Multi-Higgs boson signals of a modified muon Yukawa coupling at a muon collider

We study di-Higgs and tri-Higgs boson productions at a muon collider as functions of the modification of the muon Yukawa coupling resulting from new physics parametrized by the dimension-six mass operator. We show that the di-Higgs signal can be used to observe a deviation in the muon Yukawa coupling at the 10% level for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msqrt><a:mrow><a:mi>s</a:mi></a:mrow></a:msqrt><a:mo>=</a:mo><a:mn>10</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>TeV</a:mi></a:mrow></a:math> and at the 3.5% level for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msqrt><c:mi>s</c:mi></c:msqrt><c:mo>=</c:mo><c:mn>30</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>TeV</c:mi></c:math>. The tri-Higgs signal improves the sensitivity dramatically with increasing <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msqrt><e:mi>s</e:mi></e:msqrt></e:math>, reaching 0.8% at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msqrt><g:mi>s</g:mi></g:msqrt><g:mo>=</g:mo><g:mn>30</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>TeV</g:mi></g:math>. We also study all processes involving Goldstone bosons originating from the same operator, discuss possible model dependence resulting from other operators of dimension-six and higher, and identify <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>μ</i:mi><i:mo>+</i:mo></i:msup><i:msup><i:mi>μ</i:mi><i:mo>−</i:mo></i:msup><i:mo stretchy="false">→</i:mo><i:mi>h</i:mi><i:mi>h</i:mi></i:math>, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi>μ</l:mi><l:mo>+</l:mo></l:msup><l:msup><l:mi>μ</l:mi><l:mo>−</l:mo></l:msup><l:mo stretchy="false">→</l:mo><l:mi>h</l:mi><l:mi>h</l:mi><l:mi>h</l:mi></l:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>μ</o:mi><o:mo>+</o:mo></o:msup><o:msup><o:mi>μ</o:mi><o:mo>−</o:mo></o:msup><o:mo stretchy="false">→</o:mo><o:mi>h</o:mi><o:msub><o:mi>Z</o:mi><o:mi>L</o:mi></o:msub><o:msub><o:mi>Z</o:mi><o:mi>L</o:mi></o:msub></o:math> as golden channels. We further extend the study to an effective field theory including two Higgs doublets with type-II couplings and show that di-Higgs and tri-Higgs signals involving heavy Higgs bosons can be enhanced in the alignment limit by a factor of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mo stretchy="false">(</r:mo><r:mi>tan</r:mi><r:mi>β</r:mi><r:msup><r:mo stretchy="false">)</r:mo><r:mn>4</r:mn></r:msup></r:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mo stretchy="false">(</v:mo><v:mi>tan</v:mi><v:mi>β</v:mi><v:msup><v:mo stretchy="false">)</v:mo><v:mn>6</v:mn></v:msup></v:math>, respectively, which results in the potential sensitivity to a modified muon Yukawa coupling at the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msup><z:mn>10</z:mn><z:mrow><z:mo>−</z:mo><z:mn>6</z:mn></z:mrow></z:msup></z:math> level already at a <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msqrt><bb:mi>s</bb:mi></bb:msqrt><bb:mo>=</bb:mo><bb:mn>10</bb:mn><bb:mtext> </bb:mtext><bb:mtext> </bb:mtext><bb:mi>TeV</bb:mi></bb:math> muon collider. The results can easily be customized for other extensions of the Higgs sector. Published by the American Physical Society 2024