⚛️ phenomenology

Flavour-Changing Neutral Current Top Decays in the Three Higgs Doublet Model

This paper investigates flavour-changing neutral current top quark decays within a $Z_3$ -symmetric democratic Three Higgs Doublet Model, demonstrating that one-loop contributions from an extended scalar sector can produce branching ratios significantly exceeding Standard Model predictions while remaining consistent with current constraints and potentially detectable at the High-Luminosity LHL.

Original authors: Baradhwaj Coleppa, Benjamin Fuks, Akshat Khanna

Published 2026-01-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Baradhwaj Coleppa, Benjamin Fuks, Akshat Khanna

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, bustling city where every particle is a citizen. In this city, there is a very famous, heavy celebrity known as the Top Quark. According to the current "rulebook" of physics (called the Standard Model), this celebrity is very strict: they only interact with specific people in very specific ways. One of the strictest rules is that the Top Quark cannot simply change into a lighter, less famous citizen (like an Up or Charm quark) while staying neutral. In the rulebook, this is forbidden, or at least so incredibly rare that it's like winning the lottery every second for a billion years.

However, scientists suspect there might be a hidden layer to this city that the rulebook hasn't written down yet. This paper explores a specific theory called the Three Higgs Doublet Model (3HDM). Think of the "Higgs" as the energy field that gives particles their mass. In our standard rulebook, there is only one "Higgs building." In this new theory, there are three Higgs buildings, creating a much more complex neighborhood.

Here is how the paper breaks down this complex neighborhood using simple analogies:

1. The "Three Higgs" Neighborhood

Imagine the Higgs field isn't just one building, but a complex of three identical-looking towers.

The Problem: If you have three towers, you might expect them to mix up the citizens, causing the Top Quark to accidentally change into a lighter quark (a "Flavour-Changing Neutral Current" or FCNC).
The Solution (The "Z3" Rule): To keep the city orderly, the authors impose a special rule called Natural Flavour Conservation. It's like a strict bouncer at the door of each tower. The bouncer says, "You can only enter Tower 1 if you are a Lepton, Tower 2 if you are a Down-type quark, and Tower 3 if you are an Up-type quark."
The Result: Because of this bouncer, the Top Quark cannot change into a lighter quark at the front door (tree-level). It's strictly forbidden.

2. The Secret Backdoor (Loop Effects)

Even though the front door is locked, the paper asks: Can the Top Quark sneak in through the back?
In the world of quantum physics, particles can take "detours." Instead of going straight from A to B, they can briefly pop into a virtual state, interact with a ghost particle, and come back out. This is called a loop.

In this three-tower model, the Top Quark can take a detour involving the extra Higgs bosons (the ghosts from the other two towers).
These detours allow the Top Quark to change its identity (turn into an Up or Charm quark) and emit a particle like a photon (light), a gluon (strong force), or a Z boson.
The paper calculates how often these "sneaky" detours happen.

3. The Three Scenarios (Mass Hierarchies)

The authors looked at three different ways the "Higgs towers" could be arranged based on their weight (mass). They call these Regular, Medial, and Inverted hierarchies. Think of these as three different ways the three towers could be stacked:

Regular Hierarchy (The Lightest is the Star):
- The lightest tower is the one that looks exactly like the famous 125 GeV Higgs boson we already found.
- The other two towers are heavy and hidden.
- The Finding: In this scenario, the "sneaky" changes are still very rare. The numbers are small, but they are much bigger than the Standard Model predicts. However, they are currently too small for our detectors to see easily.
Medial Hierarchy (The Middle Child is the Star):
- The middle-weight tower is the famous 125 GeV Higgs.
- There is a lighter tower and a heavier tower.
- The Finding: This is the most exciting scenario. Because there is a lighter non-standard Higgs tower, the Top Quark can easily "jump" into it. The paper predicts that the Top Quark could decay into this light, new Higgs boson much more frequently than in the other scenarios.
- The Catch: Some of these predicted rates are getting close to what the next generation of particle colliders (like the High-Luminosity LHC) might be able to detect. It's like the Top Quark is whispering a secret that we might finally hear soon.
Inverted Hierarchy (The Heaviest is the Star):
- The heaviest tower is the famous 125 GeV Higgs.
- There are two lighter towers.
- The Finding: While this setup allows for a lot of "sneaky" changes (because all the new particles are light and accessible), it turns out this specific arrangement doesn't work when you check it against real-world data. The math says it's possible, but the real world (experimental constraints) says "No, this doesn't fit." So, this scenario is ruled out.

