Baryon Asymmetry
The origin of baryon asymmetry (the imbalance between matter and antimatter) in the universe is one of the most important unsolved problems in modern particle physics and cosmology. The baryon number is defined as the difference between the baryon number density and the antibaryon number density. In the observable universe, matter overwhelmingly dominates while antimatter is exceedingly scarce. For example, observations of Big Bang Nucleosynthesis (BBN) and the Cosmic Microwave Background (CMB) indicate that when the baryon number is normalized by the photon number density, the baryon‐to‐photon ratio is estimated to be about six parts in ten billion. In other words, even if only a few extra matter particles per ten billion particles existed in the early universe, that slight excess would eventually account for all of the matter present today. The theoretical framework that seeks to answer why matter and antimatter are not symmetric---that is, why such a tiny asymmetry arose---is known as baryogenesis.
In 1967, Andrei Sakharov proposed three necessary conditions for generating a baryon asymmetry. These Sakharov conditions are as follows:
1. Baryon Number Violation:
Reactions that violate baryon number must occur. If baryon number were conserved in all interactions, the observed baryon asymmetry would reflect an asymmetric initial condition. However, any such initial asymmetry would be exponentially diluted by inflation, effectively erasing it, so the baryon asymmetry must be generated after inflation.
2. C and CP Violation:
C (Charge conjugation) symmetry, which exchanges particles and antiparticles, and the combined CP symmetry (particle-antiparticle exchange and spatial inversion) must be violated. If C were conserved, left-handed particles and right-handed antiparticles would be symmetric, and similarly, right-handed particles and left-handed antiparticles would be symmetric. That is, regardless of whether one focuses on left-handed or right-handed states, no asymmetry would arise. Likewise, if CP were conserved, left-handed particles would be symmetric with their antiparticles and right-handed particles would be symmetric with their antiparticles. In such cases, no asymmetry between particles and antiparticles would be generated.
3. Departure from Thermal Equilibrium:
In a situation where thermal equilibrium is maintained, any reaction producing a positive baryon number will naturally be accompanied by the reverse reaction that produces a negative baryon number, thereby canceling the effect. Therefore, a departure from equilibrium is essential.
If all these conditions are met, the universe has the necessary ingredients to generate baryon asymmetry. However, within the framework of the Standard Model (SM) of particle physics, these conditions are not sufficiently satisfied. First, the Standard Model has no renormalizable operator that explicitly violates baryon number, so B is conserved in every perturbative reaction. Non-perturbative electroweak sphalerons do violate B+L; however, they conserve the difference B−L. This means they convert any pre-existing B−L asymmetry into equals shifts of B and L (ΔB=ΔL), rather than creating a new B−L excess from scratch. Because the observed baryon excess requires a net B−L to appear somewhere in the thermal history, and the SM cannot dynamically produce B-L, the SM alone cannot satisfy the first condition.
Moreover, although the SM contains a source of CP violation through the Kobayashi-Maskawa (CKM) phase, this CP violation is extremely small, and calculations show that the baryon asymmetry generated by it is many orders of magnitude (about ten billion times) smaller than observed. Hence, while the second condition is formally met, it is not sufficient. Furthermore, with the parameters of the SM, the electroweak phase transition is not first order but rather a smooth crossover. With a smooth crossover, there is no out-of-equilibrium bubble dynamics, so the third condition is not naturally realized.
For these reasons, to explain the observed baryon asymmetry, one must consider some form of physics beyond the Standard Model (BSM). Below, we describe three representative baryogenesis scenarios in BSM theories---GUT baryogenesis, leptogenesis (LG), and electroweak baryogenesis (EWBG)---detailing their mechanisms and current challenges.
GUT Baryogenesis
Baryogenesis based on Grand Unified Theories (GUTs) is a scenario that is believed to occur in the early universe at ultra-high energy scales (around 10^{15}–10^{16} GeV). GUTs aim to unify the electroweak and strong interactions under a single symmetry, and one of their typical features is the violation of baryon number. Specifically, extremely heavy gauge bosons called X and Y gauge bosons with masses near the unification scale 10^{15}--10^{16} GeV mediate interactions that connect quarks and leptons, and their decays change the baryon number. For example, in an SU(5) GUT the X boson can decay into two quarks (which carry a baryon number of 2/3) or into an anti-quark and an anti-lepton (which carry baryon number –1/3 and lepton number –1, respectively). Because these decays proceed while violating baryon and lepton numbers, the first Sakharov condition is automatically satisfied. Furthermore, GUTs introduce new complex coupling constants (for example, various Yukawa couplings or mass terms) that are absent in the SM, so CP violation arises naturally, satisfying the second condition.
