Also known as "matter-parity". In many Supersymmetry (SUSY) models, R-parity ensures that protons – and hence all of the atoms in the universe – are unable to decay to other particles quickly by exchanging SUSY particles. Though this can also be prevented in models without R-parity conservation, introducing R-parity is often considered the simplest possibility.
The R-parity of a particle is defined by (-1)^3(B-L)+2s where B is baryon number, L is lepton number, and s is spin. R-parity has a value of (+1) for Standard Model particles and (-1) for their superpartners.
Conservation of R-parity prevents proton decay via exchange of a superpartner into a positron and a neutral pion. Conservation of R-parity also prevents the decay of the lightest superpartner into standard model particles, and thus the lightest superpartner becomes an appealing candidate for dark matter.
While conservation of R-parity accomplishes its purpose of preventing proton decay, other choices are possible. Extending the Standard Model with a new gauge symmetry with charge (B–L) would give a natural way to suppress unwanted baryon- and lepton-number-violating interactions, and would allow the lightest superpartner to decay.