>μ</ob:mi><ob:mo>+</ob:mo></ob:msup><ob:mo stretchy="false">→</ob:mo><ob:msup><ob:mi>μ</ob:mi><ob:mo>+</ob:mo></ob:msup><ob:msup><ob:mi mathvariant="normal">Σ</ob:mi><ob:mo>+</ob:mo></ob:msup></ob:math> process, where <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msup><sb:mi mathvariant="normal">Σ</sb:mi><sb:mo>+</sb:mo></sb:msup></sb:math> decays into <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msup><vb:mi>μ</vb:mi><vb:mo>+</vb:mo></vb:msup><vb:mi>j</vb:mi><vb:mi>j</vb:mi></vb:math> mode through <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi>Z</xb:mi></xb:math> boson exchange. Considering a triplet at 1 TeV and studying SM backgrounds, we estimate the discovery potential of the <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msup><zb:mi>μ</zb:mi><zb:mo>+</zb:mo></zb:msup><zb:msup><zb:mi>μ</zb:mi><zb:mo>+</zb:mo></zb:msup><zb:mi>j</zb:mi><zb:mi>j</zb:mi></zb:math> signal at <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:mi>μ</bc:mi><bc:mi>TRISTAN</bc:mi></bc:math> with respect to projected luminosity.