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

6

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

9

Gatto-like Relation

Neutrino masses for a particular mixing scheme

Ex: TBM Mixing

Normal Hierarchy

Predictions

10

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

11

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

12

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

15

Extreme hierarchy dictates a subgroup of SU(3)

Neutrino mixing seems to indicate a finite subgroup

Choice of Family Group

Traceless!

16

Kronecker Products

17

• A single Dim-6 Operator

Similar to the Dim-5 case.

The form of nesting is quite suggestive.