⚛️ phenomenology

The Higgs boson decay $h \to bs$ in the Generational Three-Higgs-Doublet Model

This paper presents a systematic analysis of the flavor-changing Higgs decay $h \to bs$ within the Generational Three-Higgs-Doublet Model (G3HDM), evaluating its viability against current experimental constraints and highlighting its potential as a sensitive probe for new physics.

Original authors: Hao-Ran Ma, Ti-Bin Hou, Jin-Lei Yang, Tai-Fu Feng

Published 2026-08-18

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CC BY 4.0

Original authors: Hao-Ran Ma, Ti-Bin Hou, Jin-Lei Yang, Tai-Fu Feng

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

In the universe of particle physics, the Higgs boson is the most famous particle discovered in recent decades. It is the manifestation of an invisible field that fills all of space, giving mass to other fundamental particles. Since its discovery, scientists have been meticulously measuring how it behaves, checking if it acts exactly as the Standard Model—the current best theory of how the universe works—predicts it should. So far, it has behaved with remarkable consistency. However, physicists remain eager to find cracks in this perfect picture. One specific area of interest is whether the Higgs boson can change the "flavor" of a particle as it decays. In the standard theory, the Higgs should almost never turn a bottom quark into a strange quark; if it does, it happens so rarely that it is effectively invisible. But if the Higgs were to do this more often, it would be a clear sign that new, undiscovered physics is at work.

A team of researchers has recently explored this possibility within a specific theoretical framework called the Generational Three-Higgs-Doublet Model. This model suggests that the universe might contain not just one Higgs field, but three, each interacting with different generations of matter particles. In this scenario, the Higgs boson could interact with quarks in a way that allows it to transform a bottom quark into a strange quark directly, rather than through the slow, complex loops required by the standard theory. The researchers set out to calculate how often this transformation might happen in their model and whether it could be detected by future experiments. They had to be careful, however, because this same model also predicts effects on other particles, such as B-mesons, which have been measured with high precision. If the model predicted too many changes in those other particles, it would be ruled out by existing data.

The team performed a massive numerical simulation, testing millions of possible combinations of parameters within their model to see which ones survived the strict constraints of current experimental data. They checked the model against measurements of the Higgs boson's known signals, the precision of electroweak forces, and the rare decay rates of B-mesons. After filtering out every scenario that contradicted what we already know, they found that a significant portion of the model's possibilities remained valid. In these surviving scenarios, the Higgs boson could indeed decay into a bottom quark and a strange quark with a frequency roughly ten thousand times higher than what the standard theory predicts. This is a massive enhancement, pushing the probability of this event from a near-impossible one-in-a-billion chance to a level that might be observable.

The researchers then investigated the source of this dramatic increase. They broke down the calculation to see which parts of the model were driving the result. They discovered that the large number of events was not caused by the complex loops of particles that usually dominate such calculations in other theories. Instead, the effect was driven by a direct, tree-level interaction, a fundamental coupling between the Higgs and the quarks that exists naturally in this three-Higgs model. The strength of this interaction depends on how the three Higgs fields are arranged and how heavy the new, heavier Higgs particles predicted by the model are. Specifically, the effect is strongest when the new heavy particles are relatively light and when the mathematical terms describing the interaction between the Higgs fields are large.

This finding is significant because it offers a concrete target for future experiments. The researchers mapped out how much of their model's valid parameter space could be tested by upcoming colliders. They found that while current experiments at the Large Hadron Collider are not sensitive enough to see this signal, future machines like the Circular Electron Positron Collider (CEPC) or the Future Circular Collider (FCC-ee) could potentially detect it. If these future experiments reach a sensitivity where they can spot this decay in about one out of every ten thousand Higgs bosons, they would be able to test a small but meaningful fraction of the remaining valid scenarios. If they can reach a sensitivity of one in one hundred thousand, they could probe half of the model's allowed possibilities.

The study concludes that the Generational Three-Higgs-Doublet Model is not dead; it is still alive and hiding in the data, waiting for more precise tools to find it. The fact that the Higgs boson could transform a bottom quark into a strange quark at such a high rate is a direct consequence of the model's structure, specifically the way the different Higgs fields mix and misalign. This misalignment creates a pathway for the flavor change that the standard model forbids. While the researchers cannot say for certain that this model is the correct description of nature, they have shown that it is a viable possibility that has not been ruled out. The search for this specific decay, h to b and s, is now a critical test. If future experiments observe it, it would be a smoking gun for new physics, revealing that the Higgs sector is far more complex and rich than we currently believe. If they do not, it will place even tighter limits on these theories, forcing physicists to look elsewhere for answers.

Technical Summary: The Higgs boson decay $h \to b\bar{s}$ in the Generational Three-Higgs-Doublet Model

Problem Statement
The Standard Model (SM) predicts that the flavor-changing neutral current (FCNC) decay of the Higgs boson, $h \to b\bar{s}$ , is highly suppressed, occurring only at the loop level with a branching ratio of $\mathcal{O}(10^{-7})$ . Consequently, any experimental observation of this decay with a significantly larger rate would serve as a sensitive probe for physics beyond the Standard Model (BSM). While the Large Hadron Collider (LHC) faces challenges in distinguishing $s$ -quark jets from $d$ -quark jets and $b$ -jets due to QCD backgrounds, future colliders like the International Linear Collider (ILC) offer the potential for sub-percent level sensitivity. The Generational Three-Higgs-Doublet Model (G3HDM) extends the SM scalar sector by introducing three Higgs doublets that couple separately to different generations of fermions. This structure allows for tree-level FCNCs, potentially enhancing the $h \to b\bar{s}$ decay rate, but simultaneously introduces constraints from neutral-meson mixing and rare $B$ -meson decays.

