Antimatter asymmetry

The antimatter asymmetry — also called the baryon asymmetry of the universe — is the observation that the visible universe consists almost entirely of matter, with virtually no primordial antimatter. This is one of the most profound puzzles in modern physics. The standard model of particle physics, combined with the hot Big Bang model of cosmology, predicts that the extraordinarily high temperatures of the early universe should have produced matter and antimatter in precisely equal quantities. Yet the universe we observe is overwhelmingly matter-dominated: every star, galaxy, and planet is composed of protons, neutrons, and electrons rather than their antimatter counterparts. The small excess of matter over antimatter that survived the epoch of annihilation in the first seconds after the Big Bang ultimately gave rise to all the baryonic structure in the cosmos.^{1, 12}

The magnitude of this asymmetry is remarkably small. For every billion particle–antiparticle pairs that annihilated in the early universe, roughly one extra matter particle remained. This ratio is quantified by the baryon-to-photon ratio η ≈ 6.1 × 10⁻¹⁰, determined independently from Big Bang nucleosynthesis and the cosmic microwave background.¹¹ Understanding how this tiny but consequential excess arose — a process collectively known as baryogenesis — has been a central goal of particle physics and cosmology since Andrei Sakharov first identified the necessary conditions in 1967. Despite extraordinary theoretical and experimental progress, no single mechanism has been definitively confirmed, and the origin of the matter–antimatter asymmetry remains one of the great unsolved problems in science.^{1, 8, 20}

The puzzle of a matter-dominated universe

The laws of physics as understood through the standard model exhibit a near-perfect symmetry between matter and antimatter. For every particle, there exists an antiparticle with the same mass but opposite charge and quantum numbers. When a particle meets its antiparticle, the pair annihilates into pure energy, typically in the form of photons. Conversely, when sufficient energy is available, particle–antiparticle pairs are produced in equal numbers. This symmetry, deeply embedded in quantum field theory, strongly suggests that any process producing matter in the early universe should have produced an identical amount of antimatter.^{8, 12}

In the standard hot Big Bang picture, the universe began in an extremely hot, dense state where temperatures exceeded trillions of degrees. Under such conditions, the thermal energy of the primordial plasma was far greater than the mass-energy of protons, neutrons, and their antiparticles, so these particles were continuously being created and destroyed in vast numbers. As the universe expanded and cooled below the threshold temperature for producing baryon–antibaryon pairs (roughly 10¹³ kelvin, corresponding to about 1 GeV), the remaining baryons and antibaryons annihilated almost completely with one another. If the initial numbers of baryons and antibaryons had been exactly equal, this annihilation would have been total, and the universe would contain nothing but a sea of photons and neutrinos with no residual matter at all. Galaxies, stars, planets, and life would not exist.^{8, 13}

The observational evidence against a symmetric universe — one containing equal amounts of matter and antimatter segregated into separate regions — is overwhelming. Gary Steigman's influential 1976 review catalogued the arguments: if large regions of antimatter existed anywhere within the observable universe, the boundaries between matter and antimatter domains would be sites of continuous annihilation, producing a distinctive and intense flux of gamma rays at an energy of 511 keV (the rest energy of the electron) and in a broad continuum from pion decay. No such signal has ever been detected at the levels that would be expected from domain boundaries on cosmological scales.¹³ Cohen, De Rújula, and Glashow sharpened this argument in 1998, demonstrating that the cosmic diffuse gamma-ray background and the observed smoothness of the cosmic microwave background together exclude a matter–antimatter patchwork universe unless the domain we inhabit encompasses virtually the entire observable volume.¹⁴

The conclusion is inescapable: the baryon asymmetry is a genuine feature of the universe, not an artefact of our local environment. Something in the physics of the early universe must have generated a slight excess of matter over antimatter before the epoch of annihilation. The challenge for theoretical physics is to identify the mechanism responsible.^{1, 12}

The Sakharov conditions

In 1967, the Soviet physicist Andrei Sakharov published a landmark paper identifying three necessary conditions that any physical process must satisfy in order to generate a net baryon asymmetry from an initially symmetric state. These three conditions — now universally known as the Sakharov conditions — have served as the guiding framework for all subsequent theoretical work on baryogenesis.¹