Finally, the third condition---the departure from thermal equilibrium---is naturally realized at the GUT scale. In the hot early universe, X and Y bosons are produced and annihilated in thermal equilibrium, but as the temperature drops below their masses, their equilibrium abundance become Boltzmann suppressed; once the relevant interaction rates fall below the Hubble expansion rate, the species depart from equilibrium and decay. In this way, baryon number can be violated out of equilibrium. Detailed model calculations have shown that the observed baryon asymmetry can indeed be generated under these circumstances.
GUT baryogenesis elegantly explains the origin of baryon asymmetry; however, it faces several problems. First, because the scenario depends on an extremely high energy scale, direct experimental tests are extremely challenging. One prominent prediction of GUTs is proton decay. In simple GUT models such as minimal SU(5), in which the proton lifetime was predicted to be around 10^31 years, but experiments such as Super-Kamiokande have not observed proton decay, with observational lower limits exceeding 10^{34} years. This result either rules out the simplest GUT models or implies that the X boson mass is even higher than expected, rendering proton decay extremely rare. In either case, the non-observation of proton decay strongly constrains the unification scale and the coupling structure of specific GUT realizations. Moreover, in minimal SU(5) the decays conserve B-L, so any asymmetry produced at the GUT scale would be erased by electroweak sphalerons; successful GUT baryogenesis therefore requires mechanisms that generate nonzero B-L (e.g., extended GUTs or additional interactions). Second, the relationship with inflation is problematic. If the universe experienced inflation after the GUT era, any baryon asymmetry generated before inflation would be exponentially diluted. For GUT baryogenesis to succeed, the asymmetry must be generated after inflation and at a reheating temperature high enough to produce the heavy states; if the reheating temperature is below masses of X and Y bosons, thermal GUT baryogenesis is not viable.
Thus, while GUT baryogenesis provides an elegant explanation for the origin of baryon asymmetry, it is challenged both by its dependence on ultra-high energy scales and by the interplay with other early-universe processes. In the future, if proton decay is observed, it would support GUT baryogenesis; conversely, if the experimental lower bound on the proton lifetime is further increased, the model would be even more tightly constrained.
Leptogenesis
Leptogenesis is a scenario in which a lepton asymmetry (typically a negative lepton number) is generated at temperatures typically above 10^9 GeV (up to 10^{12}--10^{13} GeV depending on the model) after inflation, and then partially converted into a baryon asymmetry via sphaleron transitions before the electroweak phase transition. Proposed in the late 1980s by Fukugita and Yanagida, leptogenesis has attracted attention because it links the origin of neutrino masses with the lepton asymmetry of the universe. Sphaleron transitions are nonperturbative processes that occur at temperatures above the electroweak crossover---when the electroweak symmetry is unbroken---and they violate B+L while conserving B–L. Thus, if the universe possesses an excess in B–L, sphaleron processes will partially convert it into baryon number. In the Standard Model, with three lepton flavors and one Higgs doublet, approximately 35% of the lepton asymmetry produced via leptogenesis survives as a net baryon asymmetry. The observed baryon asymmetry requires a B–L excess of roughly 10^{–9}, a magnitude that can feasibly be achieved within the neutrino sector.
How is the lepton asymmetry generated? A typical model introduces heavy right-handed Majorana neutrinos into the Standard Model. The so-called seesaw mechanism endows these right-handed neutrinos with large masses while leaving the left-handed neutrino masses extremely small. The extremely light nature of the SM’s left-handed neutrinos suggests the existence of heavy right-handed neutrinos. In many leptogenesis models, the mass of the right-handed neutrinos is assumed to be at least of order 10^9 GeV and may even reach the GUT scale (~10^{15} GeV). Although right-handed neutrinos interact primarily via Yukawa couplings, they can be gradually produced in the thermal bath during reheating after reheating, and as the temperature decreases, they eventually begin to decay. The right-handed neutrinos have two CP-conjugate decay modes—one producing leptons and the other producing antileptons. Because the decay rates are not equal due to CP-violating effects (see Appendix D of our paper for a one-loop calculation), an asymmetry between the number of leptons and antileptons is generated. At this stage, the net baryon number is still zero; however, sphaleron transitions then convert part of the lepton asymmetry into a baryon asymmetry, leaving a net baryon asymmetry in the universe.
