⚛️ phenomenology

Phenomenology of Spontaneous CP-violation in 2HDMs

This paper investigates spontaneous CP violation in the Two-Higgs-Doublet Model with non-decoupling Higgs bosons and flavor misalignment, demonstrating that viable parameter spaces allow for significant deviations in Higgs couplings and distinctive LHC signatures like same-sign top production, thereby highlighting the necessity of combining precision Higgs measurements with direct searches and flavor experiments to probe this scenario.

Original authors: Tanmoy Mondal, Kei Yagyu

Published 2026-10-20

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Tanmoy Mondal, Kei Yagyu

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

The universe is built on a delicate balance between matter and antimatter, a symmetry that should have caused them to annihilate each other completely in the moments after the Big Bang. Yet, we exist, a testament to a subtle imbalance known as CP violation, where the laws of physics treat particles and their mirror-image antiparticles slightly differently. For decades, physicists have understood this imbalance as a fixed feature of the universe, a complex phase embedded in the way quarks interact. However, the origin of this asymmetry remains a mystery. One compelling idea suggests that this imbalance was not written into the laws of physics from the start, but rather emerged spontaneously, much like a magnet choosing a north pole when it cools down. This concept, called spontaneous CP violation, proposes that the vacuum of space itself holds a hidden phase that breaks the symmetry, potentially offering a deeper explanation for why the universe is made of matter.

To explore this possibility, researchers Tanmoy Mondal and Kei Yagyu investigated a specific theoretical framework known as the two-Higgs-doublet model. In the standard model of particle physics, there is only one Higgs field, which gives mass to other particles. This new model introduces a second Higgs field, doubling the complexity and the potential for new phenomena. The researchers focused on a scenario where the vacuum expectation values of these two fields develop a relative complex phase, creating the necessary conditions for spontaneous CP violation. A crucial feature of their work is that this setup prevents the new, heavier Higgs particles from becoming too heavy to detect. Unlike other theories where new particles can hide at impossibly high energies, here they are forced to remain within a reachable range, making them accessible to current and future particle colliders.

The team constructed a detailed map of the possible interactions allowed by this model, paying close attention to how these new Higgs particles talk to quarks. To match the known behavior of the universe, they had to ensure that the model could reproduce the observed mixing of quark types, known as the Kobayashi-Maskawa phase. They found that this requirement forces the model to allow for "flavor misalignment," meaning the new Higgs particles can change one type of quark into another in ways the standard model does not. Specifically, they identified a significant interaction between the top quark, the heaviest known particle, and the charm quark. This interaction is not just a minor detail; it is a central prediction that leads to unique and dramatic signatures in particle collisions.

By running extensive computer simulations and applying a rigorous set of constraints, the authors filtered out impossible scenarios. They checked their results against theoretical limits on stability and against a wide array of experimental data, including measurements of how particles decay, the precision of electroweak forces, and the absence of certain electric dipole moments that would signal new sources of asymmetry. Despite these tight restrictions, they discovered that a large region of the parameter space remains viable. In this surviving landscape, the interaction between the top and charm quarks can be surprisingly strong, opening the door to distinctive events at the Large Hadron Collider.

The most striking consequence of this surviving scenario is the potential production of same-sign top quarks. In a typical collision, top quarks are produced in pairs of opposite charge. However, the flavor-violating interactions in this model allow for processes where two top quarks of the same charge are created simultaneously. This would result in a rare and clean signal: two positively charged leptons or two negatively charged leptons appearing in the detector, accompanied by other particles. The researchers calculated that the High-Luminosity upgrade of the Large Hadron Collider, which will operate with significantly more data than current runs, could probe a substantial portion of this allowed space. If such events are observed, they would provide direct evidence for the flavor-violating nature of the new Higgs bosons.

Beyond these direct searches, the study revealed a deep connection between the new particles and the properties of the Higgs boson already discovered. The model predicts that the new Higgs particles, even if they are heavy, leave a permanent imprint on the behavior of the known Higgs. Specifically, the rate at which the known Higgs decays into two photons or a photon and a Z boson is predicted to be lower than the standard model expectation, by about ten percent and four percent respectively. Furthermore, the strength of the interaction between three Higgs bosons, a property known as the trilinear self-coupling, could be altered by as much as one hundred percent. These deviations do not vanish even if the new particles are very heavy, a behavior known as non-decoupling, which makes them a robust target for precision measurements.

