Resonant multiscalar production in the generic complex singlet model in the multi-TeV region

We develop benchmarks for resonant discalar production in the generic complex singlet scalar extension of the Standard Model (SM) with no additional symmetries, which contains two new scalars. These benchmarks maximize discalar resonant production modes at future <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>p</a:mi><a:mi>p</a:mi></a:math> colliders: <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>p</c:mi><c:mi>p</c:mi><c:mo stretchy="false">→</c:mo><c:msub><c:mi>h</c:mi><c:mn>2</c:mn></c:msub><c:mo stretchy="false">→</c:mo><c:msub><c:mi>h</c:mi><c:mn>1</c:mn></c:msub><c:msub><c:mi>h</c:mi><c:mn>1</c:mn></c:msub></c:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>p</g:mi><g:mi>p</g:mi><g:mo stretchy="false">→</g:mo><g:msub><g:mi>h</g:mi><g:mn>2</g:mn></g:msub><g:mo stretchy="false">→</g:mo><g:msub><g:mi>h</g:mi><g:mn>1</g:mn></g:msub><g:msub><g:mi>h</g:mi><g:mn>3</g:mn></g:msub></g:math>, and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>p</k:mi><k:mi>p</k:mi><k:mo stretchy="false">→</k:mo><k:msub><k:mi>h</k:mi><k:mn>2</k:mn></k:msub><k:mo stretchy="false">→</k:mo><k:msub><k:mi>h</k:mi><k:mn>3</k:mn></k:msub><k:msub><k:mi>h</k:mi><k:mn>3</k:mn></k:msub></k:math>, where <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>h</o:mi><o:mn>1</o:mn></o:msub></o:math> is the observed SM-like Higgs boson and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>h</q:mi><q:mrow><q:mn>2</q:mn><q:mo>,</q:mo><q:mn>3</q:mn></q:mrow></q:msub></q:math> are new scalars. The decays <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>h</s:mi><s:mn>2</s:mn></s:msub><s:mo stretchy="false">→</s:mo><s:msub><s:mi>h</s:mi><s:mn>1</s:mn></s:msub><s:msub><s:mi>h</s:mi><s:mn>3</s:mn></s:msub></s:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msub><v:mi>h</v:mi><v:mn>2</v:mn></v:msub><v:mo stretchy="false">→</v:mo><v:msub><v:mi>h</v:mi><v:mn>3</v:mn></v:msub><v:msub><v:mi>h</v:mi><v:mn>3</v:mn></v:msub></v:math> may be the only way to discover <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>h</y:mi><y:mn>3</y:mn></y:msub></y:math>, leading to a discovery of two new scalars at once. Current LHC and projected future collider (HL-LHC, FCC-<ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mrow><ab:mi>ee</ab:mi><ab:mo>+</ab:mo><ab:mi>HL</ab:mi></ab:mrow></ab:math>-LHC, <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:mi>IL</cb:mi><cb:mrow><cb:mi mathvariant="normal">C</cb:mi><cb:mn>500</cb:mn><cb:mo>+</cb:mo><cb:mi>HL</cb:mi></cb:mrow></cb:mrow></cb:math>-LHC) constraints on this model are used to produce benchmarks at the HL-LHC for <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msub><fb:mi>h</fb:mi><fb:mn>2</fb:mn></fb:msub></fb:math> masses between 250 GeV and 1 TeV and a future <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>p</hb:mi><hb:mi>p</hb:mi></hb:math> collider (FCC-hh) for <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi>h</jb:mi><jb:mn>2</jb:mn></jb:msub></jb:math> masses between 250 GeV and 12 TeV. We update the current LHC bounds on the singlet-Higgs boson mixing angle for these benchmarks. As the mass of <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi>h</lb:mi><lb:mn>2</lb:mn></lb:msub></lb:math> approaches the multi-TeV region, certain limiting behaviors of the maximum rates are uncovered due to theoretical constraints on the parameters. These limits, which can be derived analytically, are <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mrow><nb:mi>BR</nb:mi></nb:mrow><nb:mo stretchy="false">(</nb:mo><nb:msub><nb:mi>h</nb:mi><nb:mn>2</nb:mn></nb:msub><nb:mo stretchy="false">→</nb:mo><nb:msub><nb:mi>h</nb:mi><nb:mn>1</nb:mn></nb:msub><nb:msub><nb:mi>h</nb:mi><nb:mn>1</nb:mn></nb:msub><nb:mo stretchy="false">)</nb:mo><nb:mo stretchy="false">→</nb:mo><nb:mn>0.25</nb:mn></nb:math>, <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mrow><tb:mi>BR</tb:mi></tb:mrow><tb:mo