The first condition is baryon number violation. Baryon number is a quantum number assigned to particles: baryons (such as protons and neutrons) carry baryon number +1, antibaryons carry −1, and non-baryonic particles carry 0. If baryon number is absolutely conserved — meaning that the total baryon number of the universe can never change — then a universe that begins with zero net baryon number (equal numbers of baryons and antibaryons) must remain at zero for all time. Any mechanism for generating an asymmetry therefore requires interactions that violate baryon number conservation.^{1, 8}

The second condition requires violation of C symmetry and CP symmetry. C symmetry (charge conjugation) is the symmetry that transforms every particle into its antiparticle. If C symmetry were exact, then every process that creates an excess of baryons would be perfectly matched by a process creating an equal excess of antibaryons, yielding no net asymmetry. CP symmetry is the combined operation of charge conjugation and parity inversion (spatial reflection). Even if C is violated, CP symmetry alone would ensure that the total rate of baryon production equals that of antibaryon production when summed over all helicity states. Both C and CP must therefore be violated for a net baryon excess to emerge.^{1, 2, 8}

The third condition is departure from thermal equilibrium. This requirement arises from a deep theorem of quantum field theory: CPT symmetry (the combined operation of charge conjugation, parity, and time reversal) is an exact symmetry of any local, Lorentz-invariant quantum field theory. In thermal equilibrium, CPT invariance guarantees that the rate of any reaction producing baryons is exactly equal to the rate of the reverse reaction destroying them, so no net asymmetry can develop regardless of whether the first two conditions are satisfied. Only when the system departs from equilibrium — for instance, during a rapid phase transition or through the out-of-equilibrium decay of a heavy particle — can a baryon asymmetry be generated and preserved.^{1, 8, 20}

Remarkably, the standard model of particle physics contains the ingredients to satisfy all three Sakharov conditions, at least in principle. Baryon number is violated non-perturbatively through sphaleron processes, CP violation has been experimentally observed in the quark sector, and the electroweak phase transition could potentially provide the necessary departure from equilibrium. However, as will be discussed in the following sections, quantitative analysis reveals that the standard model values of these effects are far too small to account for the observed asymmetry, requiring physics beyond the standard model.^{8, 9, 20}

CP violation in particle physics

The discovery that the laws of physics distinguish between matter and antimatter — that CP symmetry is not exact — was one of the most surprising results in twentieth-century physics. In 1964, James Cronin, Val Fitch, and their collaborators at Brookhaven National Laboratory observed that the long-lived neutral kaon (K_L), which was expected to decay exclusively into three pions under the assumption of CP conservation, occasionally decayed into two pions instead. This two-pion decay mode violated CP symmetry at a level of roughly one part in a thousand. The discovery earned Cronin and Fitch the 1980 Nobel Prize in Physics and established that nature does not treat matter and antimatter with perfect symmetry.²

For nearly four decades, the kaon system remained the only arena where CP violation had been experimentally confirmed. The theoretical explanation for CP violation in the standard model was provided by Makoto Kobayashi and Toshihide Maskawa in 1973, who showed that CP violation arises naturally if there are at least three generations of quarks. Their framework predicts that CP-violating effects should also appear in the decays of B mesons (particles containing a bottom quark), and that the magnitude of CP violation in B mesons should be substantially larger than in kaons. This prediction was dramatically confirmed in 2001, when both the BaBar experiment at SLAC and the Belle experiment at KEK independently observed large CP-violating asymmetries in the decays of neutral B mesons to the final state J/ψ K_S. The BaBar collaboration reported the quantity sin 2β = 0.59 ± 0.14 ± 0.05, definitively establishing CP violation in the B meson system and confirming the Kobayashi–Maskawa mechanism.¹⁵

In 2019, the LHCb experiment at CERN achieved another milestone: the first observation of CP violation in the charm quark sector. By comparing the decay rates of D⁰ mesons to K⁻K⁺ and π⁻π⁺ final states, LHCb measured a CP asymmetry difference of ΔA_CP = (−15.4 ± 2.9) × 10⁻⁴, deviating from zero by more than five standard deviations. This result extended the experimental observation of CP violation to a third quark flavour.¹⁶

