Non-resonant Collider Signatures of a Singlet-Driven Electroweak Phase Transition

TL;DR

This work investigates a real singlet extension of the Standard Model as a framework for a strong first-order electroweak phase transition (EWPT). The authors connect EWPT strength to the triscalar coupling λ221 and argue that non-resonant singlet-pair production, especially h2h2, provides a direct collider probe that remains sensitive even for small Higgs-singlet mixing. Through comprehensive parameter-space scans and detailed collider analyses, they show that non-resonant h2h2 production is a powerful probe at a future 100 TeV collider, with meaningful reach at the HL-LHC for favorable regions, and complementarity with hh and Zh1 measurements at lepton colliders. The study emphasizes a multi-faceted search strategy to robustly test EWPT scenarios in singlet-extended models, including trilepton channels, various production modes, and cross-checks with gauge-invariant finite-temperature analyses.

Abstract

We analyze the collider signatures of the real singlet extension of the Standard Model in regions consistent with a strong first-order electroweak phase transition and a singlet-like scalar heavier than the Standard Model-like Higgs. A definitive correlation exists between the strength of the phase transition and the trilinear coupling of the Higgs to two singlet-like scalars, and hence between the phase transition and non-resonant scalar pair production involving the singlet at colliders. We study the prospects for observing these processes at the LHC and a future 100 TeV $pp$ collider, focusing particularly on double singlet production. We also discuss correlations between the strength of the electroweak phase transition and other observables at hadron and future lepton colliders. Searches for non-resonant singlet-like scalar pair production at 100 TeV would provide a sensitive probe of the electroweak phase transition in this model, complementing resonant di-Higgs searches and precision measurements. Our study illustrates a strategy for systematically exploring the phenomenologically viable parameter space of this model, which we hope will be useful for future work.

Figures (13)

• Figure 1: The parameter space of interest for $m_2=170$ GeV (left) and $m_2=240$ GeV (right) with $\sin\theta=0.05$ consistent with our requirements of perturbativity, vacuum stability, and perturbative unitarity. The parameter $b_4$ has been marginalized over, such that the points shown are found to have some value of $b_4 < 8\pi/3$ such that these requirements hold (we scan down to $b_4 = 0.01$). These points were obtained by a grid scan over $a_2$, $b_3$ and $b_4$. The darker shaded points satisfy the above requirements at both tree- and one-loop level, while the lighter points satisfy these requirements at one-loop but not tree-level. The white regions (without points) are disallowed by our requirements at 1-loop for all values of $b_4$ considered.
• Figure 2: The parameter space of the model consistent with our requirements for $m_2=170$, 240 GeV and $\sin \theta = 0 .05$, 0.2 , now showing regions with a strong first-order electroweak phase transition. Results for both $\sin \theta = 0 .05$ and 0.2 are shown. Blue points feature an EWPT with $\phi_h(T_c)/T_c \geq 1$ for some value of $b_4 > 0.01$ in our approach utilizing the one-loop daisy-resummed thermal effective potential. Purple points additionally feature a strong first-order electroweak phase transition as predicted by the gauge-invariant high-$T$ approximation (which drops the Coleman-Weinberg potential and is thus only applied to regions with tree-level vacuum stability). Strong electroweak phase transitions are typically correlated with sizable values of $\lambda_{221}$.
• Figure 3: Representative diagrams for $h_2h_2$ production via gluon fusion through top quark loops: (left) $s$-channel $h_1$, (center) $s$-channel $h_2$, and (right) box diagram.
• Figure 4: Representative diagrams for $h_1h_1$ production via gluon fusion through top quark loops: (left) $s$-channel $h_1$, (center) $s$-channel $h_2$, and (right) box diagram.
• Figure 5: Fractional variation of $h_1h_1$ production cross section $\sigma$ and $\lambda_{111}$ away from the SM values denoted with superscript $SM$. Total cross section considering all relevant diagrams (black dots), cross sections computed with $s$-channel $h_2$ propagators removed (blue dots), and cross sections considering only $\lambda_{111}$ variation with the top quark Yukawa fixed at the SM value and $s$-channel $h_2$ propagators removed (blue dots) are shown. Two masses (left) $m_2=170$ GeV and (right) $m_2=240$ GeV are shown. The parameter region relevant of the strong first order EWPT [see Fig. \ref{['fig:PT']}] is considered: $|\sin\theta|\le 0.35$, $-5<\lambda_{221}/v<10$ and $-12<b_3/v<12$.