stretchy="false">(</tb:mo><tb:msub><tb:mi>h</tb:mi><tb:mn>2</tb:mn></tb:msub><tb:mo stretchy="false">→</tb:mo><tb:msub><tb:mi>h</tb:mi><tb:mn>3</tb:mn></tb:msub><tb:msub><tb:mi>h</tb:mi><tb:mn>3</tb:mn></tb:msub><tb:mo stretchy="false">)</tb:mo><tb:mo stretchy="false">→</tb:mo><tb:mn>0.5</tb:mn></tb:math>, and <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:mrow><zb:mi>BR</zb:mi></zb:mrow><zb:mo stretchy="false">(</zb:mo><zb:msub><zb:mi>h</zb:mi><zb:mn>2</zb:mn></zb:msub><zb:mo stretchy="false">→</zb:mo><zb:msub><zb:mi>h</zb:mi><zb:mn>1</zb:mn></zb:msub><zb:msub><zb:mi>h</zb:mi><zb:mn>3</zb:mn></zb:msub><zb:mo stretchy="false">)</zb:mo><zb:mo stretchy="false">→</zb:mo><zb:mn>0</zb:mn></zb:math>. It can also be shown that the maximum rates of <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:mi>p</fc:mi><fc:mi>p</fc:mi><fc:mo stretchy="false">→</fc:mo><fc:msub><fc:mi>h</fc:mi><fc:mn>2</fc:mn></fc:msub><fc:mo stretchy="false">→</fc:mo><fc:msub><fc:mi>h</fc:mi><fc:mn>1</fc:mn></fc:msub><fc:msub><fc:mi>h</fc:mi><fc:mn>1</fc:mn></fc:msub></fc:math> and <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"><jc:mi>p</jc:mi><jc:mi>p</jc:mi><jc:mo stretchy="false">→</jc:mo><jc:msub><jc:mi>h</jc:mi><jc:mn>2</jc:mn></jc:msub><jc:mo stretchy="false">→</jc:mo><jc:msub><jc:mi>h</jc:mi><jc:mn>3</jc:mn></jc:msub><jc:msub><jc:mi>h</jc:mi><jc:mn>3</jc:mn></jc:msub></jc:math> approach the same value. Hence, all three <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msub><nc:mi>h</nc:mi><nc:mn>2</nc:mn></nc:msub><nc:mo stretchy="false">→</nc:mo><nc:msub><nc:mi>h</nc:mi><nc:mi>i</nc:mi></nc:msub><nc:msub><nc:mi>h</nc:mi><nc:mi>j</nc:mi></nc:msub></nc:math> decays are promising discovery modes for <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:msub><qc:mi>h</qc:mi><qc:mn>2</qc:mn></qc:msub></qc:math> masses at and below <sc:math xmlns:sc="http://www.w3.org/1998/Math/MathML" display="inline"><sc:mi mathvariant="script">O</sc:mi><sc:mo stretchy="false">(</sc:mo><sc:mn>1</sc:mn><sc:mtext> </sc:mtext><sc:mtext> </sc:mtext><sc:mi>TeV</sc:mi><sc:mo stretchy="false">)</sc:mo></sc:math>, while above <xc:math xmlns:xc="http://www.w3.org/1998/Math/MathML" display="inline"><xc:mi mathvariant="script">O</xc:mi><xc:mo stretchy="false">(</xc:mo><xc:mn>1</xc:mn><xc:mtext> </xc:mtext><xc:mtext> </xc:mtext><xc:mi>TeV</xc:mi><xc:mo stretchy="false">)</xc:mo></xc:math> the decays <cd:math xmlns:cd="http://www.w3.org/1998/Math/MathML" display="inline"><cd:msub><cd:mi>h</cd:mi><cd:mn>2</cd:mn></cd:msub><cd:mo stretchy="false">→</cd:mo><cd:msub><cd:mi>h</cd:mi><cd:mn>1</cd:mn></cd:msub><cd:msub><cd:mi>h</cd:mi><cd:mn>1</cd:mn></cd:msub></cd:math> and <fd:math xmlns:fd="http://www.w3.org/1998/Math/MathML" display="inline"><fd:msub><fd:mi>h</fd:mi><fd:mn>2</fd:mn></fd:msub><fd:mo stretchy="false">→</fd:mo><fd:msub><fd:mi>h</fd:mi><fd:mn>3</fd:mn></fd:msub><fd:msub><fd:mi>h</fd:mi><fd:mn>3</fd:mn></fd:msub></fd:math> are more encouraging. We choose benchmark masses for <id:math xmlns:id="http://www.w3.org/1998/Math/MathML" display="inline"><id:msub><id:mi>h</id:mi><id:mn>3</id:mn></id:msub></id:math> to produce a large range of decay signatures including multi-<kd:math xmlns:kd="http://www.w3.org/1998/Math/MathML" display="inline"><kd:mi>b</kd:mi></kd:math>, multivector boson, and multi-SM-like Higgs production. As we will show, the behavior of the maximum rates leads to the surprising conclusion that in the multi-TeV region this model may be discovered in the Higgs quartet production mode via <md:math xmlns:md="http://www.w3.org/1998/Math/MathML" display="inline"><md:msub><md:mi>h</md:mi><md:mn>2</md:mn></md:msub><md:mo stretchy="false">→</md:mo><md:msub><md:mi>h</md:mi><md:mn>3</md:mn></md:msub><md:msub><md:mi>h</md:mi><md:mn>3</md:mn></md:msub><md:mo stretchy="false">→</md:mo><md:mn>4</md:mn><md:msub><md:mi>h</md:mi><md:mn>1</md:mn></md:msub></md:math> decays before Higgs triple production is observed. The maximum di- and four Higgs production rates are similar in the multi-TeV range. Published by the American Physical Society 2024