Despite these experimental triumphs, the CP violation observed in the standard model is quantitatively insufficient to explain the cosmological baryon asymmetry. The Kobayashi–Maskawa mechanism generates CP-violating effects that are proportional to a dimensionless quantity known as the Jarlskog invariant, which has a measured value of approximately 3 × 10⁻⁵. When this CP violation is incorporated into calculations of baryogenesis within the standard model, the predicted baryon asymmetry falls short of the observed value by many orders of magnitude. This enormous shortfall provides strong motivation for seeking new sources of CP violation beyond the standard model.^{8, 9, 20}

Baryon number violation and sphalerons

Within the standard model, baryon number and lepton number appear to be conserved at the classical level — no interaction vertex in the Lagrangian explicitly changes either quantity. However, in 1976, Gerard 't Hooft demonstrated that quantum effects fundamentally alter this picture. Through a computation of tunnelling amplitudes associated with topologically non-trivial gauge field configurations called instantons, 't Hooft showed that the standard electroweak theory contains processes that violate the conservation of baryon number (B) and lepton number (L) while preserving the combination B − L. These processes arise from the Adler–Bell–Jackiw anomaly, a quantum mechanical effect in which a classically conserved symmetry is broken at the quantum level.³

At zero temperature, the rate of these anomalous processes is extraordinarily suppressed, proportional to exp(−16π²/g²) ≈ 10⁻¹⁶⁴, where g is the electroweak coupling constant. This suppression factor makes instanton-mediated baryon number violation utterly negligible in laboratory experiments or in the present-day universe. However, in 1985, Kuzmin, Rubakov, and Shaposhnikov made the crucial observation that at the high temperatures of the early universe, this suppression disappears. At temperatures above approximately 100 GeV (roughly 10¹⁵ kelvin) — above the electroweak phase transition — the thermal energy of the plasma is sufficient to allow transitions over the energy barrier between topologically distinct vacuum states, rather than requiring quantum tunnelling through it. These thermally activated transitions are mediated by unstable, saddle-point configurations of the gauge and Higgs fields known as sphalerons (from the Greek sphaleros, meaning "ready to fall").⁴

The sphaleron rate in the symmetric phase of the electroweak theory is rapid, of order α_W⁵ T, where α_W ≈ 1/30 is the electroweak fine structure constant and T is the temperature. This rate exceeds the Hubble expansion rate at temperatures between roughly 100 GeV and 10¹² GeV, meaning that sphaleron processes are in thermal equilibrium throughout this enormous range. Each sphaleron transition simultaneously changes baryon number and lepton number by three units (one per generation of quarks and leptons), converting, for example, a state with three baryons into a state with three antileptons. Crucially, these transitions conserve B − L while violating B + L.^{4, 8, 9}

The existence of rapid sphaleron-mediated baryon number violation in the early universe has profound consequences for baryogenesis. On the one hand, it provides one of the Sakharov conditions within the standard model itself: baryon number is not absolutely conserved. On the other hand, sphalerons also act as a double-edged sword. Any baryon asymmetry generated at high temperatures by a mechanism that does not simultaneously generate a B − L asymmetry will be partially or completely erased by sphalerons before they freeze out at the electroweak scale. This observation places strong constraints on viable baryogenesis mechanisms: either the asymmetry must be produced in the B − L quantum number (which sphalerons cannot erase), or it must be produced at or below the electroweak phase transition before sphalerons decouple.^{4, 8, 20}

GUT baryogenesis

The earliest concrete models of baryogenesis emerged in the late 1970s, closely following the development of grand unified theories (GUTs) that attempted to unify the strong, weak, and electromagnetic forces into a single gauge interaction at energies above approximately 10¹⁶ GeV. In 1978, Motohiko Yoshimura proposed that the decays of superheavy gauge bosons — the X and Y bosons predicted by GUTs — could generate a net baryon number in the early universe.⁵

In grand unified theories such as those based on the gauge group SU(5), the X and Y bosons carry both colour charge and electroweak charge, and their interactions directly connect quarks to leptons. As a result, these interactions violate baryon number conservation, with X bosons mediating transitions that change baryon number by one unit. The same interactions predict that the proton itself is unstable, decaying with a lifetime vastly exceeding the current age of the universe (current experimental bounds place the proton lifetime above approximately 10³⁴ years). The existence of baryon number violation at the GUT scale provides the first Sakharov condition.^{5, 8}

