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In physical cosmology, the baryon asymmetry problem, also known as the matter asymmetry problem or the matterantimatter asymmetry problem, is the observed imbalance in baryonic matter and antibaryonic matter in the observable universe. As the two form and behave in nearly identical ways, it is expected that they would have been created in near equal portions by the Big Bang, where in reality matter makes up the vast majority of the universe (including the Earth and humanity). Neither the Standard Model of particle physics nor the theory of general relativity provides a known explanation for why this should be so, and it is a natural assumption that the universe is neutral with all conserved charges. Since this does not seem to have been the case, it is likely some physical laws must have acted differently or did not exist for matter and/or antimatter. Several competing hypotheses exist to explain the imbalance of matter and antimatter that resulted in baryogenesis. However, there is as of yet no consensus theory to explain the phenomenon, which has been described as "one of the great mysteries in physics".

== Sakharov conditions ==

In 1967, Andrei Sakharov proposed 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 and CP violation in the neutral kaon system. The three necessary "Sakharov conditions" are:

Baryon number

    B
  

{\displaystyle B}

violation. C-symmetry violation and CP-symmetry violation. Interactions out of thermal equilibrium. 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.

=== Baryon number violation === 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
    ]
    =
    B
    H
    
    H
    B
    =
    0
  

{\displaystyle [B,H]=BH-HB=0}

. However, the Standard Model is known to violate the conservation of baryon number: a

    U
    (
    1
    
      )
      
        B
      
    
  

{\displaystyle U(1)_{B}}

Adler-Bell-Jackiw anomaly captured by a triangle Feynman diagram

    U
    (
    1
    
      )
      
        B
      
    
  

{\displaystyle U(1)_{B}}
    S
    U
    (
    2
    
      )
      
        w
      
    
  

{\displaystyle SU(2)_{w}}
    S
    U
    (
    2
    
      )
      
        w
      
    
  

{\displaystyle SU(2)_{w}}

with

    S
    U
    (
    2
    
      )
      
        w
      
    
  

{\displaystyle SU(2)_{w}}

weak interaction gauge group. 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.

=== CP-symmetry violation ===

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 Standard Model, CP violation appears as a complex phase in the quark mixing matrix of the weak interaction. There may also be a non-zero CP-violating phase in the neutrino mixing matrix, but this is currently unmeasured. The first in a series of basic physics principles to be violated was parity through Chien-Shiung Wu's experiment. This led to CP violation being verified in the 1964 FitchCronin experiment with neutral kaons, which resulted in the 1980 Nobel Prize in Physics (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. Despite the allowance for CP violation in the Standard Model, it is insufficient to account for the observed baryon asymmetry of the universe (BAU) given the limits on baryon number violation, meaning that beyond-Standard Model sources are needed. 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 (Λb0) 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. 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, 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 ==