majorana physics in the flavor ring

Michael Jay Pérez

In collaboration with J. Kile, P. Ramond, and J. Zhang

Phenomenology 2014, Pittsburgh, PA

May 5, 2014

Majorana Physics in the Flavor Ring

arXiv: 1311.4553

2

The Flavor Puzzle

The Flavor Ring: neutrino sector

A Special Majorana Matrix

Flavor Group : Frobenius group basics

Underlying Theory

Summary and Conclusion

Outline

The Flavor Puzzle

Quarks

Leptons

4

The Flavor Ring

5

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

7

Hierarchical Majorana Matrix

• Generic Eigenvalues :

8

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 triplets

Also 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!

13

Invariant is singled out by additional symmetries

Underlying Theory

14

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.