 Baryogenesis

Unsolved problems in physics Why does the observable universe have more matter than antimatter? Physical cosmology Universe · Big Bang
Age of the universe
Timeline of the Big Bang
Ultimate fate of the universeEarly universeExpanding universeComponentsIn physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.
Baryogenesis theories (the most important being electroweak baryogenesis and GUT baryogenesis) employ subdisciplines of physics such as quantum field theory, and statistical physics, to describe such possible mechanisms. The fundamental difference between baryogenesis theories is the description of the interactions between fundamental particles.
The next step after baryogenesis is the much better understood Big Bang nucleosynthesis, during which light atomic nuclei began to form.
Contents
Background
The Dirac equation,^{[1]} formulated by Paul Dirac around 1928 as part of the development of relativistic quantum mechanics, predicts the existence of antiparticles along with the expected solutions for the corresponding particles. Since that time, it has been verified experimentally that every known kind of particle has a corresponding antiparticle. The CPT Theorem guarantees that a particle and its antiparticle have exactly the same mass and lifetime, and exactly opposite charge. Given this symmetry, it is puzzling that the universe does not have equal amounts of matter and antimatter. Indeed, there is no experimental evidence that there are any significant concentrations of antimatter in the observable universe.
There are two main interpretations for this disparity: either the universe began with a small preference for matter (total baryonic number of the universe different from zero), or the universe was originally perfectly symmetric, but somehow a set of phenomena contributed to a small imbalance in favour of matter over time. The second point of view is preferred, although there is no clear experimental evidence indicating either of them to be the correct one. The preference is based on the following point of view:^{[citation needed]} if the universe encompasses everything (time, space, and matter), nothing exists outside of it and therefore nothing existed before it, leading to a total baryonic number of 0. From a more scientific point of view, there are reasons to expect that any initial asymmetry would be wiped out to zero during the early history of the universe.^{[citation needed]} One challenge then is to explain how the total baryonic number is not conserved.
Sakharov conditions
In 1967, Andrei Sakharov proposed^{[2]} a set of three necessary conditions that a baryongenerating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the cosmic background radiation ^{[3]} and CPviolation in the neutral kaon system. ^{[4]} The three necessary "Sakharov conditions" are:
 Baryon number B violation.
 Csymmetry and CPsymmetry violation.
 Interactions out of thermal equilibrium.
Baryon number violation is obviously a necessary condition to produce an excess of baryons over antibaryons. But Csymmetry violation is also needed so that the interactions which produce more baryons than antibaryons will not be counterbalanced by interactions which produce more antibaryons than baryons. CPsymmetry violation is similarly required because otherwise equal numbers of lefthanded baryons and righthanded antibaryons would be produced, as well as equal numbers of lefthanded antibaryons and righthanded baryons. Finally, the interactions must be out of thermal equilibrium, since otherwise CPT symmetry would assure compensation between processes increasing and decreasing the baryon number. ^{[5]}
Currently, there is no experimental evidence of particle interactions where the conservation of baryon number is broken perturbatively: this would appear to suggest that all observed particle reactions have equal baryon number before and after. Mathematically, the commutator of the baryon number quantum operator with the (perturbative) Standard Model hamiltonian is zero: [B,H] = BH − HB = 0. However, the Standard Model is known to violate the conservation of baryon number nonperturbatively: a global U(1) anomaly. Baryon number violation can also result from physics beyond the Standard Model (see supersymmetry and Grand Unification Theories).
The second condition — violation of CPsymmetry — was discovered in 1964 (direct CPviolation, that is violation of CPsymmetry in a decay process, was discovered later, in 1999). Due to CPTsymmetry, violation of CPsymmetry demands violation of time inversion symmetry, or Tsymmetry.
In the outofequilibrium decay scenario,^{[6]} the last condition states that the rate of a reaction which generates baryonasymmetry must be less than the rate of expansion of the universe. In this situation the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pairannihilation.
Baryogenesis within the Standard Model
The Standard Model can incorporate baryogenesis, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry; this issue has not yet been determined decisively.
Baryogenesis within the Standard Model requires the electroweak symmetry breaking be a firstorder phase transition, since otherwise sphalerons wipe off any baryon assymetry that happened up to the phase transition, while later the amount of baryon nonconserving interactions is negligible. ^{[7]}
The phase transition domain wall breaks the Psymmetry spontaneously, allowing for CPsymmetry violating interactions to create Casymmetry on both its sides: quarks tend to accumulate on the broken phase side of the domain wall, while antiquarks tend to accumulate on its unbroken phase side. This happens as follows:^{[5]}
Due to CPsymmetry violating electroweak interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving antiquarks, but rather have opposite phase (see CKM matrix and Kaon); since time reversal takes an amplitude to its complex conjugate, CPTsymmetry is conserved.
Though some of their amplitudes have opposite phases, both quarks and antiquarks have positive energy, and hence acquire the same phase as they move in spacetime. This phase also depends on their mass, which is identical but depends both on flavor and on the Higgs VEV which changes along the domain wall. Thus certain sums of amplitudes for quarks have different absolute values compared to those of antiquarks. In all, quarks and antiquarks may have different reflection and transmission probabilities through the domain wall, and it turns out that more quarks coming from the unbroken phase are transmitted compared to antiquarks.
