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Nonanomalous discrete R symmetry decrees three generations
Jason L Evans1, Masahiro Ibe, John Kehayias
1IPMU, University of Tokyo, Kashiwa 277-8568, Japan.
Physical Review Letters
|December 11, 2012
Summary
More than two generations of quarks and leptons are needed for an anomaly-free discrete R symmetry, linking generation number to supersymmetry breaking and proton decay. Three generations are uniquely required in grand unified theories by this symmetry.
Area of Science:
- Particle Physics
- Theoretical Physics
- Cosmology
Background:
- The Standard Model requires three generations of quarks and leptons.
- Grand Unified Theories (GUTs) aim to unify fundamental forces.
- Discrete R symmetries are crucial in some supersymmetric theories.
Purpose of the Study:
- To investigate the link between the number of particle generations and discrete R symmetries.
- To explore how discrete R symmetries can resolve issues in particle physics and cosmology.
- To determine the unique generation number required by non-anomalous discrete R symmetries in GUTs.
Main Methods:
- Analysis of anomaly-free discrete R symmetries.
- Embedding the supersymmetric Standard Model into Grand Unified Theories.
- Investigating gauge groups like (semi)simple groups.
Main Results:
- More than two generations are necessary for an anomaly-free discrete R symmetry.
- This symmetry connects generation number to supersymmetry breaking, proton decay, the mu problem, and the cosmological constant.
- Three generations are uniquely required by a non-anomalous discrete R symmetry in specific GUT classes.
Conclusions:
- A discrete R symmetry provides a compelling explanation for the three generations of matter.
- This framework unifies solutions to several outstanding problems in particle physics and cosmology.
- The requirement of three generations is a robust prediction within these classes of Grand Unified Theories.
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