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Baryogenesis and EDMs in the 2HDM with a Complex Singlet

This paper presents the first joint analysis of baryogenesis via Higgsogenesis and electric dipole moments in a two-Higgs-doublet model with a complex singlet and Majorana fermion, demonstrating that resonant enhancement allows for successful baryogenesis at singlet masses as low as $10^5$ GeV while simultaneously generating observable EDM signals without requiring a first-order electroweak phase transition.

Original author: Björn Garbrecht, Edward Wang

Published 2026-11-06

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CC BY 4.0

Original author: Björn Garbrecht, Edward Wang

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 author. For technical accuracy, refer to the original paper. Read full disclaimer

The universe we see today is made of matter: stars, planets, and the people who look up at them. Yet, according to the most basic laws of physics that govern the birth of the cosmos, matter and its mirror image, antimatter, should have been created in equal amounts. If that had happened, they would have annihilated each other instantly, leaving behind a universe filled only with light. The fact that we exist means that at some point in the early history of the universe, a tiny imbalance tipped the scales, allowing a small surplus of matter to survive. Physicists call this process baryogenesis. To understand how it happened, they look for sources of a specific kind of symmetry breaking called CP violation, which essentially means that nature treats certain processes differently from their mirror images. While the known laws of physics contain a small amount of this effect, it is far too weak to explain the abundance of matter we observe. This gap suggests that new, undiscovered particles or forces must have been at work in the hot, dense moments after the Big Bang.

A team of researchers at the Technical University of Munich and the Max Planck Institute for Physics has proposed a new scenario to fill this gap. They studied a theoretical model that extends the Standard Model of particle physics by adding two new types of particles: a complex scalar field, which is a type of energy field similar to the one that gives particles mass, and a heavy fermion, a type of matter particle that behaves like its own antiparticle. In their scenario, the story of how matter came to dominate begins with the decay of a heavy, unstable particle known as a singlet. As this particle breaks apart in the early universe, it does not decay evenly. Instead, it creates a slight imbalance between two different versions of the Higgs field, the fields responsible for giving particles mass. This initial imbalance is then passed along to other particles through standard interactions.

The process continues in two further stages. First, the imbalance is transferred to a specific type of charge known as B minus L, which relates to the difference between the number of matter particles and antiparticles. This transfer is mediated by the heavy fermion mentioned earlier, which acts as a bridge between the initial imbalance and the matter we see today. Finally, a natural process in the early universe, involving the weak nuclear force, converts this B minus L charge into a surplus of ordinary matter. The researchers performed detailed numerical simulations to see if this chain of events could actually produce the amount of matter we observe today. They found that it can, provided that the heavy singlet particle has a mass as low as 100,000 gigaelectronvolts. This is a significant finding because it allows for the creation of matter at energy scales much lower than many other theories require, largely due to a resonant effect that amplifies the initial imbalance, much like pushing a swing at just the right moment makes it go higher.

A crucial part of this work is that the researchers did not just look at how matter was created; they also checked if their model leaves any traces that we could detect today. Any theory that introduces new sources of asymmetry often predicts that particles should have a tiny separation between their positive and negative electric charges, a property known as an electric dipole moment. The team calculated the expected size of these moments for electrons and neutrons within their model. They discovered that for certain settings of their model, the predicted electric dipole moments are large enough to be detected by current or near-future experiments. This creates a powerful link between the origin of the universe and laboratory measurements: if the universe was created this way, we should see specific signals in our detectors.

The study also clarifies what is not required for this scenario to work. Unlike many other theories that rely on a violent, first-order phase transition in the early universe—a kind of cosmic boiling or freezing event—this mechanism works smoothly through the decay of particles. This removes a major hurdle that has constrained other models. The researchers found that while the model can successfully explain the existence of matter, it also predicts that the electric dipole moments of neutrons could be just below the limits of what current experiments can measure. This means that the next generation of sensitive instruments, which are currently being built, could either confirm this picture of the universe's origin or rule it out. The work suggests that the same physics that tipped the scales in favor of matter billions of years ago might be waiting to be revealed in a laboratory experiment within our lifetime.

Technical Summary: Baryogenesis and EDMs in the 2HDM with a Complex Singlet

Problem Statement
The Standard Model (SM) contains a confirmed source of CP violation via the CKM matrix, yet its contribution to permanent electric dipole moments (EDMs) of the electron and neutron is several orders of magnitude below current experimental sensitivities. Furthermore, the SM fails to explain the observed baryon asymmetry of the universe (BAU). While electroweak baryogenesis (EWBG) in extensions like the Two-Higgs-Doublet Model (2HDM) or the MSSM links the CP-violating phases required for baryogenesis to large EDM signals, these scenarios are now strongly constrained by LHC data and EDM searches. Previous proposals involving "Higgsogenesis" (generating asymmetry in the Higgs sector) often require specific 2HDM types (Type-I or Type-X) or a first-order electroweak phase transition to avoid washout by Yukawa interactions. This paper addresses the challenge of generating the BAU and predicting observable EDMs in a Type-II 2HDM extended by a complex scalar singlet and a Majorana fermion, without relying on a first-order phase transition.