The scenario for GUT baryogenesis proceeds as follows. In the very early universe, at temperatures above the GUT scale (roughly 10¹⁶ GeV), X and Y bosons were in thermal equilibrium, constantly being produced and annihilated. As the universe cooled below the mass threshold for X and Y bosons, these particles could no longer be produced but continued to decay. If the branching ratios for the decay of X bosons into quarks differed from the branching ratios for the decay of anti-X bosons into antiquarks — a difference requiring C and CP violation — then the decays would produce a slight excess of quarks over antiquarks. The departure from thermal equilibrium is provided naturally by the expansion of the universe: once the decay rate of the X bosons falls below the expansion rate, the inverse production reactions cannot maintain equilibrium, and the asymmetry generated in the decays is frozen in.^{5, 8, 20}

GUT baryogenesis was historically important as the first quantitative realisation of Sakharov's conditions. However, the scenario faces a serious challenge from sphaleron physics. Because GUT-scale baryogenesis typically generates an asymmetry in baryon number alone (with B − L = 0), sphaleron processes at the electroweak scale would subsequently erase this asymmetry entirely. Only GUT models that generate a non-zero B − L asymmetry — such as those based on the gauge group SO(10), which contains B − L as a gauge charge — can produce a baryon asymmetry that survives sphaleron washout. Additionally, if the universe underwent a period of cosmic inflation after the GUT-scale epoch, any pre-existing baryon asymmetry would be diluted to negligible levels by the exponential expansion, requiring baryogenesis to occur after inflation ends.^{8, 20}

Electroweak baryogenesis

Electroweak baryogenesis (EWBG) is the scenario in which the baryon asymmetry is generated during the electroweak phase transition, which occurred approximately 10⁻¹¹ seconds after the Big Bang when the universe cooled through a temperature of roughly 100 GeV. This framework is particularly attractive because all three Sakharov conditions can potentially be satisfied by known electroweak physics: baryon number violation through sphaleron processes, CP violation in the quark or lepton sectors, and departure from equilibrium at the phase transition itself.^{9, 20}

For EWBG to work, the electroweak phase transition must be strongly first-order: it must proceed through the nucleation and expansion of bubbles of the broken-symmetry phase (where the Higgs field has a non-zero vacuum expectation value) within a surrounding plasma that remains in the symmetric phase. As these bubbles expand at a fraction of the speed of light, particles in the plasma interact with the advancing bubble walls. If CP-violating interactions at the wall preferentially reflect certain species of particles over their antiparticles, a net chiral asymmetry develops in front of the advancing wall. This chiral asymmetry is then partially converted into a baryon asymmetry by the rapid sphaleron processes that operate in the symmetric phase outside the bubble. As the bubble wall sweeps past, the newly generated baryons are captured inside the broken-symmetry phase where sphalerons are suppressed, freezing in the asymmetry.⁹

The elegance of this scenario is tempered by two severe quantitative problems within the standard model. First, lattice calculations have demonstrated that for a Higgs boson mass above approximately 72 GeV, the electroweak phase transition in the standard model is not first-order at all but rather a smooth crossover — a continuous transition with no bubble nucleation and no departure from equilibrium. With the Higgs boson discovered at a mass of 125 GeV in 2012, the standard model electroweak transition is definitively a crossover, and the third Sakharov condition fails.^{9, 20}

Second, even if the phase transition were made first-order by extending the Higgs sector (for example, by adding a second Higgs doublet or a scalar singlet), the amount of CP violation available in the standard model quark sector is far too small. Calculations show that the baryon asymmetry produced by standard-model CP violation during a hypothetically first-order electroweak transition would be many orders of magnitude below the observed value.^{8, 9}

For these reasons, viable EWBG requires physics beyond the standard model: new scalar fields to make the phase transition strongly first-order, and new sources of CP violation to enhance the asymmetry production at the bubble walls. Extensions such as the two-Higgs-doublet model, the next-to-minimal supersymmetric standard model (NMSSM), and models with additional scalar singlets have been studied extensively. A major virtue of EWBG is that the required new physics operates at the electroweak scale and is therefore in principle accessible to current and near-future collider experiments and precision measurements, including searches for the electric dipole moments of the electron and neutron, which provide sensitive probes of new CP-violating interactions.^{9, 20}

