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Michael Jay PérezIn collaboration with J. Kile, P. Ramond, and J. Zhang
Phenomenology 2014, Pittsburgh, PAMay 5, 2014
Majorana Physics in the Flavor RingarXiv: 1311.4553
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The Flavor PuzzleThe Flavor Ring: neutrino sectorA Special Majorana MatrixFlavor Group : Frobenius group basicsUnderlying TheorySummary and Conclusion
Outline
The Flavor Puzzle
Quarks
Leptons
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The Flavor Ring
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Up-quarks display large hierarchy
GUT Puzzle ?
Seesaw
Up-Quarks and Neutrinos
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Can majorana mass undo the hierarchy?
Would need to have a severe hierarchy
What sets the physics of Majorana matrix?Should “know” what sets the hierarchy in Y(0)
Natural candidate: Family symmetry!
Majorana matrix to the rescue
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Hierarchical Majorana Matrix
• Generic Eigenvalues :
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At this special point, a vanishing sub-determinant
Can we produce it naturally with a family symmetry?
A Special Majorana Matrix
1: rλ12 : rλ12 ~ 1: 10-10 : 10-10
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Gatto-like Relation
Neutrino masses for a particular mixing scheme
Ex: TBM Mixing
Normal Hierarchy
Predictions
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Smallest Non-Abelian discrete subgroup of SU(3) that is not a subgroup of SO(3)
Also called T7 in the literature
Contains 21 Elements
Frobenius Group of order 21 : Basics
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Step I : Choose Rep’s of FieldsWant to work within SU(5) :
Choose all matter fields to transform as family tripletsAlso introduce Familons which are family triplets or anti-
triplets but gauge singlets
Model Building with
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One linear combination of dimension-five Invariants
Hierarchies carried by Familon Fields
Can also be done through single dimension-six
Producing the Majorana Matrix
gives zero sub-determinant!
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Invariant is singled out by additional symmetries
Underlying Theory
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Flavor Ring: tying Grand Unification to the flavor puzzle can lead to new insights
Using family symmetry to give Majorana physics begins to give a more connected picture
Found a compelling and predictive Majorana matrix
Natural in terms of a family symmetry
Stay tuned – more to come!
Conclusions
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Extreme hierarchy dictates a subgroup of SU(3)
Neutrino mixing seems to indicate a finite subgroup
Choice of Family Group
Traceless!
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Kronecker Products
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• A single Dim-6 Operator
Similar to the Dim-5 case.
The form of nesting is quite suggestive.