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donde ''s'' es el [[espín]], ''B'' el número bariónico, y ''L'' el número leptónico. Todas las partículas del modelo estándar tienen paridad R +1, y las partículas supersimétricas paridad R -1.
 
==Acoplamientos que violan la paridad R en el MSSM==
==Dark matter candidate==
With R-parity being preserved, the lightest supersymmetric particle ([[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]].{{Citation needed|date=March 2009}} In order to fit observations, it is assumed that this particle has a mass of {{val|100|ul=GeV/c2}} to {{val|1|ul=TeV/c2}}, is neutral and only interacts through [[weak interaction]]s and [[Gravitation|gravitational interactions]]. It is often called a [[weakly interacting massive particle]] or WIMP.
 
Los acoplamientos renormalizables del MSSM que violan la paridad R son:
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. Note that there are different forms of parity with different effects and principles, one should not confuse this parity with another parity.
 
* <math> \int d^2\theta\; \lambda_1\; U^c D^c D^c </math> viola ''B'' por 1 unidad. La acotación más fuerte para este término proviene de la no observación de oscilaciones neutrón-antineutrón[[antineutron|.]]
==R-parity violating couplings of the MSSM==
 
* <math>\int d^2 \theta\; \lambda_2\; Q D^c L </math> viola ''L'' por 1 unidad. La acotación más fuerte de este término esla violación de la universalidad dr la [[constante de Fermi]] <math>G_F</math> en desintegraciones con corrientes cargadas de quarks y leptones.
The renormalizable R-parity violating couplings of the MSSM are
 
* <math>\int d^2 \theta\; \lambda_3\; L E^cL </math> viola ''L'' por 1 unidad. La acotación más fuerte de este término esla violación de la universalidad dr la [[constante de Fermi]] <math>G_F</math> en desintegraciones con corrientes cargadas de quarks y leptones..
* <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 the non-observation of [[antineutron|neutron–antineutron oscillations.]]
 
* <math>\int d^2 \theta\; \lambda_2kappa\; Q D^c L H_u</math> violatesviola ''L'' bypor 1 unitunidad. La acotación de este término proviene de la masa de los [[Neutrino|neutrinos]].
Aunque las cotas para los acoplamientos indivinduales son bastante fuertes, si se combinan varias dan lugar a la [[desintegración del protón]]. Por lo tanto hay cotas más restrictivas en los acoplamientos teniendo en cuenta la tasa máxima de desintegración del protón.
The strongest constraint involving this coupling alone is the violation universality of [[Fermi coupling constant|Fermi constant]] <math>G_F</math> in quark and leptonic charged current decays.
 
==Desintegración del protón==
* <math>\int d^2 \theta\; \lambda_3\; L E^cL </math> violates L by 1 unit
Si los números bariónico y leptónico no se conservan y se asumen acoplamientos que violan la paridad R de orden [[Big O notation|<math>\mathcal{O}(1)</math>]], rl protón se puede desintegrar en aproximadamente en 10<sup>&minus;2</sup> segundos, o si se asume [[violación mínima del sabor]], su vida media se puede extender a 1 año. Dado que se ha observado que la vida media del protón es mayor que 10<sup>33</sup> a 10<sup>34</sup> años (dependiendo del canal de desintegración), lo que desfavorecería enormemente el modelo.
The strongest constraint involving this coupling alone is the violation universality of Fermi constant in leptonic charged current decays.
 
La paridad R hace que todos los términos renormalizables que violan el número bariónico o leptónico sean cero. De este modo el protón es estable al nivel renormalizable, y su vida media aumenta a 10<sup>32</sup> años, casi compatible con las observaciones actuales.
* <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 [[Big O notation|<math>\mathcal{O}(1)</math>]] couplings for the R-parity violating couplings, the proton can decay in approximately 10<sup>&minus;2</sup> 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 10<sup>33</sup> to 10<sup>34</sup> 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 10<sup>32</sup> years and is nearly consistent with current observational data.
 
[[Image:R-parity violating decay.svg|frame|right]]
 
Como la desintegración del protón involucra la violación tanto del número bariónico como el leptónico, la existencia de un único acoplamiento renormalizable que viole la paridad R no conduce a la desintegración del protón. La hipótesis del dominio de un único acoplamiento estudia casos de violación de la paridad R solamente en un acoplamiento.
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==
|doi=10.1016/j.physletb.2004.03.031
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== Dark matter candidate ==
With R-parity being preserved, the lightest supersymmetric particle ([[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]].{{Citation needed|date=March 2009}} In order to fit observations, it is assumed that this particle has a mass of {{val|100|ul=GeV/c2}} to {{val|1|ul=TeV/c2}}, is neutral and only interacts through [[weak interaction]]s and [[Gravitation|gravitational interactions]]. It is often called a [[weakly interacting massive particle]] or WIMP.
, is neutral and only interacts through [[Weak interaction|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 [[gauginoGaugino|gauginos]]s and [[Higgsino|Higgsinos]]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. Note that there are different forms of parity with different effects and principles, one should not confuse this parity with another parity.
 
==References==
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