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R-parity is a concept in particle physics. In the Minimal Supersymmetric Standard Model, baryon number and lepton number are no longer conserved by all of the renormalizable couplings in the theory. Since baryon number and lepton number conservation have been tested very precisely, these couplings need to be very small in order not to be in conflict with experimental data. R-parity is a
Contents
- Dark matter candidate
- R parity violating couplings of the MSSM
- Proton decay
- Possible origins of R parity
- References
or, equivalently, as
where s is spin, B is baryon number, and L is lepton number. All Standard Model particles have R-parity of +1 while supersymmetric particles have R-parity of −1.
Dark matter candidate
With R-parity being preserved, the lightest supersymmetric particle (LSP) cannot decay. This lightest particle (if it exists) may therefore account for the observed missing mass of the universe that is generally called dark matter. In order to fit observations, it is assumed that this particle has a mass of 7002100000000000000♠100 GeV/c2 to 7000100000000000000♠1 TeV/c2, is neutral and only interacts through weak interactions and gravitational interactions. It is often called a weakly interacting massive particle or WIMP.
Typically the dark matter candidate of the MSSM is an admixture of the electroweak gauginos and Higgsinos and is called a neutralino. In extensions to the MSSM it is possible to have a sneutrino be the dark matter candidate. Another possibility is the gravitino, which only interacts via gravitational interactions and does not require strict R-parity. Note that there are different forms of parity with different effects and principles, one should not confuse this parity with another parity.
R-parity violating couplings of the MSSM
The renormalizable R-parity violating couplings of the MSSM are
The strongest constraint involving this coupling alone is from the non-observation of neutron–antineutron oscillations.
The strongest constraint involving this coupling alone is the violation universality of Fermi constant
The strongest constraint involving this coupling alone is the violation universality of Fermi constant in leptonic charged current decays.
The strongest constraint involving this coupling alone is that it leads to a large neutrino mass.
While the constraints on single couplings are reasonably strong, if multiple couplings are combined together, they lead to proton decay. Thus there are further maximal bounds on values of the couplings from maximal bounds on proton decay rate.
Proton decay
Without baryon and lepton number being conserved and taking
Because proton decay involves violating both lepton and baryon number simultaneously, no single renormalizable R-parity violating coupling leads to proton decay. This has motivated the study of R-parity violation where only one set of the R-parity violating couplings are non-zero which is sometimes called the single coupling dominance hypothesis.
Possible origins of R-parity
A very attractive way to motivate R-parity is with a B − L continuous gauge symmetry which is spontaneously broken at a scale inaccessible to current experiments. A continuous
This phenomenon can arise as an automatic symmetry in SO(10) grand unified theories. This natural occurrence of R-parity is possible because in SO(10) the Standard Model fermions arise from the 16-dimensional spinor representation, while the Higgs arises from a 10 dimensional vector representation. In order to make an SO(10) invariant coupling, one must have an even number of spinor fields (i.e. there is a spinor parity). After GUT symmetry breaking, this spinor parity descends into R-parity so long as no spinor fields were used to break the GUT symmetry. Explicit examples of such SO(10) theories have been constructed.