The researchers also mapped out how the new Higgs particles would decay. They found that the heavier neutral Higgs bosons would predominantly decay into a top quark and a charm quark, reinforcing the signature of flavor violation. However, depending on the mass differences between the new particles, these heavy bosons could also decay into lighter Higgs bosons and W or Z bosons, creating a cascade of particles. The study showed a clear correlation: the size of the deviation in the Higgs self-coupling is directly linked to the specific decay patterns of the new particles. This means that by measuring the properties of the known Higgs boson with high precision, scientists could indirectly learn about the mass spectrum and decay habits of the undiscovered ones.

Ultimately, this work demonstrates that the search for the origin of matter-antimatter asymmetry is not a single-track endeavor. It requires a combined approach, looking simultaneously for the direct production of new particles, the rare decays of the known Higgs, and the subtle shifts in how these particles interact. The study confirms that if spontaneous CP violation is the key to the universe's asymmetry, the Large Hadron Collider has a real chance of finding it, provided the detectors are sensitive enough to catch the rare same-sign top quarks and precise enough to measure the slight deviations in the Higgs boson's behavior. The path forward is clear: a coordinated effort to measure the known with extreme precision while hunting for the unknown in the most energetic collisions humanity can create.

Technical Summary: Phenomenology of Spontaneous CP-violation in 2HDMs

Problem and Motivation
The origin of CP violation (CPV) remains an open question in the Standard Model (SM), where it arises explicitly from the complex phase in the quark Yukawa sector. Spontaneous CP violation (SCPV), where CP is broken by the vacuum structure rather than explicit terms in the Lagrangian, offers a dynamical alternative. While SCPV was first proposed by T. D. Lee in the Two-Higgs-Doublet Model (2HDM), reproducing the observed Kobayashi–Maskawa (KM) phase within this framework presents a specific challenge: it requires flavor misalignment in the Yukawa sector, which typically induces dangerous tree-level flavor-changing neutral currents (FCNCs). Furthermore, the SCPV scenario in 2HDMs inherently forbids a decoupling limit; the additional Higgs bosons cannot be arbitrarily heavy without violating perturbative unitarity or vacuum stability, as their masses are tied to the electroweak scale via the quartic couplings. This paper investigates the collider phenomenology of such a non-decoupling SCPV 2HDM, focusing on the interplay between flavor-violating interactions, precision Higgs measurements, and direct searches for additional Higgs bosons.

Methodology
The authors analyze a general 2HDM where the Higgs potential parameters and Yukawa matrices are real in a specific basis, with CP violation arising solely from the relative complex phase $\xi$ between the vacuum expectation values (VEVs) of the two doublets. To accommodate the observed KM phase while suppressing FCNCs in the down-type quark and charged-lepton sectors, the authors impose a "partial Yukawa alignment" scenario:

Alignment: The down-type quark and charged-lepton Yukawa matrices are flavor-aligned, rendering $\rho_d$ and $\rho_e$ flavor-diagonal.
Misalignment: The up-type quark Yukawa matrices remain general, allowing for flavor-violating interactions in the up sector. This structure naturally generates the KM phase through the spontaneous breaking of CP.

The study employs a random scan over the model's parameter space (including Higgs masses, mixing angles, and Yukawa parameters) within the Higgs alignment limit (where the discovered 125 GeV Higgs boson $h$ has SM-like tree-level couplings). The viable parameter space is constrained by:

Theoretical constraints: Vacuum stability (boundedness from below), perturbative unitarity, and perturbativity of quartic couplings.
Experimental constraints: Electroweak precision observables ( $S$ and $T$ parameters), flavor measurements ( $B_d$ - $\bar{B}_d$ , $B_s$ - $\bar{B}_s$ , $D^0$ - $\bar{D}^0$ mixing, and $b \to s\gamma$ ), electric dipole moments (specifically the electron EDM via Barr-Zee diagrams), and LHC direct search limits on additional Higgs bosons and flavor-violating processes.

