The paper "VIOLATION OF CP INVARIANCE, C ASYMMETRY AND BARYON ASYMMETRY OF UNIVERSE."(A. D. Sakharov, 1967)

The paper [1] addresses the fundamental question symmetry would assure compensation between processes of the asymmetry between matter and antimatter in increasing and decreasing the baryon number. our universe. The Dirac equation predicts the existence Currently, there is no experimental evidence of of antiparticles along with the corresponding particles. particle interactions where the conservation of baryon It has been veried experimentally that every known number is broken perturbatively: this would appear to kind of particle has a corresponding antiparticle. The suggest that all observed particle reactions have equal CPT Theorem guarantees that a particle and its baryon number before and after. Mathematically, the antiparticle have exactly the same mass and lifetime, commutator of the baryon number quantum operator and opposite charge. Given this symmetry, it is puzzling with the (perturbative) Standard Model hamiltonian that the universe does not have equal amounts of is zero: [Bˆ, Hˆ ] = BˆHˆ − Hˆ Bˆ = 0. However, the matter and antimatter. Indeed, there is no experimental Standard Model is known to violate the conservation evidence that there are any signicant concentrations of of baryon number non-perturbatively: a global U(1) antimatter in the observable universe. anomaly. Baryon number violation can also result from There are two main interpretations for this disparity: physics beyond the Standard Model (see supersymmetry either the universe began with a small preference for and Grand Unication Theories). matter (total baryonic number of the universe dierent The second condition - violation of CP-symmetry- was from zero), or the universe was originally perfectly discovered in 1964 (direct CP-violation, that is violation symmetric, but somehow a set of phenomena contributed of CP-symmetry in a decay process, was discovered to a small imbalance in favor of matter over time. The later, in 1999). Due to CPT-symmetry, violation of CP- second point of view is preferred, although there is no symmetry demands violation of time inversion symmetry, clear experimental evidence indicating either of them to or T-symmetry. be the correct one. In the out-of-equilibrium decay scenario, the last In his 1967 paper, Andrei Sakharov proposed a condition states that the rate of a reaction which set of three necessary conditions that a baryon- generates baryon-asymmetry must be less than the rate generating interaction must satisfy to produce matter of expansion of the universe. In this situation the particles and antimatter at dierent rates. These conditions and their corresponding antiparticles do not achieve were inspired by the recent discoveries of the thermal equilibrium due to rapid expansion decreasing cosmic background radiation and CP-violation in the the occurrence of pair-annihilation. neutral kaon system. The three necessary "Sakharov The work by Sakharov remained unnoticed for several conditions"are: years, and the key hypothesis of baryonic charge 1) Baryon number B violation. nonconservation, which is necessary for the generation 2) C-symmetry and CP-symmetry violation. of an asymmetry between baryons and antibaryons, was 3) Interactions out of thermal equilibrium. not accepted until the models of Grand Unication Baryon number violation is obviously a necessary were put forward in 1974. After it was understood that condition to produce an excess of baryons over anti- nonconservation of baryons might be quite a natural baryons. But C-symmetry violation is also needed so and general phenomenon, the attitude to the possibility that the interactions which produce more baryons of a dynamical generation of baryon asymmetry of the than anti-baryons will not be counterbalanced by universe changed drastically. Acceptance of Sakharov's interactions which produce more anti-baryons than ideas stimulated the ood of papers which remained baryons. CP-symmetry violation is similarly required unabated ever since. 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 [1] A. D. Sakharov JETP Lett.-USSR 5,24 (1967).