Methodology
The authors propose a three-step baryogenesis mechanism within a model extending the SM with a second Higgs doublet ( $\phi_2$ ), a complex scalar singlet ( $S$ ), and a Majorana fermion ( $N$ ). The analysis proceeds through the following stages:

Model Construction: The scalar potential includes general quartic and cubic interactions between the doublets and the singlet. A $Z_2$ symmetry is imposed to suppress flavor-changing neutral currents (FCNCs), softly broken by mass mixing terms ( $\mu_{12}$ ) and singlet-doublet couplings ( $\kappa_{4-7}$ ). The model assumes a large mass hierarchy between the doublet and singlet sectors.
Kinetic Equations and CTP Formalism: The generation of the initial CP asymmetry is modeled using Closed-Time-Path (CTP) formalism. The authors derive momentum-averaged kinetic equations for the singlet abundance and the charge asymmetry between the two Higgs doublets ( $\phi_1 - \phi_2$ $ϕ_{1} - ϕ_{2}$ ).
- Source Terms: The CP-violating source arises primarily from wavefunction-type diagrams involving the mixing of the singlet states. Due to the small decay width of the singlet (dominated by scalar interactions rather than gauge interactions), the source is resonantly enhanced when the singlet mass eigenstates are quasi-degenerate.
- Washout: The analysis includes washout terms from inverse decays and $2 \to 2$ scattering processes mediated by off-shell singlets.
Chemical Potential Analysis: The authors track the evolution of chemical potentials across different temperature regimes ( $10^6$ GeV to $10^{15}$ GeV). They account for the equilibration of various SM spectator processes (sphalerons, Yukawa interactions) to determine how the initial Higgs charge asymmetry is converted into a $B-L$ charge and subsequently into a baryon number ( $B$ ) via weak sphalerons.
EDM Calculation: The paper calculates two-loop Barr-Zee type contributions to the electron and neutron EDMs. The neutron EDM is derived from quark EDMs and chromo-EDMs (CEDMs) using QCD sum rules. The calculation utilizes a code adapted from previous literature to handle the extended scalar sector.
Numerical Scan: A numerical analysis is performed with 1000 random parameter sets. The scan varies singlet masses ( $10^4$ – $10^{10}$ GeV), mixing angles, and cubic couplings, while fixing doublet masses and mixing angles to values consistent with LHC data (alignment limit).

Key Contributions

Novel Mechanism: The paper presents a joint analysis of baryogenesis and EDMs in a 2HDM + singlet + Majorana fermion framework. Unlike standard EWBG, this mechanism relies on out-of-equilibrium decays of a heavy singlet to generate an initial asymmetry between Higgs doublets, which is then transferred to fermions and converted to $B-L$ via Majorana interactions.
Resonant Enhancement: The authors demonstrate that the CP-violating source is resonantly enhanced due to the quasi-degeneracy of the singlet mass eigenstates. This allows for successful baryogenesis even with relatively light singlet masses ( $\sim 10^5$ GeV), a regime where standard thermal leptogenesis might struggle without quasi-degenerate neutrinos.
Type-II Viability: The mechanism is shown to work for Type-II 2HDMs. By ensuring the transfer of asymmetry to a $B-L$ charge occurs before the up-quark Yukawa interactions fully equilibrate the Higgs charges, the model avoids the washout issues that typically plague Type-II Higgsogenesis scenarios.
Joint Constraints: The study provides the first combined numerical analysis linking the baryon asymmetry to EDM constraints in this specific out-of-equilibrium decay scenario.

Results

Baryogenesis: The numerical results indicate that the observed baryon asymmetry ( $\eta_B \approx 6.04 \times 10^{-10}$ ) can be reproduced for singlet masses as low as $10^5$ GeV. This is attributed to the resonant enhancement of the CP source, which compensates for the lower mass scale.
EDM Signals: The model predicts significant contributions to both electron and neutron EDMs. The contributions are dominated by the Higgs kinetic terms.
Correlation: A negative correlation is observed between the magnitude of the EDMs and the resulting baryon asymmetry. Large cubic couplings required for large EDMs also induce large washout terms, which can deplete the asymmetry. However, the authors identify specific parameter sets that satisfy the baryogenesis requirement while producing EDM signals close to, but currently below, experimental bounds (JILA for electrons, PSI for neutrons).
Mass Constraints: The analysis suggests that for the model to produce the correct BAU, the Majorana fermion must equilibrate at temperatures above $\mathcal{O}(10^6)$ GeV to prevent the washout of the $C_\lambda$ charge by up-quark Yukawa interactions.

Significance
The paper claims that this scenario offers a new perspective on interpreting observational bounds in terms of cosmology. It establishes a direct link between CP violation in the Higgs sector and EDM signals without requiring the additional assumption of a first-order electroweak phase transition. The authors emphasize that the mechanism allows for baryogenesis at lower mass scales ( $10^5$ GeV) than typically expected in resonant leptogenesis scenarios, and that future improvements in EDM sensitivity (e.g., at Imperial College and PSI) could probe the viable parameter space of this model. The work demonstrates that baryogenesis and EDM constraints can be simultaneously satisfied in a 2HDM with a complex singlet, providing a testable framework for physics beyond the Standard Model.

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