An important test of leptogenesis lies in neutrino-related observations. In particular, whether neutrinos are Majorana particles is under intense scrutiny. If heavy right-handed Majorana neutrinos exist, the Lagrangian should contain Majorana mass terms, which would necessarily imply that the low-energy left-handed neutrinos are also Majorana particles. Thus, the detection of neutrinoless double beta decay (0νββ) would provide strong support for the leptogenesis scenario. Current and next-generation 0νββ experiments (such as KamLAND-Zen, LEGEND, and nEXO) are expected to have significant sensitivity, particularly in the case of an inverted neutrino mass hierarchy. If 0νββ decay is observed, it would confirm that neutrinos are Majorana particles, thereby fulfilling a key prerequisite for leptogenesis. Conversely, the non-observation of 0νββ at improved sensitivities would not by itself exclude Majorana neutrinos or leptogenesis; rather, it would push the allowed parameter space to smaller effective masses and weaker mixings. If neutrinos were proven to be strictly Dirac, that would disfavor the simplest Majorana-based scenarios, though some variants (e.g., Dirac leptogenesis or mechanisms in which B-L is generated elsewhere) could still be considered.
In summary, leptogenesis is a promising hypothesis for the origin of baryon asymmetry—supported by the experimental fact of the extremely small left-handed neutrino masses---and it provides several indirect avenues for testing the idea even if it occurs at very high energy scales (e.g., the GUT scale). However, since most leptogenesis models assume extremely heavy right-handed neutrinos, direct detection of these particles is impractical, and one must rely on neutrino experiments or indirect signatures from future accelerators. Furthermore, studies have examined the possibility of detecting gravitational wave signals from phase transitions or topological defects associated with leptogenesis in the early universe.
Electroweak Baryogenesis (EWBG)
Electroweak baryogenesis (EWBG) is a scenario in which baryon asymmetry is generated during the electroweak phase transition (at temperatures around 100 GeV) by utilizing the electroweak interactions augmented by beyond-SM ingredients. Unlike GUT baryogenesis or leptogenesis, which occur at much higher energy scales, EWBG takes place at the weak scale (~100 GeV), making it testable in modern accelerator experiments and through gravitational wave observations. The basic idea is to create a departure from thermal equilibrium via a first-order phase transition, and then to generate baryon asymmetry by combining the CP-violating effects present in the Standard Model (or its extensions) with sphaleron processes.
First, consider the electroweak first-order phase transition. In general, spontaneous symmetry breaking can occur either continuously or discontinuously; the discontinuous case is called a first-order phase transition. This is analogous to supercooled water suddenly freezing. If the electroweak phase transition were first order, then as the universe cools from the symmetric phase (with the Higgs field’s vacuum expectation value (φ = 0) to the broken phase (φ≠0), bubbles of the broken phase would nucleate and expand, eventually growing and merging within the surrounding symmetric phase. During the coexistence of the two phases, the universe would be out of thermal equilibrium, much like the coexistence of liquid and gas during boiling. However, with the parameters of the Standard Model (specifically, with a Higgs mass of 125 GeV), calculations indicate that the electroweak phase transition is a smooth crossover, and distinct bubbles do not form. In that case, the third Sakharov condition is not met, and EWBG cannot occur. Therefore, to realize EWBG, one must extend the Standard Model in some way to “improve” the electroweak phase transition into a first-order one. Specifically, one introduces additional terms into the one-loop finite-temperature effective potential of the Higgs field that generate an energy barrier between the symmetric and broken phases. In the Standard Model, the effective potential is roughly given by V = D(T² − T₀²)φ² + ETφ³ + (λ/4)φ⁴, where D and E are model-dependent coefficients, T₀ parametrizes the zero-temperature mass term, and λ is the zero-temperature Higgs self-coupling. The φ³ term, which is proportional to the thermal energy and acts as a barrier, is crucial for a first-order phase transition; however, in the Standard Model the coefficient E is too small, so that for a 125 GeV Higgs the barrier is almost absent. On the other hand, if a gauge-singlet scalar that couples to the Higgs is introduced, the φ³ term and higher-order terms can be enhanced, allowing for the coexistence of two degenerate vacua at the critical temperature and thus a clear first-order phase transition. In fact, it has been noted that even the addition of a weakly interacting singlet that couples to the Higgs can readily achieve a first-order phase transition. This is a generic feature common to many BSM theories (such as Two Higgs Doublet Model or Composite Higgs Model) invoked to satisfy the conditions for EWBG.
