2 7 Michael Jay Perez Phenomenology 2015 May 5 2015 Arxiv 14126107 13114553 Following the Hierarchy Uptype quarks display a large hierarchy Follow this hierarchy to the Neutrino Sector ID: 399066
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Slide1
Hunting for Hierarchies in PSL2(7)
Michael Jay PerezPhenomenology 2015May 5, 2015Arxiv : 1412.6107 / 1311.4553Slide2
Following the Hierarchy
Up-type quarks display a large hierarchyFollow this hierarchy to the Neutrino SectorThen use Flavor symmetry to follow it to the Higgs Sector2Slide3
Majorana Sector
Hierarchy not seen in the light neutrino massesSeesaw3Slide4
Hierarchical Majorana Matrix
Generic Eigenvalues : Don’t want the lightest eigenvalue to be too light4Slide5
A Special Majorana Matrix (SMM)
5Increased degeneracy at special point(1: rλ12 : rλ
12
~ 1:
10
-7
: 10
-7
)
Gatto – like Relation
TBM, Normal HierarchySlide6
The SMM
M0 ~ 1014 GeVPrecise relations amongst matrix elementsCan it be natural in terms of a flavor Symmetry?How to produce it ? Tree-LevelHigher-Dimensional Operator
6Slide7
Why ?Smallest Non-Abelian subgroup of SU(3)
Only 21 ElementsIrreps : Cubic Invariants distinguishes diagonal from off-diagonal couplingEx: Top quark mass7Slide8
SMM in An attractive solution with two
Flavon anti-triplets (N ~ 3)Flavon vev’s almost aligned Requires a special linear combination of two operators!How do we fix this sign? -> Higher Symmetry!
8Slide9
PSL2(7) Basics
Finite subgroup of SU(3) with 168 elementsProjective Special Linear group of (2 × 2) matrices over F7 (Galois field of seven elements)Irreps : 3 , 3* , 6 , 7 , 8 (6 , 7 , and 8 are all real)
9Slide10
Looking up
Triplet and anti-triplet the sameSinglet of Z7 X Z3 in the septetSix in symmetric product10Slide11
SMM in PSL2(7)
Want to produce the linear combination :Transformation of Fields :
11Slide12
Septet to the rescue
PSL2(7) Kronecker Product : Two Z7 X Z3 singlets in product of 6’s12Slide13
Simple Underlying Theory
Coupling we want : Add additional intermediate field which are PSL2(7) 6’sVEV of S7 breaks PSL2(7) down to Z7 X Z3Integrating over the 6’s gives desired coupling!
13Slide14
Higgs Sector
Exploring idea of giving Higgs flavor quantum numbers How do Higgs fields look in PSL2(7) ?In previous work Q , U, D, L , E , N ~ 3 Possible Yukawa Couplings : 14Slide15
Higgses in PSL2(7)
Choose the Higgses to be 6’s Recall : Z7 X Z3 In our new PSL2(7) notation, want :
15Slide16
Higgs Hierarchies
Lots of Higgses !Need a hierarchy between them (only one seen so far!)One should be “light”Can we use the same Flavons to produce the hierarchy ?What determines the masses of the Higgs Fields ? 16Slide17
The µ Term and Flavor SymmetryIf the Higgs have flavor partners “µ” is now a matrix
Diagonalization of the µ matrix leads to supersymmetric Higgs mass spectrumFlavor Symmetry could :Forbid it explicitly (Ex : Z7 X Z3 with both Higgses being anti-triplets)Allow it but give a hierarchy amongst the Higgses 17Slide18
The µ Term in PSL2(7)
Higgses are 6’s under PSL2(7)µ term now a matrixWant to use the Flavons from the Majorana sector !
18Slide19
A Simple Underlying Theory Try to mimic the Majorana sector
Generates the termWill generate the µ matrix when PSL2(7) breaks and Flavons acquire vev's
19Slide20
The µ matrix
20Slide21
A Suitable Hierarchy ?
Want there to be one “light” eigenvalueQuestion of scale Light eigenvalue should have the correct eigenvectorBasis fixed by getting the top-quark mass right Light eigenvalue should be mostly along this direction
21Slide22
Spectrum
Suitable spectrum ? Yes ! Eigenvalues : Eigenvector of light eigenvalue in the right direction! 22
10
-7
10
-6Slide23
Top Quark Yukawa’sNot the full picture
Up and charm quark masses too small
23Slide24
Summary & Future Work
Successfully transferred top-quark hierarchy to Majorana and Higgs sectorsSpecial predictive Majorana matrix and Hierarchical µ-termComplete SO(10) modelSeems to imply large tan β ~ 40 Mechanism for generating mass of first two flavors
Flavon
Potential
24Slide25
More PSL2(7)
Maximal discrete subgroup of SU(3)25Slide26
The µ Term : Review Minimal Supersymmetric Standard Model has one new parameter µ
Supersymmetric mass termGives common mass to Hu and HdGives mass to Higgsinos Cubic Scalar couplingsAlso contributes to chargino and neutralino mass matricesThis common mass is then split by SUSY breaking terms
Breaks PQ symmetry
26Slide27
The µ Problem
Correct EWSB then leads to Implies µ should be ~ SUSY breaking scale (unless cancellations)µ appears in Superpotential, so natural value is cutoff of the theory Why is it so small ? Giudice-Masiero mechanism NMSSM Flavor Symmetry ?
27Slide28
Spectrum One light Higgs with eigenvalue : ~ 30 f GeV
With SUSY breaking ~ TeV or not much higher, this will be the only Higgs to obtain a vacuum value Automatically aligned to give the right top quark mass!28