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Correlating Resonant Di-Higgs and Tri-Higgs Production to $H\to VV$ in the 2HDM

This paper demonstrates that in the Two-Higgs-Doublet Model with a heavy scalar $H$ , the branching ratios for resonant di-Higgs ( $H \to hh$ ) and tri-Higgs ( $H \to hhh$ ) production are directly correlated with the $H \to VV$ decay rate solely by the scalar mass, predicting a fixed ratio of approximately 9.4 between $H \to hh$ and $H \to ZZ$ for masses between 500 GeV and 1 TeV, thereby establishing $H \to hh$ as the primary probe for heavy scalar resonances at current and future colliders.

Original authors: Guglielmo Coloretti, Andreas Crivellin, Howard E. Haber

Published 2026-06-23

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CC BY 4.0

Original authors: Guglielmo Coloretti, Andreas Crivellin, Howard E. Haber

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, complex orchestra. For a long time, scientists thought they knew the entire lineup of instruments (particles) in this orchestra. Then, in 2012, they finally found the "conductor" of the mass-giving section: the Higgs boson. It was a huge discovery, but it left a mystery. The conductor seemed to be working alone, while the rest of the orchestra (the fermions like quarks and electrons) had many copies of themselves. It felt a bit odd that the "mass" section was so simple while the rest was so complex.

This paper suggests that the Higgs conductor might not be working alone. It proposes that there is a "twin" conductor, a heavier, hidden version of the Higgs boson, waiting to be found. The authors are essentially saying: "If you look for this heavy twin, here is exactly what you should see, and here is how it will behave."

Here is a breakdown of their findings using everyday analogies:

1. The "Heavy Twin" and the "Decoupling"

The paper focuses on a theory called the Two-Higgs-Doublet Model (2HDM). Think of this as having two Higgs fields instead of one. One is the light Higgs we already found (let's call it "Lighty"). The other is a heavy, hidden one (let's call it "Heavy").

The authors are looking at a specific scenario called the "decoupling limit." Imagine Heavy is so massive (between 500 GeV and 1 TeV) that it's like a giant boulder sitting in a pond, while Lighty is a pebble. Because Heavy is so heavy, it barely interacts with the light stuff, except in very specific ways.

2. The "Magic Ratio" (The Smoking Gun)

The most exciting part of this paper is a prediction about how Heavy breaks apart. When Heavy decays (falls apart), it can turn into:

Two Lighty particles (Di-Higgs).
Two Z or W particles (which are like heavy messengers of the weak force).

The authors discovered a magic, unchangeable ratio between these two events. It's like a recipe that never changes, no matter how you cook it, as long as the oven temperature (the mass of Heavy) is in a certain range.

The Prediction: If you find Heavy, it will break into two Lighty particles about 9.4 times more often than it breaks into two Z messengers.
The Analogy: Imagine a magician who pulls rabbits out of a hat. If the magician is "Heavy," they will pull out a pair of rabbits (two Lighty Higgs) roughly 9 times for every single pair of doves (two Z messengers) they pull out. If you see a different ratio, the "Heavy Twin" theory is wrong. If you see this specific ratio, it's a strong sign that the 2HDM is real.

3. The "Triple Rabbit" Trick

The paper also predicts a rarer trick: Tri-Higgs production. Sometimes, Heavy doesn't just break into two Lighty particles; it breaks into three at once.

The Analogy: If the magician pulls out two rabbits, that's common. But sometimes, they pull out three rabbits at once.
The Catch: This happens less often than the two-rabbit trick, but the authors calculate that with the upcoming "High-Luminosity LHC" (a super-powered version of the current particle collider), we might finally have enough "magic tricks" (data) to actually see this three-rabbit event.

4. Why This Matters for Discovery

Currently, scientists are searching for Heavy by looking at how it breaks into Z messengers. But the paper argues that this might be the wrong way to look.

The Insight: Because Heavy breaks into two Lighty particles so much more often (thanks to that 9.4 ratio), the best way to find Heavy is to look for the two Lighty particles.
The "Busy" Signal: The authors note that this behavior makes the Higgs sector look "busy." Instead of being a quiet, simple particle, the heavy Higgs is constantly churning out pairs and triplets of the lighter Higgs.

5. The "Secret Sauce" (The Math Behind the Magic)

Why does this ratio exist? The authors explain that in the "Higgs basis" (a specific way of writing the math), there is a specific term in the energy equation (the "potential") that acts like a master switch. This switch controls how Heavy talks to Lighty.

Because this switch is the same for both the "two Lighty" and "two Z" interactions, it forces them to follow that strict 9.4 ratio. It's like a factory assembly line where the same machine part is used to build both the red cars and the blue cars, ensuring they come off the line in a fixed proportion.

Summary

The paper claims that if a heavy Higgs boson exists in the mass range of 500 GeV to 1 TeV:

It will decay into two lighter Higgs bosons about 9.4 times more often than it decays into two Z bosons.
This ratio is a "smoking gun" that can distinguish this theory from other ideas.
The best way to find this heavy particle is to look for it breaking into two Higgs bosons, not just Z bosons.
We might also see it breaking into three Higgs bosons soon with better detectors.

The authors are essentially handing experimentalists a precise map: "Don't just look anywhere; look here, and when you find it, check if the ratio is 9.4. If it is, you've found the Heavy Twin."

