Multistep strong first-order electroweak phase transitions in the inverted type-I 2HDM: Parameter space, gravitational waves, and collider phenomenology

We investigate the electroweak phase transition (EWPT) within the inverted type-I two-Higgs-doublet model, where the observed 125 GeV Higgs boson is identified as the heavier <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>C</a:mi><a:mi>P</a:mi></a:mrow></a:math>-even scalar <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>H</c:mi></c:math>. Through a comprehensive parameter-space scan consistent with current theoretical and experimental constraints, we identify regions supporting strong first-order EWPTs (SFOEWPTs), including multistep transitions. We find that two-step SFOEWPTs occur as frequently as one-step transitions, while three-step transitions can occur, albeit rarely. Crucially, the parameter spaces inducing one-step and two-step transitions are partially yet significantly separated: one-step transitions restrict the charged Higgs mass and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>tan</e:mi><e:mi>β</e:mi></e:math> to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:msup><g:mi>H</g:mi><g:mo>±</g:mo></g:msup></g:msub><g:mo>∈</g:mo><g:mo stretchy="false">[</g:mo><g:mn>295</g:mn><g:mo>,</g:mo><g:mn>441</g:mn><g:mo stretchy="false">]</g:mo><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>GeV</g:mi></g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>tan</k:mi><k:mi>β</k:mi><k:mo>∈</k:mo><k:mo stretchy="false">[</k:mo><k:mn>4.2</k:mn><k:mo>,</k:mo><k:mn>8.8</k:mn><k:mo stretchy="false">]</k:mo></k:math>, whereas two-step transitions allow <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>m</o:mi><o:msup><o:mi>H</o:mi><o:mo>±</o:mo></o:msup></o:msub><o:mo>∈</o:mo><o:mo stretchy="false">[</o:mo><o:mn>100</o:mn><o:mo>,</o:mo><o:mn>350</o:mn><o:mo stretchy="false">]</o:mo><o:mtext> </o:mtext><o:mtext> </o:mtext><o:mi>GeV</o:mi></o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>tan</s:mi><s:mi>β</s:mi><s:mo>∈</s:mo><s:mo stretchy="false">[</s:mo><s:mn>2.5</s:mn><s:mo>,</s:mo><s:mn>45.4</s:mn><s:mo stretchy="false">]</s:mo></s:math>. Notably, negative values of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>sin</w:mi><w:mo stretchy="false">(</w:mo><w:mi>β</w:mi><w:mo>−</w:mo><w:mi>α</w:mi><w:mo stretchy="false">)</w:mo></w:math> arise almost exclusively in one-step scenarios. We present the calculation of gravitational wave (GW) signal-to-noise ratios (SNRs) at Laser Interferometer Space Antenna for multistep EWPTs, finding that detectable GW signals (<ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>SNR</ab:mi><ab:mo>></ab:mo><ab:mn>10</ab:mn></ab:math>) predominantly emerge from two-step transitions. Furthermore, we demonstrate that the previously established correlation between the vacuum uplifting measure <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi mathvariant="normal">Δ</cb:mi><cb:msub><cb:mi mathvariant="script">F</cb:mi><cb:mn>0</cb:mn></cb:msub></cb:math> and EWPT strength <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>ξ</gb:mi><gb:mi>c</gb:mi></gb:msub></gb:math> persists only in one-step transitions and breaks down in multistep cases. Finally, we perform a dedicated collider analysis for representative SFOEWPT parameter points at the 1.5 TeV Compact Linear Collider, identifying <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msup><ib:mi>e</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:msup><ib:mi>e</ib:mi><ib:mo>−</ib:mo></ib:msup><ib:mo stretchy="false">→</ib:mo><ib:msup><ib:mi>H</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:msup><ib:mi>H</ib:mi><ib:mo>−</ib:mo></ib:msup><ib:mo stretchy="false">→</ib:mo><ib:msup><ib:mi>W</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:msup><ib:mi>W</ib:mi><ib:mo>−</ib:mo></ib:msup><ib:mi>h</ib:mi><ib:mi>h</ib:mi></ib:math> as a promising discovery channel. Enhanced <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>h</mb:mi><mb:mo stretchy="false">→</mb:mo><mb:mi>γ</mb:mi><mb:mi>γ</mb:mi></mb:math> branching ratios for negative <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mi>sin</pb:mi><pb:mo stretchy="false">(</pb:mo><pb:mi>β</pb:mi><pb:mo>−</pb:mo><pb:mi>α</pb:mi><pb:mo stretchy="false">)</pb:mo></pb:math> motivate two complementary golden final states, <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:msup><tb:mi>W</tb:mi><tb:mo>+</tb:mo></tb:msup><tb:msup><tb:mi>W</tb:mi><tb:mo>−</tb:mo></tb:msup><tb:mi>b</tb:mi><tb:mover accent="true"><tb:mi>b</tb:mi><tb:mo stretchy="false">¯</tb:mo></tb:mover><tb:msup><tb:mi>τ</tb:mi><tb:mo>+</tb:mo></tb:msup><tb:msup><tb:mi>τ</tb:mi><tb:mo>−</tb:mo></tb:msup></tb:math> and <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msup><xb:mi>W</xb:mi><xb:mo>+</xb:mo></xb:msup><xb:msup><xb:mi>W</xb:mi><xb:mo>−</xb:mo></xb:msup><xb:mi>b</xb:mi><xb:mover accent="true"><xb:mi>b</xb:mi><xb:mo stretchy="false">¯</xb:mo></xb:mover><xb:mi>γ</xb:mi><xb:mi>γ</xb:mi></xb:math>, which demonstrate high discovery potential due to negligible Standard Model backgrounds.