Leptogenesis

Leptogenesis, proposed by Masataka Fukugita and Tsutomu Yanagida in 1986, is one of the most compelling and widely studied scenarios for explaining the baryon asymmetry. In this framework, the asymmetry originates not in the baryon sector but in the lepton sector: a lepton asymmetry is first generated at high energies, and sphalerons subsequently convert a portion of this lepton asymmetry into a baryon asymmetry. The title of Fukugita and Yanagida's seminal paper, "Baryogenesis without grand unification," reflects the fact that their mechanism does not require the superheavy gauge bosons of GUTs, relying instead on heavy right-handed neutrinos.⁶

The connection between leptogenesis and neutrino physics is provided by the seesaw mechanism, a theoretical framework that explains why the observed neutrino masses are extraordinarily small compared to those of all other known fermions. In the simplest (Type I) seesaw, right-handed neutrinos with very large Majorana masses (typically 10⁹ to 10¹⁵ GeV) are introduced. The interplay between these heavy Majorana masses and the ordinary Dirac mass terms that couple left- and right-handed neutrinos produces light neutrino mass eigenstates with masses inversely proportional to the heavy Majorana mass — hence the "seesaw" metaphor. The same Majorana mass terms violate lepton number by two units, providing the first Sakharov condition (lepton number violation, which sphalerons convert to baryon number violation).^{6, 10}

The mechanism of leptogenesis proceeds as follows. In the early universe, the heavy right-handed neutrinos are produced thermally (in thermal leptogenesis) or through other processes such as inflaton decay (in non-thermal leptogenesis). As the universe cools below their mass threshold, the heavy neutrinos decay into standard model leptons and Higgs bosons. If CP is violated in these decays — meaning the rate of decay into leptons differs from the rate of decay into antileptons — a net lepton asymmetry is generated. The departure from thermal equilibrium is provided by the same out-of-equilibrium decay mechanism that operates in GUT baryogenesis: when the decay rate of the heavy neutrinos falls below the expansion rate, inverse processes cannot maintain equilibrium. The resulting lepton asymmetry is then partially processed into a baryon asymmetry by sphaleron transitions, which are active at these temperatures and efficiently interconvert lepton and baryon number while conserving B − L.^{6, 10, 20}

A key virtue of leptogenesis is its deep connection to independently motivated neutrino physics. The observation of neutrino oscillations has confirmed that neutrinos have non-zero masses, which is naturally explained by the seesaw mechanism. Leptogenesis therefore links two otherwise unrelated puzzles — the smallness of neutrino masses and the baryon asymmetry of the universe — within a single theoretical framework. However, the primary challenge for leptogenesis is testability: the heavy right-handed neutrinos in the simplest versions of the scenario have masses far beyond the reach of any foreseeable collider experiment. Indirect constraints from low-energy neutrino physics, lepton-flavour-violating processes, and cosmological observables provide some handles, but a definitive experimental confirmation remains elusive.^{10, 20}

Variants of leptogenesis have been developed to address this challenge, including resonant leptogenesis (where the heavy neutrinos are nearly degenerate in mass, enhancing the CP asymmetry), ARS (Akhmedov–Rubakov–Shaposhnikov) leptogenesis (which uses GeV-scale right-handed neutrinos that could be produced at colliders), and leptogenesis through the decays of heavy scalar triplets (Type II seesaw). The richness of the leptogenesis framework ensures that it remains at the forefront of baryogenesis research.^{10, 20}

The Affleck–Dine mechanism

In 1985, Ian Affleck and Michael Dine proposed an entirely different approach to baryogenesis based on the dynamics of scalar fields in supersymmetric extensions of the standard model. In supersymmetric theories, every known fermion and gauge boson has a scalar partner, and the scalar potential of the theory generically contains "flat directions" — field configurations along which the potential energy is approximately zero. These flat directions carry non-zero baryon or lepton number, meaning that a scalar field condensate displaced along such a direction corresponds to a state with a net baryon or lepton charge.⁷

