In ordinary perturbative Standard Model reactions all three interactions conserve electric charge, four-momentum, total angular momentum, baryon number, and total lepton number. The last two are accidental conservation laws of these perturbative processes, not exact nonperturbative statements: electroweak sphalerons violate while preserving baryon-minus-lepton number. Total color charge is respected throughout.
The strong interaction and electromagnetic interaction also conserve each net quark flavor number, including strangeness, charm and bottom flavour. The weak charged current can change them through the Cabibbo-Kobayashi-Maskawa matrix. Isospin is an approximate strong interaction symmetry in the small light-quark mass difference limit; the different electric charges of and break it in the electromagnetic interaction. Approximate flavor symmetry is distinct from exact net-flavour-number conservation by those interactions.
Parity conservation and charge conjugation symmetry hold for the electromagnetic interaction and, assuming a negligible strong CP parameter, the strong interaction. The weak interaction violates both, and also violates CP symmetry in suitable processes. CPT symmetry holds under the usual local Lorentz invariant quantum field theory assumptions. Individual lepton family numbers are conserved in the conventional massless-neutrino approximation but not in neutrino oscillations; an assertion of exact family conservation in all observed reactions would therefore be false.
A grand unified theory embeds the strong and electroweak gauge groups in a larger group, for example . quarks and leptons can belong to common representations, while heavy extra gauge or scalar bosons connect them. The resulting interactions can violate baryon number, unlike ordinary perturbative Standard Model reactions. Running gauge couplings and proton-decay searches test such ideas; unification is a theoretical possibility, not an established observation.[ref]
baryogenesis must explain why a nearly matter-antimatter-symmetric early state evolves into a surviving baryon asymmetry. In the usual local CPT-invariant framework, the Sakharov conditions require baryon-number violation, C and CP violation, and departure from thermal equilibrium. baryon conservation would forbid creating a net excess; exact conjugation symmetries would pair baryon-producing processes with equal antibaryon production; equilibrium with no imposed asymmetry would erase a source term through detailed balance.
For heavy particles and , let decay channels carry different baryon numbers. CP-violating interference can make their branching fractions differ, even though CPT symmetry requires equal total widths. Defining the mean baryon number produced per decay as , an out-of-equilibrium abundance can generate of order times its initial number per entropy, reduced by inefficient production and washout. A rough condition is that decays become effective after inverse production has ceased, with the relevant reaction rate compared with the Hubble parameter. Complex couplings alone do not guarantee a nonzero rate asymmetry: a relative absorptive phase is also needed.
Survival matters as much as production. Electroweak sphalerons violate while conserving baryon-minus-lepton number , so a minimal GUT-generated asymmetry with can be washed out if sphalerons and the other relevant reactions equilibrate. Generating nonzero , as in suitable heavy-Majorana-neutrino leptogenesis, can avoid this problem. A viable GUT baryogenesis model must generate an asymmetry and demonstrate that subsequent reactions do not erase it. The Sakharov conditions are necessary ingredients under these assumptions, not a numerical prediction of the observed abundance.