Technical Summary: Correlating Resonant Di-Higgs and Tri-Higgs Production to H → V V in the 2HDM

Problem Statement
The observation of resonant di-Higgs production ( $pp \to H \to hh$ ) would provide strong evidence for a new heavy neutral scalar ( $H$ ) and an extended scalar sector beyond the Standard Model (SM). While extensively searched for at the Large Hadron Collider (LHC), distinguishing between various theoretical models (such as the Two-Higgs-Doublet Model, or 2HDM) upon a potential discovery remains a challenge. The authors address the need for robust, model-specific predictions that can correlate different decay channels of a heavy scalar resonance, specifically linking the branching ratios of $H \to hh$ , $H \to VV$ (where $V=W, Z$ ), and $H \to hhh$ .

Methodology
The authors analyze the 2HDM in the decoupling limit, defined by a heavy scalar mass $m_H \gg m_h$ (where $m_h \approx 125$ GeV) and the Higgs alignment limit, where the observed Higgs boson $h$ mimics the SM Higgs. The analysis proceeds as follows:

Formalism: The study utilizes the Higgs basis, where the vacuum expectation value resides entirely in one doublet ( $H_1$ ), and the second doublet ( $H_2$ ) contains the heavy states. The scalar potential is parameterized by coefficients $Z_i$ , with a specific focus on the parameter $Z_6$ , which governs the mixing between the doublets and the couplings of the heavy scalar to the light Higgs.
Coupling Derivation: The authors derive the leading-order Feynman rules for the $HVV$, $Hhh$, and $Hhhh$ interaction vertices in the decoupling limit. They assume CP conservation initially, setting complex phases to zero, and later extend the analysis to the CP-violating case.
Approximation: By assuming $m_H \gg m_V, m_h$ and $|c_{\beta-\alpha}| \ll 1$ (alignment), the authors simplify the expressions for partial decay widths. They demonstrate that the ratio of decay widths depends primarily on $m_H$ and $m_V$ , becoming largely independent of other scalar potential parameters ( $Z_2, Z_3, Z_7$ , etc.) due to the suppression of terms involving $c_{\beta-\alpha}$ .
Phenomenological Constraints: The study incorporates current LHC constraints on $H \to ZZ$ , $H \to hh$ , and $H/A \to t\bar{t}$ to map the allowed parameter space, specifically examining the interplay between the flavor-alignment parameter $a_F$ and the mixing angle $c_{\beta-\alpha}$ .

Key Contributions and Results

Direct Correlation of Branching Ratios: The central result is a direct correlation between the branching ratios of $H \to hh$ and $H \to VV$ that depends only on the heavy scalar mass $m_H$ . In the mass range $500 \text{ GeV} < m_H < 1 \text{ TeV}$ , the authors find:
$\frac{\text{Br}(H \to hh)}{\text{Br}(H \to ZZ)} \approx 9.4 \pm 0.25$
This ratio is derived from the asymptotic limit where $\Gamma(H \to hh) / \Gamma(H \to VV) \approx 9/2$ for $V=W$ and $9/1$ for $V=Z$ (accounting for degrees of freedom).
Tri-Higgs Production: The paper establishes that the same parameter ( $Z_6$ ) driving the $Hhh$ coupling also governs the $Hhhh$ coupling. Consequently, resonant prompt tri-Higgs production ( $pp \to H \to hhh$ ) is directly correlated with di-Higgs production. The ratio $\Gamma(H \to hhh)/\Gamma(H \to hh)$ is predicted to be small ( $0.01 \lesssim \text{ratio} \lesssim 0.1$ in the relevant mass range) but potentially measurable.
Dominant Decay Mode: Through a scan of the parameter space constrained by LHC data (specifically $t\bar{t}$ and $ZZ$ searches), the authors identify a significant region where $H \to hh$ is the dominant decay mode, with branching ratios exceeding 70%. In this region, the top-quark alignment parameter $a_U$ is small, suppressing the $H \to t\bar{t}$ channel.
Tri-Higgs Rates: For a benchmark mass of $m_H = 800$ GeV, the resonant tri-Higgs cross section $\sigma(pp \to H \to hhh)$ is predicted to reach up to $0.1$ fb at $\sqrt{s} = 14$ TeV. The authors estimate that with the High-Luminosity LHC (HL-LHC) integrated luminosity of $3000 \text{ fb}^{-1}$ , up to 3 events could be observed in the $6b$ final state (assuming specific cut efficiencies), rising to 35 events at a future 100 TeV collider (FCC-hh).
CP-Violation Extension: The authors demonstrate that these correlations generalize to the CP-violating 2HDM. In this scenario, the heavy mass eigenstates $h_2$ and $h_3$ (indefinite CP) exhibit similar relations where the real and imaginary parts of $Z_6 e^{-i\eta}$ replace $Z_6$ .

Significance
The paper claims that these derived relations serve as a "smoking-gun" test for the 2HDM in the decoupling limit. If a heavy scalar resonance is discovered, measuring the ratio of its di-Higgs to vector-boson decay rates can immediately test the validity of the 2HDM framework without needing precise knowledge of the entire scalar potential. Furthermore, the work highlights that resonant tri-Higgs production, often neglected, could be a viable discovery channel at the HL-LHC and future colliders, directly linked to the same mechanism driving di-Higgs production. The results suggest that $H \to hh$ is the primary probe for heavy scalar resonances in specific regions of the 2HDM parameter space, potentially offering stronger constraints than $H \to ZZ$ or $H \to t\bar{t}$ .