Baryogenesis
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Baryogenesis

In physical cosmology, baryogenesis is the hypothetical physical process that took place during the early universe that produced baryonic asymmetry, i.e. the imbalance of matter (baryons) and antimatter (antibaryons) in the observed universe.

One of the outstanding problems in modern physics is the predominance of matter over antimatter in the universe. The universe, as a whole, seems to have a nonzero positive baryon number density – that is, matter exists. Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, it would normally be expected that the overall baryon number should be zero, as matter and antimatter should have been created in equal amounts. This has led to a number of proposed mechanisms for symmetry breaking that favour the creation of normal matter (as opposed to antimatter) under certain conditions. This imbalance would have been exceptionally small, on the order of 1 in every (1010) particles a small fraction of a second after the Big Bang, but after most of the matter and antimatter annihilated, what was left over was all the baryonic matter in the current universe, along with a much greater number of bosons. Experiments reported in 2010 at Fermilab, however, seem to show that this imbalance is much greater than previously assumed. In an experiment involving a series of particle collisions, the amount of generated matter was approximately 1% larger than the amount of generated antimatter. The reason for this discrepancy is yet unknown.[1]

Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons or massive Higgs bosons (
H0
). The rate at which these events occur is governed largely by the mass of the intermediate
X
or
H0
particles, so by assuming these reactions are responsible for the majority of the baryon number seen today, a maximum mass can be calculated above which the rate would be too slow to explain the presence of matter today. These estimates predict that a large volume of material will occasionally exhibit a spontaneous proton decay.

Baryogenesis theories are based on different descriptions of the interaction between fundamental particles. Two main theories are electroweak baryogenesis (standard model), which would occur during the electroweak epoch, and the GUT baryogenesis, which would occur during or shortly after the grand unification epoch. Quantum field theory and statistical physics are used to describe such possible mechanisms.

Baryogenesis is followed by primordial nucleosynthesis, when atomic nuclei began to form.

Question, Web Fundamentals.svg Unsolved problem in physics:
Why does the observable universe have more matter than antimatter?
(more unsolved problems in physics)

Background

The Dirac equation,[2] 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 then, experiments have verified that every known kind of particle has a corresponding antiparticle. Under the CPT theorem, a particle and its antiparticle have the same mass and lifetime, and 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.

GUT Baryogenesis under Sakharov conditions

In 1967, Andrei Sakharov proposed[3] a set of three necessary conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the cosmic background radiation[4] and CP-violation in the neutral kaon system.[5] The three necessary "Sakharov conditions" are:

Baryon number violation is obviously a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons. CP-symmetry violation is similarly required because otherwise equal numbers of left-handed baryons and right-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed 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.[6]

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: . However, the Standard Model is known to violate the conservation of baryon number only non-perturbatively: a global U(1) anomaly. To account for baryon violation in baryogenesis, such events (including proton decay) can occur in Grand Unification Theories (GUTs) and supersymmetric (SUSY) models via hypothetical massive bosons such as the X boson.

The second condition - violation of CP-symmetry - was discovered in 1964 (direct CP-violation, that is violation of CP-symmetry in a decay process, was discovered later, in 1999). Due to CPT symmetry, violation of CP-symmetry demands violation of time inversion symmetry, or T-symmetry.

In the out-of-equilibrium decay scenario,[7] the last condition states that the rate of a reaction which generates baryon-asymmetry 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 pair-annihilation.

Baryogenesis within the Standard Model

Electroweak baryogenesis

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 first-order phase transition, since otherwise sphalerons wipe off any baryon asymmetry that happened up to the phase transition, while later the amount of baryon non-conserving interactions is negligible.[8]

The phase transition domain wall breaks the P-symmetry spontaneously, allowing for CP-symmetry violating interactions to create C-asymmetry on both its sides: quarks tend to accumulate on the broken phase side of the domain wall, while anti-quarks tend to accumulate on its unbroken phase side. This happens as follows:[6]

Due to CP-symmetry violating electroweak interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving anti-quarks, but rather have opposite phase (see CKM matrix and Kaon); since time reversal takes an amplitude to its complex conjugate, CPT-symmetry is conserved.