Methodology
The authors perform a systematic phenomenological analysis of the $h \to b\bar{s}$ process within the G3HDM framework. The study involves:

Theoretical Framework: The model is defined by three Higgs doublets ( $\Phi_1, \Phi_2, \Phi_3$ ) with a softly broken $U(1)^3$ symmetry. The Yukawa textures are constructed such that each doublet couples predominantly to a specific generation of fermions, addressing the flavor hierarchy. The scalar potential includes CP-conserving terms, and the physical spectrum consists of three CP-even scalars ( $h, H, H'$ ), two CP-odd scalars ( $A_{min}, A_{max}$ ), and two pairs of charged Higgs bosons ( $H^\pm_{min}, H^\pm_{max}$ ).
Amplitude Calculation: The decay amplitude for $h \to b\bar{s}$ is computed including contributions from tree-level FCNCs, neutral-Higgs loops, charged-Higgs loops, and $W$ -boson loops. The calculation utilizes Passarino–Veltman scalar functions for loop integrals.
Constraint Implementation: A comprehensive set of experimental and theoretical constraints is imposed on the parameter space:
- Higgs Signal Strengths: Measurements of the 125 GeV Higgs boson signal strengths ( $\mu_{\gamma\gamma}, \mu_{WW^*}, \mu_{ZZ^*}, \mu_{b\bar{b}}, \mu_{\tau\tau}$ ) at the LHC.
- Electroweak Precision Observables: Constraints on the $S, T, U$ parameters.
- Flavor Physics: Neutral-meson mixing observables ( $\Delta M_{B_d}, \Delta M_{B_s}, \Delta M_K, \epsilon_K$ ) and rare decays ( $\bar{B} \to X_s \gamma$ and $B^0_s \to \mu^+\mu^-$ ).
Numerical Analysis: A Monte Carlo scan is performed over the model's parameter space (including quartic couplings $\lambda_i$ , mixing angles $\beta, \beta'$ , and scalar masses). The surviving parameter points are analyzed using Spearman rank-correlation coefficients to identify monotonic dependencies between the branching ratio $\text{BR}(h \to b\bar{s})$ and model parameters. The decay amplitude is decomposed to isolate the dominant dynamical contributions.

Key Contributions and Results

Enhanced Branching Ratio: Despite the stringent constraints from flavor physics and Higgs signal strengths, the analysis demonstrates that the branching ratio $\text{BR}(h \to b\bar{s})$ in the G3HDM can reach values up to $\sim 10^{-3}$ . This represents an enhancement of approximately four orders of magnitude compared to the SM prediction ( $\sim 8.9 \times 10^{-8}$ ).
Dominance of Tree-Level FCNC: Decomposition of the decay amplitude reveals that the large branching ratio is predominantly driven by the tree-level FCNC interaction mediated by the lightest neutral Higgs boson ( $h$ ), rather than by loop diagrams involving charged Higgs bosons or $W$ bosons. The interference between different contributions is found to be predominantly destructive (reducing the incoherent sum by $\sim 10\text{--}20\%$ ), but the tree-level term remains the primary driver.
Scalar Misalignment Mechanism: The study identifies the scalar misalignment parameter, $\Delta^h_{23} = v \left( \frac{Z^H_{hH}}{v_2} - \frac{Z^H_{hH'}}{v_3} \right)$ $Δ_{23}^{h} = v (\frac{Z _{h H}^{H}}{v _{2}} - \frac{Z _{h H^{'}}^{H}}{v _{3}})$ , as the key quantity controlling the effective FCNC Yukawa coupling $Y^h_{\text{FCNC}}$ $Y_{FCNC}^{h}$ .
- A strong correlation is found between $\text{BR}(h \to b\bar{s})$ and the combination of quartic couplings $|\lambda_6 + \lambda_9|$ (positive correlation) and the mass of the lightest charged Higgs $M_{H^\pm_{min}}$ (negative correlation).
- The enhancement mechanism is traced to the relation $|\Delta^h_{23}| \simeq \frac{v^2 |2\lambda_3 - \lambda_6 - \lambda_9|}{M^2_{H^\pm_{min}}}$ . A large scalar-potential combination and a light charged Higgs mass scale enhance the misalignment, thereby increasing the tree-level FCNC coupling.
Experimental Testability: The authors map the surviving parameter space against projected sensitivities of future colliders.
- The median branching ratio in the allowed space is $\sim 1.6 \times 10^{-5}$ .
- Future experiments like CEPC (sensitivity $\sim 3.0 \times 10^{-4}$ ) and FCC-ee (sensitivity $\sim 9.6 \times 10^{-4}$ ) can probe the high-end tail of the distribution (covering $\sim 5.8\%$ and $\sim 0.2\%$ of the parameter space, respectively).
- To test at least 50% of the allowed parameter space, a sensitivity of $\text{BR} \lesssim 1.6 \times 10^{-5}$ would be required.

Significance and Claims
The paper claims that the G3HDM provides a viable mechanism to significantly enhance the $h \to b\bar{s}$ decay rate to levels potentially observable at future high-precision colliders, without violating current experimental bounds from flavor physics and Higgs measurements. The study clarifies that the enhancement is a tree-level effect arising from scalar misalignment, distinct from the loop-induced enhancements often discussed in other BSM scenarios. The authors emphasize that while current LHC data cannot probe this process effectively due to background limitations, the decay $h \to b\bar{s}$ serves as a complementary and sensitive probe for the extended Higgs sector and tree-level flavor-changing interactions in the G3HDM. The work underscores that a significant portion of the model's parameter space remains accessible to future experimental efforts, particularly if sensitivities reach the $10^{-5}$ level.

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