⚛️ phenomenology

Branching Ratios of $H_{1,2,3} \rightarrow μ^{+}μ^{-}$ in the Broken-Phase N2HDM

This paper investigates the branching ratios of the rare decay $H \rightarrow \mu^+\mu^-$ for three CP-even Higgs bosons within the broken-phase Next-to-Two-Higgs-Doublet Model (N2HDM), incorporating one-loop corrections to identify viable parameter regions that explain the ATLAS signal strength enhancement and demonstrate the utility of dimuon precision measurements in probing extended Higgs sectors.

Original authors: T. V. Obikhod, Ie. O. Petrenko

Published 2026-01-23

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: T. V. Obikhod, Ie. O. Petrenko

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 is a giant, complex orchestra. For decades, physicists have been listening to the "Standard Model" symphony, which explains how particles interact. In this orchestra, there is a specific instrument called the Higgs boson. It's famous for giving mass to other particles, but until recently, we only heard it playing loudly with heavy instruments (like top quarks). We had never clearly heard it playing a quiet, delicate note with a "second-generation" instrument: the muon (a heavy cousin of the electron).

Recently, the ATLAS experiment at the Large Hadron Collider (LHC) finally heard a faint, promising whisper of the Higgs boson talking to muons. It wasn't a perfect match to the old sheet music (the Standard Model), but it was close enough to be exciting.

This paper asks: "What if the orchestra is actually bigger than we thought?"

The authors explore a theory called the N2HDM (Next-to-Two-Higgs-Doublet Model). Think of the Standard Model as a piano with two keyboards. The N2HDM adds a third keyboard (a "singlet" field) and a second piano. This creates a much richer, more complex instrument with three different Higgs bosons instead of just one.

Here is what the paper found, translated into everyday terms:

1. The "Familiar" Higgs (H1)

Imagine the three Higgs bosons as three siblings: H1, H2, and H3.

H1 is the "famous" sibling. It's the one we've been studying for years, weighing about 125 GeV.
The paper calculates how often H1 decays into muons in this new, expanded model.
The Result: No matter how they tweak the model's settings, H1 still behaves almost exactly like the Standard Model predicts. It's the "good student" who follows the rules. This matches the recent ATLAS data perfectly, confirming that our current understanding of the main Higgs is solid, even in this more complex world.

2. The "Hidden" Siblings (H2 and H3)

H2 and H3 are the heavier, mysterious siblings. They haven't been seen yet, but the theory says they must exist.
The paper asks: "If we could find them, how often would they turn into muons?"
The Result: This is where the magic happens. The answer depends entirely on which "family type" the model belongs to. The authors tested four different "family rules" (Type I, II, X, and Y), which dictate how these particles talk to each other.

3. The Four "Family Rules" (Yukawa Types)

Think of these four types as different dialects the particles speak. The paper found that the "muon conversation" changes drastically depending on the dialect:

Type I & Y (The Quiet Families): In these versions, the heavy siblings (H2 and H3) are very shy about talking to muons. The signal is so faint (like a whisper in a hurricane) that it would be incredibly hard to hear them with current equipment.
Type II (The Loud Family): Here, the heavy siblings talk to muons much more confidently. The signal is about 10 to 100 times stronger than in the quiet families. This makes them much easier to spot.
Type X (The Super-Loud Family): This is the most exciting scenario. In this version, the heavy siblings love talking to muons. The signal is the strongest of all, potentially up to 40 times stronger than the quiet versions. It's like turning the volume knob up to maximum.

4. The Hunt for New Physics

The paper acts like a treasure map for the ATLAS and CMS experiments at the LHC.

If the universe follows the Type II or Type X rules, the "treasure" (the heavy Higgs decaying into muons) is right there, waiting to be found with current data. The signal is strong enough that we might see it soon.
If the universe follows Type I or Type Y, the treasure is buried deep, and we might need the future "High-Luminosity" upgrade (which will collect much more data) to find it.

