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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