The Affleck–Dine mechanism exploits the observation that during inflation, the scalar fields of the supersymmetric standard model can acquire large expectation values along these flat directions, driven by quantum fluctuations or by tachyonic (negative mass-squared) terms induced by supersymmetry breaking in the inflationary background. After inflation ends, the flat direction is lifted by supersymmetry-breaking terms and higher-dimensional operators in the scalar potential. As the condensate begins to oscillate and decay, CP-violating phases in the scalar potential cause the trajectory of the field in the complex plane to spiral rather than oscillate linearly. This spiralling motion corresponds to a time-varying baryon (or lepton) number charge density, generating a net asymmetry as the condensate decays into ordinary particles.^{7, 8}

A distinctive feature of the Affleck–Dine mechanism is its efficiency: it can naturally produce baryon asymmetries much larger than the observed value, which must then be diluted to the correct level by subsequent entropy production (for example, during the reheating epoch after inflation). The mechanism is also highly flexible, with the magnitude of the asymmetry depending on parameters such as the initial field value, the scale of supersymmetry breaking, and the specific flat direction involved. If the Affleck–Dine field fragments into non-topological solitons called Q-balls, these objects can have interesting cosmological consequences, potentially contributing to dark matter or providing a delayed source of baryons.^{7, 8, 20}

The Affleck–Dine mechanism is contingent on the existence of supersymmetry and its associated scalar flat directions. Since no evidence for supersymmetric partners has been found at the Large Hadron Collider as of the mid-2020s, the viability of the simplest Affleck–Dine scenarios is increasingly constrained, though the mechanism remains viable at energy scales beyond the reach of current colliders. Variants that do not require full supersymmetry, employing other scalar fields with baryon-number-carrying flat directions, continue to be explored.²⁰

Observational constraints on the baryon asymmetry

The baryon asymmetry of the universe is not merely a qualitative observation but a precisely measured quantity. The primary parameter characterising the asymmetry is the baryon-to-photon ratio η, defined as the number density of baryons minus antibaryons divided by the number density of photons. Two independent observational methods — Big Bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) — provide concordant determinations of this quantity, lending powerful support to the standard cosmological model.^{11, 12}

Big Bang nucleosynthesis is sensitive to the baryon-to-photon ratio because η determines the density of baryons available for nuclear reactions in the first few minutes after the Big Bang. A higher baryon density allows deuterium to survive photodissociation at a higher temperature, leading to more efficient processing of deuterium into helium-4 and leaving less residual deuterium. The observed primordial abundances of deuterium and helium-4, measured in high-redshift quasar absorption systems and metal-poor galaxies respectively, constrain η to be approximately (5.8–6.5) × 10⁻¹⁰.^{11, 12}

The cosmic microwave background provides an entirely independent measurement. The pattern of temperature fluctuations in the CMB — specifically the relative heights of the odd and even acoustic peaks in the angular power spectrum — is sensitive to the ratio of baryonic matter to photons at the epoch of recombination, approximately 380,000 years after the Big Bang. The Planck satellite's 2018 analysis yields a baryon density parameter Ω_bh² = 0.02237 ± 0.00015, corresponding to η = (6.12 ± 0.04) × 10⁻¹⁰.¹¹

Measurements of the baryon-to-photon ratio from independent cosmological probes^{11, 12}

The remarkable agreement between these two independent measurements, probing the baryon-to-photon ratio at two vastly different epochs (minutes versus hundreds of thousands of years after the Big Bang), provides strong evidence that the asymmetry was established very early in cosmic history and has remained stable since. This agreement also rules out scenarios in which significant baryon number was generated or destroyed between the BBN and CMB epochs. The precision of these measurements, particularly the Planck determination, places stringent quantitative targets for any theoretical model of baryogenesis: the mechanism must produce η ≈ 6 × 10⁻¹⁰, no more and no less.^{11, 12, 20}

Antimatter searches in cosmic rays

While theoretical and cosmological arguments strongly indicate that the universe is matter-dominated, direct experimental searches for antimatter in cosmic rays provide complementary constraints. If large pockets of antimatter existed anywhere in the observable universe, their interactions with surrounding matter or their ejection of antiparticles into the cosmic ray flux would produce detectable signatures. Two major experiments — PAMELA and AMS-02 — have conducted precision searches for antimatter in space over the past two decades.^{13, 17, 18}

The PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) satellite, launched in 2006, was the first space-based magnetic spectrometer dedicated to cosmic ray antimatter detection. In 2009, the PAMELA collaboration reported the detection of an anomalous excess of positrons (the antimatter counterpart of the electron) in the cosmic ray flux at energies between 10 and 100 GeV, with the positron fraction rising with energy rather than falling as expected from standard cosmic ray propagation models. This positron excess attracted enormous attention as a possible signature of dark matter annihilation, though astrophysical explanations involving nearby pulsars or supernova remnants have since been shown to account for the data. Importantly, PAMELA also measured the antiproton-to-proton ratio in cosmic rays, finding results consistent with secondary production (antiprotons produced by collisions of ordinary cosmic rays with interstellar gas) and no evidence for a primary antimatter source.¹⁸

The Alpha Magnetic Spectrometer (AMS-02), installed on the International Space Station in 2011, represents a major leap in sensitivity. Over more than a decade of continuous operation, AMS-02 has collected data on over 230 billion cosmic ray events spanning energies from sub-GeV to multi-TeV. The experiment confirmed the positron excess observed by PAMELA with far greater statistical precision and extended the measurement to higher energies. AMS-02 has also provided the most precise measurements of the cosmic ray antiproton flux, with results consistent with secondary production and placing stringent limits on exotic antimatter sources.¹⁷

Perhaps the most tantalising result from AMS-02 is the tentative detection of a handful of antihelium-3 candidate events. By the early 2020s, approximately eight candidate events had been recorded with charge Z = −2 and mass consistent with helium-3, at a rate of roughly one event per year against a background rejection requirement of one in a billion. If confirmed, the detection of even a single antihelium nucleus in cosmic rays would be extraordinary, as there is no known astrophysical process that can produce antihelium at detectable fluxes through secondary interactions alone. Such a detection could point to the existence of antimatter domains, exotic dark matter annihilation channels, or entirely new physics. However, the statistical significance of these events remains below the threshold for a definitive discovery, and the AMS-02 collaboration continues to accumulate data and refine its analysis to confirm or exclude these candidate signals.^{12, 17}

Current and future experimental programs

The search for the origin of the matter–antimatter asymmetry is being pursued on multiple experimental fronts, spanning collider physics, neutrino experiments, precision measurements, and cosmic ray observations. Each approach targets different aspects of the baryogenesis puzzle, and together they provide a comprehensive program for testing the theoretical scenarios described in previous sections.²⁰

At the energy frontier, the LHCb experiment at CERN continues to make precision measurements of CP violation in the decays of B mesons, D mesons, and baryons. Following its upgrade (the LHCb Upgrade I, which began collecting data in 2022), the detector operates at significantly higher luminosity, enabling measurements of CP-violating observables with unprecedented precision. These measurements test the Kobayashi–Maskawa mechanism in detail and search for deviations from standard model predictions that could indicate new sources of CP violation relevant to baryogenesis. The observation of CP violation in charm decays in 2019 was itself a product of LHCb's capabilities and demonstrates the experiment's power to probe subtle asymmetries between matter and antimatter.^{16, 20}

The Belle II experiment at the SuperKEKB collider in Japan represents another major effort in the precision CP violation programme. SuperKEKB is the world's highest-luminosity electron–positron collider, designed to produce enormous samples of B meson pairs and tau leptons. Belle II aims to measure CP-violating phases and branching ratios in rare B meson decays with precision sufficient to reveal contributions from virtual particles not present in the standard model. Early results, including measurements of time-dependent CP violation in B⁰ decays, demonstrate the experiment's potential to constrain or discover new sources of CP violation.²¹

In the neutrino sector, the Deep Underground Neutrino Experiment (DUNE) is specifically designed to search for CP violation in neutrino oscillations. DUNE will direct an intense beam of muon neutrinos from Fermilab, Illinois, to massive liquid argon detectors located 1,300 kilometres away at the Sanford Underground Research Facility in South Dakota. By comparing the oscillation probabilities of neutrinos and antineutrinos — specifically the rate at which muon neutrinos convert to electron neutrinos versus the rate at which muon antineutrinos convert to electron antineutrinos — DUNE can measure the CP-violating phase δ_CP in the lepton sector. Simulations indicate that DUNE can discover CP violation at the three-sigma level after five years of operation for fifty percent of possible δ_CP values, and at five-sigma after ten years. While the discovery of leptonic CP violation would not by itself prove that leptogenesis is the source of the baryon asymmetry, it would establish the existence of a crucial ingredient and provide strong circumstantial evidence in favour of leptogenesis scenarios.¹⁹