The Bottom Line

The paper concludes that while our main Higgs boson (H1) is doing exactly what we expected, the heavier, hidden Higgs bosons (H2 and H3) could be hiding a massive surprise.

If we look for them in the "dimuon" channel (two muons), we might find them very soon, but only if the universe is playing by the Type II or Type X rules. If we find them, it won't just be a new particle; it will be proof that the "orchestra" has a third keyboard we didn't know about, fundamentally changing our understanding of how the universe works.

In short: The main Higgs is normal, but its heavier cousins might be shouting at us in a language (muons) that we are finally starting to understand. The paper tells us exactly where to listen and how loud they might be.

Technical Summary: Branching Ratios of $H_{1,2,3} \to \mu^+\mu^-$ in the Broken-Phase N2HDM

Problem Statement
Recent evidence from the ATLAS Collaboration regarding the rare decay $H \to \mu^+\mu^-$ , observed with a local significance of 3.4 $\sigma$ and a signal strength of $\mu = 1.4 \pm 0.4$ , provides a critical probe into the Higgs boson's coupling to second-generation fermions. While consistent with the Standard Model (SM) prediction, this measurement opens a window for testing Beyond the Standard Model (BSM) physics. The Next-to-Two-Higgs-Doublet Model (N2HDM), which extends the SM scalar sector with two Higgs doublets and a real scalar singlet, offers a framework where branching ratios for $H \to \mu^+\mu^-$ can deviate significantly due to modified Yukawa couplings, scalar mixing, and singlet-doublet interactions. The specific problem addressed is the computation of these branching ratios for the three CP-even Higgs bosons ( $H_1, H_2, H_3$ ) within the broken phase of the N2HDM to determine if the model can accommodate the ATLAS signal while predicting distinct signatures for heavier scalars.

Methodology
The authors perform a phenomenological analysis within the Type-I, Type-II, Type-X (lepton-specific), and Type-Y (flipped) realizations of the N2HDM. The methodology involves:

Model Construction: Defining the scalar potential with two $SU(2)_L$ doublets ( $\Phi_1, \Phi_2$ ) and a real singlet ( $S$ ). Electroweak symmetry breaking is assumed to occur in the broken phase where all fields acquire non-zero vacuum expectation values (VEVs).
Mixing and Mass Eigenstates: The CP-even neutral fields ( $\rho_1, \rho_2, \rho_S$ ) are mixed via a $3 \times 3$ orthogonal rotation matrix $R(\alpha_1, \alpha_2, \alpha_3)$ to form physical mass eigenstates $h_1, h_2, h_3$ . The lightest state $h_1$ is identified with the observed 125 GeV Higgs.
Parameter Constraints: The analysis utilizes a constrained parameter space derived from recent global $\chi^2$ $χ^{2}$ fits (referenced as [5]) incorporating:
- Theoretical constraints (boundedness-from-below, perturbative unitarity, vacuum stability).
- Electroweak precision observables.
- Flavor physics constraints (e.g., $B \to X_s\gamma$ , $B_s \to \mu^+\mu^-$ ).
- Direct LHC Higgs measurements (HiggsSignals) and searches for additional scalars (HiggsBounds).
Calculation of Branching Ratios:
- Partial decay widths $\Gamma(H_i \to \mu^+\mu^-)$ are calculated including leading one-loop radiative corrections.
- Coupling modifiers ( $c_{H_i\mu\mu}$ ) are derived based on the Yukawa type and the mixing matrix elements $R_{ij}$ .
- Total widths $\Gamma_{tot}(H_i)$ are computed considering dominant decay channels (e.g., $t\bar{t}, WW, ZZ, hh$ ) for the heavier scalars.
- Branching ratios are obtained via $BR = \Gamma(H_i \to \mu^+\mu^-) / \Gamma_{tot}(H_i)$ .
Benchmarking: Results are compared against the ATLAS signal strength $\mu = 1.4 \pm 0.4$ and current LHC dimuon search sensitivities ( $\sigma \times BR \gtrsim 0.1$ fb for masses 600–800 GeV).

