Baryon asymmetry

Antimatter
Antiparticles Positron Antiproton Antineutron Antihydrogen Antihelium Onia Antiprotonic hydrogen Antiprotonic helium Muonium True muonium Pionium Positronium Quarkonium
Concepts and phenomena Annihilation Baryogenesis Baryon asymmetry Comet CP violation Gravitational interaction Positron emission
Devices Cloud chamber Particle accelerator Antiproton decelerator Relativistic Heavy Ion Collider Penning trap
Uses Positron emission tomography Fuel Weapon
People and bodies Carl David Anderson Paul Dirac Andrei Sakharov CERN
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In

In 1967, Andrei Sakharov proposed^[5] 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 microwave background^[6] and CP violation in the neutral kaon system.^[7] The three necessary "Sakharov conditions" are:

• Baryon number ${\displaystyle B}$ violation.
• CP-symmetry
  violation.
• Interactions out of thermal equilibrium.

Baryon number violation

Baryon number violation is 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.^[8]

Currently, there is no experimental evidence of particle interactions where the conservation of baryon number is broken

is zero: ${\displaystyle [B,H]=BH-HB=0}$. 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

The second condition for generating baryon asymmetry—violation of charge-parity symmetry—is that a process is able to happen at a different rate to its antimatter counterpart. In the

A possible new source of CP violation was found at the Large Hadron Collider (LHC) by the LHCb collaboration during the first three years of LHC operations (beginning March 2010). The experiment analyzed the decays of two particles, the bottom Lambda (Λ_b⁰) and its antiparticle, and compared the distributions of decay products. The data showed an asymmetry of up to 20% of CP-violation sensitive quantities, implying a breaking of CP-symmetry. This analysis will need to be confirmed by more data from subsequent runs of the LHC.^[9]

One method to search for additional CP-violation is the search for electric dipole moments of fundamental or composed particles. The existence of electric dipole moments in equilibrium states requires violation of T-symmetry. That way finding a non zero electric dipole moment would imply the existence of T-violating interactions in the vacuum corrections to the measured particle. So far all measurements are consistent with zero putting strong bounds on the properties of the yet unknown new CP-violating interactions.

Interactions out of thermal equilibrium

In the out-of-equilibrium decay scenario,^[10] 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.

Other explanations

Regions of the universe where antimatter dominates

Another possible explanation of the apparent baryon asymmetry is that matter and antimatter are essentially separated into different, widely distant regions of the

The state of the universe, as it is, does not violate the CPT symmetry, because the Big Bang could be considered as a double sided event, both classically and quantum mechanically, consisting of a universe-antiuniverse pair. This means that this universe is the charge (C), parity (P) and time (T) image of the anti-universe. This pair emerged from the Big Bang epochs not directly into a hot, radiation-dominated era. The antiuniverse would flow back in time from the Big Bang, becoming bigger as it does so, and would be also dominated by antimatter. Its spatial properties are inverted if compared to those in our universe, a situation analogous to creating electron–positron pairs in a vacuum. This model, devised by physicists from the Perimeter Institute for Theoretical Physics in Canada, proposes that temperature fluctuations in the cosmic microwave background (CMB) are due to the quantum-mechanical nature of space-time near the Big Bang singularity.^[13] This means that a point in the future of our universe and a point in the distant past of the anti-universe would provide fixed classical points, while all possible quantum-based permutations would exist in between.^{[citation needed]} Quantum uncertainty causes the universe and antiuniverse to not be exact mirror images of each other.^[14]

This model has not shown if it can reproduce certain observations regarding the inflation scenario, such as explaining the uniformity of the cosmos on large scales. However, it provides a natural and straightforward explanation for

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 3000 kelvin, corresponding to an average kinetic energy of 3000 K / (10.08×10³ K/eV) = 0.3 eV. 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

${\displaystyle n_{\gamma }={\frac {1}{\pi ^{2}}}\left({\frac {k_{B}T}{\hbar c}}\right)^{3}\times \int _{0}^{\infty }{\frac {x^{2}}{e^{x}-1}}\,dx={\frac {1}{\pi ^{2}}}\left({\frac {k_{B}T}{\hbar c}}\right)^{3}\times 2\,\zeta (3)\approx 20.3\left({\frac {T}{1{\text{K}}}}\right)^{3}{\text{cm}}^{-3},}$

with k_B as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant. 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,

${\displaystyle \eta _{s}={\frac {n_{B}-n_{\bar {B}}}{s}}}$

because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is

${\displaystyle s\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\mathrm {entropy} }{\mathrm {volume} }}={\frac {p+\rho }{T}}={\frac {2\pi ^{2}}{45}}g_{*}(T)T^{3}}$

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 mc² ≪ k_BT holds) at temperature T,

${\displaystyle g_{*}(T)=\sum _{i=\mathrm {bosons} }g_{i}\left({\frac {T_{i}}{T}}\right)^{3}+{\frac {7}{8}}\sum _{j=\mathrm {fermions} }g_{j}{\left({\frac {T_{j}}{T}}\right)}^{3},}$

for bosons and fermions with g_i and g_j degrees of freedom at temperatures T_i and T_j respectively. Presently, s = 7.04n_γ.

See also

• Baryogenesis
• CP violation
• List of unsolved problems in physics

References