R-parity
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'''R-parity''' is a concept in [[particle physics]]. In the [[MSSM|supersymmetric extension]] of the [[standard model|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 <math>Z_2</math> symmetry acting on the [[Minimal Supersymmetric Standard Model]] (MSSM) fields that forbids these couplings and can be defined as:
:''R'' = (-1)<sup>''2j+3B+L''</sup>.
With [[Spin (physics)|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.
==Dark matter candidate==
With R-parity being preserved, the lightest supersymmetric particle ([[Lightest Supersymmetric Particle|LSP]]) can not 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 have a mass of 100 GeV to 1 TeV, is neutral and only interacts through [[weak force|weak interactions]] and [[Gravitation|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 [[gaugino]]s and [[Higgsino]]s 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 [[Gravitation|gravitational interactions]] and does not require strict R-parity.
==R-parity violating couplings of the MSSM==
The renormalizable R-parity violating couplings of the MSSM are
* <math> \int d^2\theta\; \lambda_1\; U^c D^c D^c </math> violates B by 1 unit
The strongest constraint involving this coupling alone is from to neutron - antineutron oscillations.
* <math>\int d^2 \theta\; \lambda_2\; Q D^c L </math> violates L by 1 unit
The strongest constraint involving this coupling alone is the violation universality of Fermi constant <math>G_F</math> in quark and leptonic charged current decays.
* <math>\int d^2 \theta\; \lambda_3\; L E^cL </math> violates L by 1 unit
The strongest constraint involving this coupling alone is the violation universality of Fermi constant in leptonic charged current decays.
* <math>\int d^2 \theta\; \kappa\; L H_u</math> 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. 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 <math>\mathcal{O}(1)</math> couplings for the R-parity violating couplings, the proton can decay in approximately
<math>10^{-2}</math> 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 <math>10^{33} - 10^{34}</math> 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 <math>\mathcal{O}(10^{32})</math> years and is nearly consistent with current observational data.
[[Image:R-parity violating decay.svg|frame|right]]
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==
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 theory|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.
==External links==
*[http://arxiv.org/abs/hep-ph/0406039 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.
[[Category:Particle physics]]
[[Category:Supersymmetry]]
[[pl:parzystość R]]