If a first-order phase transition occurs, the bubble walls of the nucleated Higgs vacuum become the dynamic stage for Electroweak Baryogenesis. The next crucial ingredient is CP violation. The CP violation arising from the CKM phase in the Standard Model is too weak, so a new source of CP violation from physics beyond the SM is required. For example, in Two Higgs Doublet Model, the interaction between the two Higgs fields can contain a CP-violating phase, leading to a space-time dependent phase effect during the electroweak phase transition. In supersymmetric models, complex phases are introduced in the mixing of charginos and neutralinos or in the mass parameters of squarks (scalar quarks), and these can become effective near the bubble walls. With such new CP-violating sources, differences in the behavior of matter versus antimatter---or between left-handed and right-handed particles---can arise across the bubble wall. Specifically, when particles are transmitted or reflected at the wall, subtle differences in their velocities or transmission probabilities lead, for instance, to a slight excess of left-handed particles accumulating on the symmetric-phase side of the wall. This chiral asymmetry is the source of the non-equilibrium that ultimately produces baryon asymmetry. Outside the bubbles, electroweak symmetry remains unbroken and sphaleron transitions are active, converting part of the left-handed excess into baryon number. In these sphaleron processes, three left-handed baryons and leptons are involved, leading to ΔB = ΔL = ±3. Consequently, the left-handed particle excess is immediately converted into a net baryon asymmetry. Inside the bubbles, where the Higgs vacuum expectation value is nonzero, sphaleron processes are rapidly suppressed, so that the generated baryon asymmetry is preserved. In this way, the net baryon asymmetry is imprinted on the universe. Quantitatively, by solving the diffusion equations for particles near the bubble walls together with the CP-violating reaction rates, one can evaluate the final baryon number B. Depending on the model, the necessary amount of CP violation must be several orders of magnitude larger than that from the CKM phase, yet its phase must remain sufficiently hidden to evade current experimental detection. This constitutes one of the stringent constraints in model building.
Electroweak Baryogenesis presents several challenges as well as opportunities for experimental verification. First, one major challenge is that only a limited number of models can simultaneously achieve the required first‐order phase transition and generate new sources of CP violation. Although many BSM theories can accommodate a first‐order phase transition, the presence of additional scalar particles (beyond the Higgs) would make them accessible to accelerator searches. For example, in the Two Higgs Doublet Model, extra neutral and charged Higgs bosons are predicted, yet no clear signals of these particles have been observed at the LHC. Moreover, in Composite Higgs Models, there is the possibility that a new resonant state (often referred to as the “dilatonic” scalar) may appear around the 1 TeV scale. In this way, if new particles exist in the 100 GeV–TeV range, they are likely to be discovered or excluded by ongoing LHC experiments or by future experiments at the HL-LHC. Furthermore, because a first‐order phase transition alters the self-interaction (i.e. the self-coupling) of the Higgs boson, measurements of the Higgs self-coupling can indirectly impose constraints on such scenarios.
On the other hand, the source of CP violation often competes with the very stringent limits from electric dipole moment (EDM) experiments. For instance, the electron EDM has been constrained to extremely small values by the ACME experiment, which places strong limits on the CP-violating phases assumed in many EWBG models such as the Two Higgs Doublet Model. In fact, extending the SM to enhance CP violation typically also contributes to the EDMs of electrons and nucleons, leading to the exclusion of many simple models. As a result, theorists are actively exploring novel ideas—such as dynamical Yukawa couplings (where the CP phase appears only during the phase transition), scenarios with higher transition temperatures, or indirect CP violation mediated by dark-sector particles---to generate sufficient CP violation while evading EDM constraints. In this way, models realizing EWBG are increasingly constrained by LHC new particle searches and EDM measurements, and the remaining viable solutions are gradually becoming more limited.
Nevertheless, EWBG remains attractive because it is particularly compatible with experimental and observational tests compared to other scenarios. A notable example is the observation of the primordial gravitational wave background. If the electroweak phase transition is first order, the collisions of the nucleated bubbles and the associated sound waves in the plasma are expected to emit gravitational waves with a peak frequency in the sub-mHz to mHz range. This signal is expected to have a frequency spectrum distinct from that of gravitational waves originating from inflation or cosmic strings, allowing one to distinguish whether it is indeed due to an “electroweak-scale phase transition.” Upcoming space-based gravitational wave observatories such as LISA and DECIGO, which are sensitive in this frequency range, will directly search for the gravitational wave signatures potentially produced by EWBG. A detection would constitute a dramatic breakthrough; conversely, if no signal is observed, the sensitivity limits would constrain the strength of the phase transition, thereby excluding parts of the EWBG model parameter space.
In summary, while EWBG requires new physics to overcome the shortcomings of the Standard Model (namely, the weak phase transition and the smallness of the CKM CP phase), it is an appealing scenario because it can be tested through a variety of observational channels.