Though some of their amplitudes have opposite phases, both quarks and anti-quarks have positive energy, and hence acquire the same phase as they move in space-time. 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 anti-quarks. In all, quarks and anti-quarks 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 anti-quarks.

Thus there is a net baryonic flux through the domain wall. Due to sphaleron transitions, which are abundant in the unbroken phase, the net anti-baryonic 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, non-perturbative electroweak interactions (i.e. the sphaleron) are responsible for the B-violation, the perturbative electroweak Lagrangian is responsible for the CP-violation, and the domain wall is responsible for the lack of thermal equilibrium; together with the CP-violation it also creates a C-violation in each of its sides.

Matter content in the universe

Baryon 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, naïvely given by

.

This quantity relates the overall number density difference between baryons and antibaryons (nB and nB, respectively) and the number density of cosmic background radiation photons n?.

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly kelvin, corresponding to an average kinetic energy of / = . After the decoupling, the total number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T per cubic centimeter, is given by

,

with kB as the Boltzmann constant, ? as the Planck constant divided by 2? and c as the speed of light in vacuum, and ?(3) as Apéry's constant. At the current CBR photon temperature of , this corresponds to a photon density n? of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameter ?, as defined above, is not the "best" 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 ? as the pressure and density from the energy density tensor T, and g? as the effective number of degrees of freedom for "massless" particles at temperature T (in so far as holds),

,

for bosons and fermions with gi and gj degrees of freedom at temperatures Ti and Tj respectively. At the present epoch,

See also

References

Articles

  1. ^ V.M. Abazov; et al. (2010). "Evidence for an anomalous like-sign dimuon charge asymmetry". Physical Review D. 82 (3): 032001. arXiv:1005.2757. Bibcode:2010PhRvD..82c2001A. doi:10.1103/PhysRevD.82.032001.
  2. ^ 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.
  3. ^ A. D. Sakharov (1967). "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe". Journal of Experimental and Theoretical Physics Letters. 5: 24-27. and in Russian, A. D. Sakharov (1967). "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe". ZhETF Pis'ma. 5: 32-35. republished as A. D. Sakharov (1991). "Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe". Soviet Physics Uspekhi (in Russian and English). 34 (5): 392-393. Bibcode:1991SvPhU..34..392S. doi:10.1070/PU1991v034n05ABEH002497.
  4. ^ A. A. Penzias; R. W. Wilson (1965). "A Measurement of Excess Antenna Temperature at 4080 Mc/s". Astrophysical Journal. 142: 419-421. Bibcode:1965ApJ...142..419P. doi:10.1086/148307.
  5. ^ J. W. Cronin; V. L. Fitch; et al. (1964). "Evidence for the 2? decay of the
    K0
    2
    meson". Physical Review Letters. 13 (4): 138-140. Bibcode:1964PhRvL..13..138C. doi:10.1103/PhysRevLett.13.138.
  6. ^ 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:hep-ph/9305274. Bibcode:1993PhRvL..70.2833F. doi:10.1103/PhysRevLett.70.2833. PMID 10053665.
  7. ^ A. Riotto; M. Trodden (1999). "Recent progress in baryogenesis". Annual Review of Nuclear and Particle Science. 49: 46. arXiv:hep-ph/9901362. Bibcode:1999ARNPS..49...35R. doi:10.1146/annurev.nucl.49.1.35.
  8. ^ V. A. Kuzmin; V. A. Rubakov; M. E. Shaposhnikov (1985). "On anomalous electroweak baryon-number non-conservation in the early universe". Physics Letters B. 155 (1-2): 36-42. Bibcode:1985PhLB..155...36K. doi:10.1016/0370-2693(85)91028-7.

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Baryogenesis
 



 



 
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