Fermion Masses
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Fermion Masses. G.G.Ross, Corfu, September 2005. The Standard Model. Masses. 1. GeV. DATA :. ?. Mixing. Masses. 1. GeV. Mixing. 10 -1. 10 -2. 10 -3. 10 -4. eV. DATA :. ?. Bi-Tri Maximal Mixing … Non Abelian Structure?. Perturbative analysis (hierarchical basis).

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Fermion Masses

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Fermion Masses

G.G.Ross, Corfu, September 2005

The Standard Model


Masses

1

GeV

DATA :

?

Mixing


Masses

1

GeV

Mixing

10-1

10-2

10-3

10-4

eV

DATA :

?

Bi-Tri Maximal

Mixing …

Non Abelian

Structure?


Perturbative analysis (hierarchical basis)

(small) off diagonal

Diagonal

Off diagonal


Quark Textures

Hierarchical :


Quark Textures

Hierarchical :


Symmetric fit

Asymmetric fit

Roberts

Romanino

GGR

Velasco Sevilla


GATTO, SARTORI, TONIN

symmetric

/

CP SM phase

Texture zero

Fritzsch,

Weinberg

Roberts,

Romanino,

GGR,Velasco


Symmetric fit

Asymmetric fit

Roberts

Romanino

GGR

Velasco Sevilla


Infra red fixed point

Pendleton, Ross

Hill

Kobayashi, Kubo, Mondragon, Zoupanos


… dimension of operator

… order of radiative corrections


Textures and flavour models

Symmetries

Coherent picture of quark and lepton masses and mixing?

Family?

Family?


FAMILY SYMMETRY?

MESSENGER SECTOR?

Symmetries and textures

Hierarchical structure strongly suggests a broken symmetry

Froggatt, Nielsen


Abelian Family symmetry

-3 2 1

-3

2

1

1

-1

Ibanez GGR


Symmetric fit

Asymmetric fit

Is one favoured?


Probes RH angles

Cannot align Yukawa and A terms

Vives, GGR

Favours near symmetric structure

With similar structure for charged leptons

Neutrino mixing not related to large RH mixing


Quark masses and mixing angles

Lepton masses and mixing angles


Extension to charged leptons – GUT?

?


Extension to charged leptons – GUT?

Georgi Jarlskog


10

100

10-1

10-2

10-3

10-4

eV

Extension to neutrinos???

Possible with “see-saw”

Dirac Mass

Majorana Mass

King, GGR


CP violation

SUSY CP problem -

In string theory CP is a discrete gauge symmetry :

Dine, Leigh, MacIntyre

Vives, GGR

Cannot align Yukawa and A terms

OK with suitable family symmetry


Masses

1

GeV

Mixing

10-1

10-2

10-3

10-4

eV

Fermion Masses II

?

Bi-Tri Maximal

Mixing …

Non Abelian

Structure?


Textures and flavour models

Symmetries

Coherent picture of quark and lepton masses and mixing?


Abelian Family symmetry

-3 2 1

-3

2

1

1

-1


Probes RH angles

D-term problems for FCNC

Family dependent soft mass

Murayama

Discrete family symmetry

Gauge mediated breaking

Gravity mediation


Abelian Family symmetry

-3 2 1

-3

2

1

1

-1

Ibanez GGR


Abelian Family symmetry

-3 2 1

-3

2

1

Need special choice of O(1) coefficients

1

-1

Ibanez GGR


Masses

1

GeV

Mixing

10-1

10-2

10-3

10-4

eV

DATA :

?

Bi-Tri Maximal

Mixing …

Non Abelian

Structure?


Non-Abelian family symmetry

Symmetries

Coherent picture of quark and lepton masses and mixing?

Simple(?) flavour

Group restricting

Yukawa couplings


I de Medeiros, GGR

King, Vives, Velasco Sevilla…

Spontaneous symmetry breaking

c.f. Georgi-Jarskog

only terms allowed by G


Dirac mass structure


Dirac mass structure


Dirac mass structure


Structure determinedfrom

symmetries too

Neutrino masses

Actually cancelled by small off diagonal

Majorana terms

Bi-Tri Maximal Mixing


Bi-maximal

Vacuum alignment

Discrete (Non Abelian) family symmetry?


Vacuum alignment

Altarelli,

Feruglio


Ma;

Altarelli,

Feruglio

Bi-Tri-maximal mixing

X

Grand Unified

King,GGR

Allows symmetric invariant

- vacuum alignment

since only small high dimension corrections

Bi-Tri-maximal mixing

Grand Unified


Summary

Texture and texture zero hints at underlying structure

Family symmetry ? GUT symmetry?

Due to the see-saw mechanism, the quark, charged lepton and neutrino

masses and mixing angles can be consistent with a similar structure for

their Dirac mass matrices.

Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)?

Extraction of Yukawa couplings crucial to understanding fermion structure

Bounded off diagonal terms (anti)symmetric, hermitian SUSY data


Summary

Texture and texture zero hints at underlying structure

Family symmetry ? GUT symmetry?

Due to the see-saw mechanism, the quark, charged lepton and neutrino

masses and mixing angles can be consistent with a similar structure for

their Dirac mass matrices.

Hints at an underlying (spontaneously broken) family symmetry? SO(10)XSU(3)?

gives a new solution to the SUSY FCNC and CP problems

Extraction of Yukawa couplings crucial to understanding fermion structure

Bounded off diagonal terms (anti)symmetric, hermitian SUSY data

A discrete non-Abelian subgroup can give vacuum alignment needed

For bi-tri-maximal mixing


Ramage,GGR


Majorana Mass Matrix


Ramage,GGR


Ma;

Altarelli,

Feruglio

Neutrinos

Charged leptons

3


Ma;

Altarelli,

Feruglio

Neutrinos

Charged leptons

3

Bi-tri maximal

Harrison, Scott

-Ma


10

100

10-1

10-2

10-3

10-4

eV

Degenerate

Normal

Inverted

Phenomenological implications :

Degenerate, normal and

inverted spectra possible

No connection

between quark,

charged lepton

and neutrino

masses


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