R-parity
Encyclopedia
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
symmetry acting on the Minimal Supersymmetric Standard Model
(MSSM) fields that forbids these couplings and can be defined as:
Or as:
With spin
s, baryon number B, and lepton number L. All Standard Model particles have R-parity of 1 while supersymmetric particles have R-parity -1.
) 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 100 GeV to 1 TeV, 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 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 gravitational interactions
and does not require strict R-parity.
The strongest constraint involving this coupling alone is from to neutron - antineutron oscillations.
The strongest constraint involving this coupling alone is the violation universality of Fermi constant
in quark and leptonic charged current decays.
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.
couplings for the R-parity violating couplings, the proton can decay in approximately
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
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
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.
forbids renormalizable terms which violate B and L. If 
is only broken by scalar vacuum expectation values (or other order parameters) that carry even integer values of 3(B-L), then there exist an exactly conserved discrete remnant subgroup at our scale which has the desired properties.
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.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
. In the supersymmetric extension
Minimal Supersymmetric Standard Model
The Minimal Supersymmetric Standard Model is the minimal extension to the Standard Model that realizes supersymmetry, although non-minimal extensions do exist. Supersymmetry pairs bosons with fermions; therefore every Standard Model particle has a partner that has yet to be discovered...
of the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, baryon number and lepton number
Lepton number
In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...
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
symmetry acting on the Minimal Supersymmetric Standard ModelMinimal Supersymmetric Standard Model
The Minimal Supersymmetric Standard Model is the minimal extension to the Standard Model that realizes supersymmetry, although non-minimal extensions do exist. Supersymmetry pairs bosons with fermions; therefore every Standard Model particle has a partner that has yet to be discovered...
(MSSM) fields that forbids these couplings and can be defined as:
- PR = (-1)2s+3B+L.
Or as:
- PR = (-1)3(B-L)+2s.
With spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
s, 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 (LSPLightest Supersymmetric Particle
In particle physics, the Lightest Supersymmetric Particle is the generic name given to the lightest of the additional hypothetical particles found in supersymmetric models. In models with R-parity conservation, the LSP is stable. There is extensive observational evidence for an additional...
) 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
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
. In order to fit observations, it is assumed that this particle has a mass of 100 GeV to 1 TeV, is neutral and only interacts through weak interactions and gravitational interactions
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
. 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
Gaugino
In particle physics, a gaugino is the hypothetical superpartner of a gauge field, as predicted by gauge theory combined with supersymmetry. They are fermions.In the minimal supersymmetric extension of the standard model the following gauginos exist:...
s and Higgsino
Higgsino
In particle physics, a Higgsino, symbol , is the hypothetical superpartner of the Higgs boson, as predicted by supersymmetry. The Higgsino is a Dirac fermion and that is a weak isodoublet with hypercharge half under the Standard Model gauge symmetries...
s and is called a neutralino
Neutralino
In particle physics, the neutralino is a hypothetical particle predicted by supersymmetry. There are four neutralinos that are fermions and are electrically neutral, the lightest of which is typically stable...
. In extensions to the MSSM it is possible to have a sneutrino be the dark matter candidate. Another possibility is the gravitino
Gravitino
The gravitino is the supersymmetric partner of the graviton, as predicted by theories combining general relativity and supersymmetry; i.e. supergravity theories...
, which only interacts via gravitational interactions
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
and does not require strict R-parity.
R-parity violating couplings of the MSSM
The renormalizable R-parity violating couplings of the MSSM are-
violates B by 1 unit
The strongest constraint involving this coupling alone is from to neutron - antineutron oscillations.
-
violates L by 1 unit
The strongest constraint involving this coupling alone is the violation universality of Fermi constant
in quark and leptonic charged current decays.-
violates L by 1 unit
The strongest constraint involving this coupling alone is the violation universality of Fermi constant in leptonic charged current decays.
-
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
Proton decay
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
. 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 takingBig O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...
couplings for the R-parity violating couplings, the proton can decay in approximately
seconds or if minimal flavor violation is assumed the proton lifetime can be extended to1 year. Since the proton lifetime is observed to be greater than
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
years and is nearly consistent with current observational data.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 forbids renormalizable terms which violate B and L. If is only broken by scalar vacuum expectation values (or other order parameters) that carry even integer values of 3(B-L), then there exist an exactly conserved discrete remnant subgroup at our scale which has the desired properties.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
Spinor representation
In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature . More precisely, they are representations of the spin groups, which are double covers of the special orthogonal groups...
, 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
- 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.
- R-parity Violating on arxiv.org
- R-parity Violating on arxiv.org
- R-parity Violating on fnal