Rparity

R-parity is a discrete symmetry used in supersymmetric theories to assign a multiplicative quantum number to each particle. It is defined as R = (-1)^{3(B-L)+2s}, where B is baryon number, L is lepton number, and s is spin. Under this definition, all Standard Model particles have R = +1, whereas their superpartners have R = -1.

The primary purpose of imposing R-parity is to forbid renormalizable interactions that violate baryon or lepton number in the Minimal Supersymmetric Standard Model (MSSM). Conservation of R-parity therefore prevents rapid proton decay and, if preserved, implies the lightest supersymmetric particle (LSP) is stable, making it a natural dark matter candidate. Collider events involving R-parity conserving SUSY typically feature pair production of superpartners and a final state with missing transverse energy carried away by LSPs.

R-parity need not be exact; models with R-parity violation (RPV) allow the LSP to decay into Standard Model particles, removing a dark matter candidate and altering collider signatures. The MSSM can accommodate RPV through additional terms in the superpotential such as LLE^c, LQD^c, and U^cD^cD^c, which violate lepton and/or baryon number. To avoid rapid proton decay, a combination of suppressed couplings is typically required or only certain terms are kept.

R-parity is related to matter parity P_M = (-1)^{3(B-L)} and the spin factor, R = (-1)^{2s} P_M. The idea originated in the 1980s when physicists introduced a discrete symmetry to suppress dangerous interactions in SUSY theories.

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