Key Contributions and Results

Non-Decoupling Effects in Precision Observables:
The study confirms that the non-decoupling nature of the additional Higgs bosons leads to significant deviations in SM-like Higgs properties, even in the alignment limit.
- Loop-induced decays: The decay rates $h \to \gamma\gamma$ and $h \to Z\gamma$ receive corrections from charged Higgs loops that do not vanish as the charged Higgs mass increases. The authors find these rates can deviate by approximately $-10\%$ and $-4\%$ , respectively, from SM predictions.
- Trilinear Self-Coupling: The trilinear Higgs self-coupling $\lambda_{hhh}$ receives one-loop corrections scaling as $m_\phi^4/v^3$ . This allows for $\mathcal{O}(100)\%$ corrections to the SM value, providing a direct probe of the SCPV mechanism.
Flavor-Violating Signatures:
The partial alignment scenario permits sizable flavor-violating Yukawa couplings in the up-type sector, specifically the top-charm coupling ( $\rho_{tc}$ ).
- Production and Decay: The flavor-violating coupling $\rho_{tc}$ drives the associated production of additional neutral Higgs bosons ( $H_2, H_3$ ) with a top quark ( $cg \to tH_{2,3}$ ).
- Distinctive Signatures: The subsequent decay $H_{2,3} \to t\bar{c} + \bar{t}c$ leads to same-sign top-quark pairs ($tt$ or $\bar{t}\bar{t}$ ) and three-top final states. The paper identifies same-sign dilepton events as a promising signature with low SM background.
- Charged Higgs: The model also predicts enhanced production of charged Higgs bosons in association with top and bottom quarks ( $pp \to tbH^\pm$ ) or charm and bottom quarks ( $pp \to cbH^\pm$ ), depending on the mass hierarchy and coupling strengths.
Correlations between Precision and Direct Searches:
A central finding is the correlation between the deviation in the trilinear Higgs self-coupling ( $\Delta \kappa_\lambda$ ) and the decay patterns of the additional neutral Higgs bosons.
- Regions with hierarchical mass spectra (e.g., $m_{H_3} \gg m_{H_2}$ ) that yield large deviations in $\lambda_{hhh}$ also favor specific bosonic cascade decays (e.g., $H_3 \to H_2 Z$ or $H_3 \to H^\pm W^\mp$ ) over fermionic modes.
- This establishes a direct link between precision measurements of the 125 GeV Higgs self-coupling and the branching ratios of heavier Higgs states.
EDM Constraints:
The electron EDM ( $d_e$ ) imposes a stringent constraint on the CP-violating phase. The authors demonstrate that the predicted $d_e$ can be suppressed to satisfy experimental bounds through destructive interference between scalar-loop and top-quark-loop contributions in the Barr-Zee diagrams, achievable by tuning the parameters of the unitary matrix $U_u$ .

Significance
The paper demonstrates that the SCPV 2HDM is a highly constrained but phenomenologically rich scenario. Its significance lies in the necessity of combining multiple experimental frontiers to test it:

Complementarity: Direct searches for flavor-violating signatures (same-sign tops, three-tops) and cascade decays are essential to probe the Yukawa structure, while precision measurements of the Higgs self-coupling and loop-induced decays ( $h \to \gamma\gamma, Z\gamma$ ) probe the non-decoupling scalar sector.
Distinctiveness: The specific correlation between the trilinear coupling deviation and the decay patterns of additional Higgs bosons offers a unique "smoking gun" for SCPV, distinguishing it from other 2HDM scenarios where such correlations may not exist or where decoupling is possible.
Future Prospects: The authors conclude that the High-Luminosity LHC (HL-LHC) has the potential to probe a significant portion of the viable parameter space, particularly through searches for same-sign top-quark production and improved precision on the Higgs trilinear coupling.

In summary, the work establishes that probing the origin of CP violation requires a coordinated effort involving flavor physics, electric dipole moment experiments, precision Higgs measurements, and direct searches for heavy Higgs bosons with distinctive flavor-violating decay modes.

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