Key Contributions

First Exhaustive Computation: The paper presents the first detailed calculation of dimuon branching ratios for all three CP-even Higgs bosons ( $H_1, H_2, H_3$ ) across all four Yukawa types in the broken-phase N2HDM.
Integration of Radiative Corrections: The study incorporates one-loop radiative corrections into the decay width calculations, ensuring precision consistent with current experimental standards.
Systematic Comparison of Yukawa Types: The work systematically contrasts the predictions of Type-I, Type-II, Type-X, and Type-Y models, highlighting how specific Yukawa structures (e.g., lepton-specific vs. down-type enhanced) lead to distinct phenomenological outcomes for heavy scalars.
Benchmark Point Definition: Representative benchmark points are established for $H_2$ and $H_3$ (masses 600 GeV and 800 GeV) consistent with global fit constraints, providing concrete targets for experimental searches.

Results

SM-like Higgs ( $H_1$ ): The calculated branching ratios for $H_1 \to \mu^+\mu^-$ are tightly clustered around the SM prediction ( $2.17 \times 10^{-4}$ ) for all Yukawa types (ranging from $1.91 \times 10^{-4}$ to $2.18 \times 10^{-4}$ ). This confirms that the $H_1$ state remains SM-like under current constraints, consistent with the ATLAS observation of $\mu = 1.4 \pm 0.4$ .
Heavy Scalars ( $H_2, H_3$ ): The branching ratios for the heavier states exhibit variations spanning seven orders of magnitude ( $10^{-11}$ $1 0^{- 11}$ to $10^{-4}$ $1 0^{- 4}$ ), heavily dependent on the Yukawa type:
- Type-I and Type-Y: Show suppressed branching ratios ( $\lesssim 10^{-7}$ ) due to the dominance of up-type quark couplings and moderate $\tan\beta$ .
- Type-II: Displays moderately enhanced branching ratios ( $\sim 10^{-6}$ ) for both $H_2$ and $H_3$ , driven by down-type lepton coupling enhancements at large $\tan\beta$ .
- Type-X (Lepton-Specific): Yields the largest branching ratios, reaching up to $4.03 \times 10^{-6}$ for $H_2$ , reflecting the potential for order-of-magnitude enhancements in lepton couplings.
Experimental Accessibility:
- Type-II and Type-X: Predict signal rates ( $\sigma \times BR$ ) of $1–40$ fb for masses in the 600–800 GeV range, placing them well within the reach of current LHC Run-2 and Run-3 datasets.
- Type-I and Type-Y: Predict rates of $0.03–0.3$ fb, which are near current detection thresholds but may become accessible with combined Run-2+3 analyses or the High-Luminosity LHC (HL-LHC).

Significance and Claims
The paper claims that precision measurements of $H \to \mu\mu$ serve as a powerful tool to test extended Higgs sectors. The primary significance lies in the demonstrated dichotomy: while the lightest Higgs ( $H_1$ ) is constrained to be SM-like, the heavier scalars ( $H_2, H_3$ ) offer distinct, type-dependent signatures that can be used to discriminate between different N2HDM realizations. The authors assert that Type-II and Type-X scenarios are particularly promising for discovery in current and future high-luminosity runs due to their enhanced dimuon rates. The study concludes that dimuon decays provide a "pristine experimental avenue" to uncover new physics, with the N2HDM offering a robust platform to probe Yukawa hierarchies and scalar mixing parameters that are otherwise difficult to access. The results are presented as concrete targets for ongoing LHC searches and future collider programs, including potential precision measurements at lepton colliders (ILC, CLIC, FCC-ee).

1. The "Familiar" Higgs (H1)

2. The "Hidden" Siblings (H2 and H3)

3. The Four "Family Rules" (Yukawa Types)

4. The Hunt for New Physics

The Bottom Line

More like this