Thus there is a net baryonic flux through the domain wall. Due to sphaleron transitions, which are abundant in the unbroken phase, the net antibaryonic content of the unbroken phase is wiped off. However, sphalerons are rare enough in the broken phase as not to wipe off the excess of baryons there. In total, there is net creation of baryons.
In this scenario, nonperturbative electroweak interactions (i.e. the sphaleron) are responsible for the Bviolation, the perturbative electroweak Lagrangian is responsible for the CPviolation, and the domain wall is responsible for the lack of thermal equilibrium; together with the CPviolation it also creates a Cviolation in each of its sides.
Matter content in the universe
See also: Baryon asymmetryBaryon asymmetry parameter
The challenges to the physics theories are then to explain how to produce this preference of matter over antimatter, and also the magnitude of this asymmetry. An important quantifier is the asymmetry parameter,
 .
This quantity relates the overall number density difference between baryons and antibaryons (n_{B} and n_{B}, respectively) and the number density of cosmic background radiation photons n_{γ}.
According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3,000 kelvin, corresponding to an average kinetic energy of 3,000 K / (10.08×10^{4} K/eV) = 0.3 eV. After the decoupling, the total number of CBR photons remains constant. Therefore due to spacetime expansion, the photon density decreases. The photon density at equilibrium temperature T, per cubic kelvin and per cubic centimeter, is given by
 ,
with k_{B} as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum. At the current CBR photon temperature of 2.725 K, this corresponds to a photon density n_{γ} of around 411 CBR photons per cubic centimeter.
Therefore, the asymmetry parameter η, as defined above, is not the "good" parameter. Instead, the preferred asymmetry parameter uses the entropy density s,
because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is
with p and ρ as the pressure and density from the energy density tensor T_{μν}, and g_{*} as the effective number of degrees of freedom for "massless" particles (inasmuch as mc^{2} ≪ k_{B}T holds) at temperature T,
 ,
for bosons and fermions with g_{i} and g_{j} degrees of freedom at temperatures T_{i} and T_{j} respectively. At the present era, s = 7.04n_{γ}.
See also
 Lepton
 Leptogenesis
 CP violation
 Anthropic principle
 AffleckDine mechanism
References
Articles
 ^ P.A.M. Dirac (1928). "The Quantum Theory of the Electron". Proceedings of the Royal Society of London A 117 (778): 610–624. Bibcode 1928RSPSA.117..610D. doi:10.1098/rspa.1928.0023.
 ^ A. D. Sakharov (1967). "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe". Journal of Experimental and Theoretical Physics 5: 24–27., republished as A. D. Sakharov (1991). "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe". Soviet Physics Uspekhi 34 (5): 392–393. Bibcode 1991SvPhU..34..392S. doi:10.1070/PU1991v034n05ABEH002497.
 ^ A. A. Penzias and R. W. Wilson (1965). "A Measurement of Excess Antenna Temperature at 4080 Mc/s". Astrophysical Journal 5: 419–421. Bibcode 1965ApJ...142..419P. doi:10.1086/148307.
 ^ J. W. Cronin, V. L. Fitch et al. (1964). "Evidence for the 2π decay of the K0
2 meson". Physical Review Letters 13 (4): 138–140. Bibcode 1964PhRvL..13..138C. doi:10.1103/PhysRevLett.13.138.  ^ ^{a} ^{b} M. E. Shaposhnikov, G. R. Farrar (1993). "Baryon Asymmetry of the Universe in the Minimal Standard Model". Physical Review Letters 70 (19): 2833–2836. arXiv:hepph/9305274. Bibcode 1993PhRvL..70.2833F. doi:10.1103/PhysRevLett.70.2833.
 ^ A. Riotto, M. Trodden (1999). "Recent progress in baryogenesis". Annual Review of Nuclear and Particle Science 49: 46. arXiv:hepph/9901362. Bibcode 1999ARNPS..49...35R. doi:10.1146/annurev.nucl.49.1.35.
 ^ V. A. Kuzmin, V. A. Rubakov, M. E. Shaposhnikov (1985). "On anomalous electroweak baryonnumber nonconservation in the early universe". Physic Letters B 155: 36–42. Bibcode 1985PhLB..155...36K. doi:10.1016/03702693(85)910287.
Textbooks
 E. W. Kolb and M. S. Turner (1994). The Early Universe. Perseus Publishing. ISBN 0201626748.
Preprints
 A. D. Dolgov (1997). "Baryogenesis, 30 Years After". arXiv:hepph/9707419 [hepph].
 A. Riotto (1998). "Theories of Baryogenesis". arXiv:hepph/9807454 [hepph/9807454].
 M. Trodden (1998). "Electroweak Baryogenesis". Reviews of Modern Physics 71 (5): 1463. arXiv:hepph/9803479. Bibcode 1999RvMP...71.1463T. doi:10.1103/RevModPhys.71.1463.
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