4. The Bottom Line

The paper concludes that while we haven't seen these rare Top Quark changes yet, the Three Higgs Doublet Model offers a very promising place to look.

If the universe follows the Medial Hierarchy rules, the Top Quark might be decaying into new, light Higgs particles at a rate that our future machines could catch.
The study acts like a map, showing scientists exactly where to look and what to expect. It tells them: "Don't just look for the standard particles; look for these specific 'sneaky' decays involving new, light Higgs bosons."

In short, the paper says: "We built a model with three Higgs fields. We checked the rules, and while the Top Quark is mostly well-behaved, it has a secret backdoor that might let it change into lighter quarks more often than we thought. If we look closely enough at the 'middle-weight' version of this model, we might finally catch the Top Quark in the act."

Technical Summary: Flavour-Changing Neutral Current Top Decays in the Three Higgs Doublet Model

Problem Statement
While the Standard Model (SM) successfully describes elementary particles, it leaves several phenomenological questions unanswered. Flavour-Changing Neutral Current (FCNC) processes involving the top quark serve as sensitive indirect probes for Beyond the Standard Model (BSM) physics. In the SM, top FCNC decays ( $t \to qX$ , where $q=u,c$ and $X$ is a neutral boson) are absent at tree level and highly suppressed at the one-loop level by the Glashow-Iliopoulos-Maiani (GIM) mechanism, yielding branching ratios in the range of $10^{-17}$ to $10^{-12}$ . Current experimental limits from the LHC are orders of magnitude above these predictions, leaving room for new physics contributions. This work investigates these rare decays within the framework of the democratic Three Higgs Doublet Model (3HDM), a model featuring an extended scalar sector with three CP-even, two CP-odd, and four charged Higgs bosons.

Methodology
The authors analyze the 3HDM with a $Z_3$ -symmetric scalar potential and Natural Flavour Conservation (NFC) enforced via a democratic Yukawa structure. This structure ensures that each Higgs doublet couples to a specific fermion type, eliminating tree-level FCNCs while allowing for significant loop-level contributions.

Model Definition: The scalar sector is defined by three doublets $\Phi_{1,2,3}$ with a $Z_3$ symmetry. The model is parameterized by vacuum expectation values (VEVs) $v_{1,2,3}$ , mixing angles ( $\alpha_{1,2,3}$ for CP-even, $\theta$ for CP-odd, $\gamma$ for charged), and scalar masses. The study focuses on three distinct "alignment-limit" scenarios corresponding to different mass hierarchies among the CP-even states ( $H_1, H_2, H_3$ ):
- Regular Hierarchy: $H_1$ is the SM-like Higgs ( $\sim 125$ GeV).
- Medial Hierarchy: $H_2$ is the SM-like Higgs.
- Inverted Hierarchy: $H_3$ is the SM-like Higgs.
Calculation Framework: The model was implemented in SARAH to generate FeynArts-compatible files. One-loop amplitudes for $t \to qX$ (with $X = \gamma, g, Z, H_{1,2,3}, A_{2,3}$ ) were generated and evaluated analytically using FormCalc and numerically with LoopTools. Branching ratios were computed relative to a top quark total width of $\Gamma_t = 1.42$ GeV.
Parameter Scan and Constraints: A multidimensional parameter scan was performed using Sobol quasi-random sequences. Points were filtered by:
- Theoretical Consistency: Vacuum stability, perturbativity of couplings ( $|\lambda| \le 4\pi$ ), and tree-level unitarity (scattering matrix eigenvalues $< 8\pi$ ).
- Experimental Constraints: Electroweak precision tests (oblique parameters $S, T, U$ ), direct LHC/LEP/Tevatron exclusion limits on new scalars, Higgs signal strength measurements (requiring the SM-like state to match 125 GeV properties), and the branching ratio of $B \to X_s \gamma$ .

