R-parity

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R-parity is a concept in particle physics. In the supersymmetric extension of the 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 $Z 2$ symmetry acting on the MSSM fields that forbids these couplings and can be defined as:

R = (-1)^2j+3B+L.

With spin j, baryon number B, and lepton number L. All Standard Model particles have R-parity of 1 while supersymmetric particles have R-parity -1.

1 Dark Matter Candidate
2 R-parity violating couplings of the MSSM
3 Proton decay
4 Possible origins of R-parity
5 External links

[edit] Dark Matter Candidate

With R-parity being preserved, the lightest supersymmetric particle (LSP) can not decay. This lightest particle typically has a mass of 100 GeV to 1 TeV, is neutral and only interacts through weak interactions and is often called a weakly interacting massive particle or WIMP. Because this particle can not decay, there will be a cosmic background of LSPs and their relic abundance is typically the correct size to coincide with the observed missing mass of the universe that is generally called dark matter.

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.

[edit] R-parity violating couplings of the MSSM

The renormalizable R-parity violating couplings of the MSSM are

$\int d^2\theta\; \lambda_1\; U^c D^c D^c$ violates B by 1 unit

The strongest constraint involving this coupling alone is from to neutron - antineutron oscillations.

$\int d^2 \theta\; \lambda_2\; Q D^c L$ violates L by 1 unit

The strongest constraint involving this coupling alone is the violation universality of Fermi constant $G F$ in quark and leptonic charged current decays.

$\int d^2 \theta\; \lambda_3\; L E^cL$ violates L by 1 unit

The strongest constraint involving this coupling alone is the violation university of Fermi constant in leptonic charged current decays.

$\int d^2 \theta\; \kappa\; L H_u$ violates L by 1 unit

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.

[edit] Proton decay

Without baryon and lepton number being conserved and taking $\mathcal{O}(1)$ couplings for the R-parity violating couplings, the proton can decay in approximately $10 - 2$ seconds or if minimal flavor violation is assumed the proton lifetime can be extended to 1 year. Since the proton lifetime is observed to be greater than $1033 - 10 34$ years (depending on the exact decay channel), this would highly disfavour the model. R-parity sets all of the renormalizable baryon and lepton number violating couplings to zero and the proton is stable at the renormalizable level and the lifetime of the proton is increased to $\mathcal{O}(10^{32})$ years and is nearly consistent with current observational data.

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.

[edit] Possible origins of R-parity

While on the face of it, R-parity is an ad hoc imposition upon the MSSM, it 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.

[edit] External links

R-parity Violating Supersymmetry by R.Barbier, C.Berat, M.Besancon, M.Chemtob, A.Deandrea, E.Dudas, P.Fayet, S.Lavignac, G.Moreau, E.Perez, and Y.Sirois.

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Categories: Particle physics | Supersymmetry