Probing a scalar singlet-triplet extension of the standard model via vector boson fusion at a muon collider

In this article, we investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Y</a:mi><a:mo>=</a:mo><a:mn>0</a:mn></a:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi><c:mi>U</c:mi><c:mo stretchy="false">(</c:mo><c:mn>2</c:mn><c:mo stretchy="false">)</c:mo></c:math> scalar triplet and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>Z</g:mi><g:mn>2</g:mn></g:msub></g:math>-odd scalar singlet extension of the standard model (SM). Here, the triplet charged Higgs boson decays to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Z</i:mi><i:msup><i:mi>W</i:mi><i:mo>±</i:mo></i:msup></i:math>, breaking the custodial symmetry at the tree level, proportional to the triplet vacuum expectation value, while the singlet provides the dark matter (DM) relic. The triplet neutral Higgs boson (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>T</k:mi><k:mn>0</k:mn></k:msup></k:math>) can decay fully invisibly owing to the triplet-singlet portal coupling <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>λ</m:mi><m:mrow><m:mi>s</m:mi><m:mi>t</m:mi></m:mrow></m:msub></m:math>. The other SM Higgs portal couplings <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>λ</o:mi><o:mrow><o:mi>h</o:mi><o:mi>t</o:mi></o:mrow></o:msub><o:mo>,</o:mo><o:msub><o:mi>λ</o:mi><o:mrow><o:mi>h</o:mi><o:mi>s</o:mi></o:mrow></o:msub></o:math> are constrained by the Higgs boson to diphoton observations, and the dark matter relic and direct searches as well as invisible Higgs decay bounds, respectively. For a cleaner signature, we indulge in a futuristic multi-TeV muon collider (MuC) to probe both the triplet scalars (<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>T</q:mi><q:mo>±</q:mo></q:msup><q:mo>,</q:mo><q:msup><q:mi>T</q:mi><q:mn>0</q:mn></q:msup></q:math>) via vector boson fusion with forward muon tagging, at the center-of-mass energies of 3 and 10 TeV. The analysis is comprised of a traditional cut-based approach and a boosted decision tree (BDT) classifier, where the latter is more effective for lower energies. With large missing energy contributions to the final states from combinations of DM mass and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>λ</s:mi><s:mrow><s:mi>s</s:mi><s:mi>t</s:mi></s:mrow></s:msub></s:math>, the 3 TeV MuC is projected to probe triplet scalar masses of 450 GeV with the BDT classifier. The 10 TeV MuC can pinpoint the custodial symmetry breaking <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>T</u:mi><u:mo>±</u:mo></u:msup><u:mo stretchy="false">→</u:mo><u:mi>Z</u:mi><u:msup><u:mi>W</u:mi><u:mo>±</u:mo></u:msup><u:mo stretchy="false">→</u:mo><u:mn>3</u:mn></u:math>-lepton decay up to 800 GeV of triplet scalar mass from cut-based analysis, with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>λ</y:mi><y:mrow><y:mi>s</y:mi><y:mi>t</y:mi></y:mrow></y:msub></y:math> as low as 1.5 being adequate. Published by the American Physical Society 2024