Triple Higgs boson production and electroweak phase transition in the two-real-singlet model

TL;DR

This work investigates the Z2-symmetric two-real-singlet extension of the SM (TRSM) as a framework for simultaneously enlarging triple-Higgs production at the LHC and achieving a strong electroweak phase transition. It derives perturbativity bounds via one-loop RGEs, updates the benchmark landscape to include 140 points with cross sections for pp→h1h1h1 exceeding 100× the SM value, and analyzes the finite-temperature effective potential to assess first-order transitions. The key finding is that, when both singlets have nonzero vevs today, a first-order phase transition is incompatible with the required double-resonant enhancement; allowing one singlet to have zero vev can restore a strong FOPT while preserving some resonant di-Higgs or triple-Higgs phenomenology. To realize both a strong FOPT and large multi-Higgs production, further model-building — e.g., adding more scalars or breaking the Z2 symmetry — would be necessary, as discussed in the conclusions.

Abstract

The production of three Higgs bosons at hadron colliders can be enhanced by a double-resonant effect in the $\mathbb{Z}_2$-symmetric two-real-singlet extension of the Standard Model, making it potentially observable in future LHC runs. The production rate is maximized for large scalar couplings, which prompts us to carefully reconsider the perturbativity constraints on the theory. This leads us to construct a new set of 140 benchmark points that have a triple Higgs boson production cross-section at least 100 times larger than the SM value. Furthermore, we study the dynamics of the electroweak phase transition, both analytically at leading order, and numerically without the high-temperature expansion. Both analyses indicate that a first-order phase transition is incompatible with the requirement that both singlets have a non-zero vev in the present-day vacuum, as required by doubly-enhanced triple Higgs boson production. Allowing instead one of the singlets to remain at zero field value opens up the possibility of a first-order phase transition, while di-Higgs boson production can still be enhanced by a (single) resonance.

Figures (5)

• Figure 1: Double-resonant triple SM-like Higgs boson ($h_1$) production in a model with two heavy scalars $h_3$ and $h_2$.
• Figure 2: Enhancement of the triple Higgs boson production cross section $\sigma(p p \rightarrow h_1 h_1 h_1)$ at 13.6 TeV, given in terms of multiples of the SM value, and the resonant fraction contribution from $p p \rightarrow h_3 \rightarrow h_2 h_1 \rightarrow h_1 h_1 h_1$. Only points with a factor 10 enhancement or greater are shown. The density of points increases from the dark blue to yellow shade.
• Figure 3: Scatter plot of the values of $M_2$ and $M_3$ for the 140 points with triple Higgs boson production cross section over 100 times the SM value. The black solid line denotes the region where double resonant production is kinematically viable, i.e. the boundary $M_3 = M_2 + M_1$.
• Figure 4: Visualization of possible phase transitions. To the left is the case of the low-temperature vev at $\mathbf x_{123}$. To the right is the case of low-temperature vev at $\mathbf x_{12}$
• Figure 5: Evolution of the field expectation values in the minimum of the potential for a representative third BM point in Table \ref{['tab:benchmark']}. The Higgs field is represented by gray solid, $\phi_2$ by dashed pink, and $\phi_3$ by dotted cyan.