Key Contributions and Results

Regular Hierarchy ( $H_1 \approx 125$ GeV):
- Experimental constraints (particularly oblique parameters) force the extra scalars to be nearly mass-degenerate, suppressing loop contributions.
- Predicted branching ratios for $t \to q\gamma$ and $t \to qg$ in the theoretically allowed region range from $10^{-13}$ to $10^{-9}$ .
- Upon applying experimental constraints ('T+E'), these values are reduced by 2–4 orders of magnitude, remaining well below current LHC limits ( $BR \lesssim 10^{-4}$ ).
- The $t \to qH_1$ channel shows a wide variation ( $10^{-19}$ to $10^{-8}$ ), probing the degree of alignment.
Medial Hierarchy ( $H_2 \approx 125$ GeV):
- This scenario allows for lighter non-SM scalars ( $H_1, A_2, A_3$ ) that are not subject to the same alignment suppression as the SM-like state.
- The $t \to qH_1$ channel can reach branching ratios as high as $O(10^{-1})$ in the theory-only scan, driven by sizeable Yukawa couplings and lack of alignment suppression.
- Experimental constraints significantly reduce these rates (typically to $O(10^{-13} - 10^{-9})$ ), but the $t \to qH_1$ mode remains a distinct signature compared to the regular hierarchy.
- The $t \to qA_2$ channel becomes kinematically forbidden in the 'T+E' scan due to mass constraints, while $t \to qA_3$ remains accessible but suppressed.
Inverted Hierarchy ( $H_3 \approx 125$ GeV):
- No region of the parameter space satisfies both theoretical and experimental constraints simultaneously. The tension arises from the large mass splittings required between the heavy SM-like state and lighter scalars, which violate electroweak precision tests.
- However, the theoretically allowed region ('T') serves as a benchmark, showing that if all neutral scalars are kinematically accessible (masses $< m_t$ ), branching ratios for $t \to qH_{1,2}$ can approach $O(10^{-4})$ .

Significance and Conclusions
The paper concludes that FCNC top decays are a powerful probe of the extended scalar sector in the 3HDM. The study highlights that:

Alignment and Hierarchy Matter: The predicted branching ratios are heavily dependent on the mass hierarchy of the CP-even scalars and the specific alignment limit. The SM-like Higgs remains aligned with the electroweak vacuum, suppressing its FCNC couplings, while non-SM scalars carry the complementary interactions that drive the loop-induced rates.
Sensitivity to Light Scalars: Scenarios with a medial hierarchy, featuring light non-standard scalars, can yield branching ratios significantly exceeding SM expectations. While current experimental limits are not yet violated, the predicted rates for channels like $t \to qH_1$ in viable regions are within the projected sensitivity of the High-Luminosity LHC (HL-LHC).
Future Prospects: The results suggest that rare top decays into non-SM scalar states offer a promising discovery channel for the 3HDM. Future collider experiments, particularly the HL-LHC and next-generation hadron colliders, will be capable of probing the phenomenologically viable regions of the parameter space identified in this work, providing crucial insights into the structure of the scalar sector and electroweak symmetry breaking.

1. The "Three Higgs" Neighborhood

2. The Secret Backdoor (Loop Effects)

3. The Three Scenarios (Mass Hierarchies)

4. The Bottom Line

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