Precision low-energy experiments provide complementary probes. Searches for the electric dipole moment (EDM) of the electron and neutron are sensitive to new sources of CP violation at energy scales far beyond the reach of colliders. The current experimental bound on the electron EDM, below 10⁻²⁹ e·cm, already constrains many models of electroweak baryogenesis. Next-generation EDM experiments aim to improve this sensitivity by one to two orders of magnitude, potentially ruling out or confirming entire classes of baryogenesis models. Similarly, searches for neutron–antineutron oscillations, which would directly demonstrate baryon number violation by two units, are being pursued at facilities such as the European Spallation Source.^{9, 20}

Unresolved questions and outlook

Despite more than half a century of theoretical and experimental effort since Sakharov's original paper, the origin of the baryon asymmetry remains unknown. Each of the major baryogenesis scenarios — GUT baryogenesis, electroweak baryogenesis, leptogenesis, and the Affleck–Dine mechanism — can produce the observed asymmetry for appropriate choices of parameters, but none has been singled out by experimental evidence. The problem is not a lack of viable mechanisms but rather a surfeit of them, compounded by the difficulty of directly testing physics at the extreme energy scales where most baryogenesis scenarios operate.^{8, 20}

Several specific open questions define the frontier of the field. First, what is the nature of the electroweak phase transition? If future collider experiments discover an extended Higgs sector or new scalar particles that could render the transition strongly first-order, electroweak baryogenesis would become a viable and testable scenario. Conversely, if the Higgs sector is confirmed to be minimal, EWBG would be definitively excluded. Gravitational wave observatories such as LISA (the Laser Interferometer Space Antenna, planned for launch in the 2030s) could detect the stochastic gravitational wave background produced by a strongly first-order electroweak phase transition, providing a striking cosmological probe of this question.^{9, 20}

Second, is there CP violation in the lepton sector? The answer to this question, expected from DUNE and other long-baseline neutrino experiments within the next decade, has direct implications for leptogenesis. The discovery of leptonic CP violation would not prove leptogenesis but would establish the existence of one of its key ingredients. Conversely, the absence of measurable CP violation in neutrino oscillations would not rule out leptogenesis (because the CP violation relevant to leptogenesis can involve different phases than those accessible in oscillation experiments), but it would reduce the circumstantial motivation for the scenario.^{10, 19}

Third, does the proton decay? Proton decay is a generic prediction of grand unified theories and would constitute direct evidence for baryon number violation at high energy scales. Current limits from the Super-Kamiokande experiment place the proton lifetime above approximately 10³⁴ years, already excluding the simplest SU(5) GUT models. The Hyper-Kamiokande experiment, under construction in Japan, aims to extend the sensitivity to proton decay by roughly an order of magnitude, testing a broader range of GUT predictions.^{8, 20}

Fourth, what is the nature of dark matter, and is it connected to baryogenesis? Several theoretical frameworks, including asymmetric dark matter models and Affleck–Dine scenarios that produce both baryonic and dark matter from the same mechanism, predict a deep connection between the baryon asymmetry and the dark matter density. The observed ratio of dark matter to baryonic matter (Ω_DM/Ω_b ≈ 5) is suggestively close to unity on a logarithmic scale, hinting at a common origin. If such a connection exists, the discovery and characterisation of dark matter could simultaneously illuminate the origin of the baryon asymmetry.^{12, 20}

The antimatter asymmetry stands at the intersection of cosmology, particle physics, and fundamental symmetry principles. Its resolution will likely require new physics beyond the standard model — physics that may be within reach of the current generation of experiments. Whether the answer lies in the lepton sector, at the electroweak scale, or at energies far beyond current collider reach, the question of why we exist in a universe of matter rather than a featureless sea of radiation remains one of the most profound in all of science.^{1, 8, 20}