Three Family SU(5) GUT

Zurab Tavartkiladze

Low Dimensional Physics & Gauge Principles (Tbilisi Sep. 28 – 29, 2011)

[Anomaly-free U(1)Flavor x SU(5) Models]

(Ilia State Univ, Georgia)

hep-ph/1109.2642

Aim of the work:

● Within SUSY GUT, find anomaly free U(1)F flavor Symmetries (with simplest content possible)

● Classify U(1)F charge assignments & Yukawa textures YU,D,E leading to natural explanation of hierarchies in fermion sector.

Some related works:

-- Within MSSM, anom. free U(1)F ‘s with successful YU,D,E

Dudas, Pokorski, Savoy, hp/9504292;

-- Within MSSM & SU(5) GUT, some examples/models of anom. free U(1)F ‘s : Mu-Chun Chen, et al, ph/0612017, 0801.0248;

-- Within SM, non-Abelian anom. free fl. symmetries have been listed:Babu, Frank, Rai, 1104.4782

● Intro: Shortcomings, Problems & Puzzles of SM / MSSM New Physics

● Motivations for GUT

● Some shortcomings & problems

● New SUSY SU(5)xU(1)Flavor models are built:

- Non-anomalous flavor sym. with economical setup ;

- several successful charged fermion mass patterns

emerged

● Summary

Outline

c c=

c=l

uq u d

d

νe

e

( (1) 12)SM Interactions : 3( ) ( EW B(3) 8 gluo oso )ns nsL YC USUSU

-( , 2 ,3 1/3) ( , ,13 4/3) -( ,1,3 2/3)

(1, 2 ,1) (1,1, -2)

Fractional charges-Charge quantizat( ) n1 io ?YU

C L Y C emBreaking: SU(3) ×SU(2) ×U(1) SU(3) ×U(1)H

Higgs H(1,2, 1) is required (undiscovered yet)Why/how it is light? –Gauge Hierarchy Problem

---- ---- ----

---- ----

Shortcomings of SM:

Interactions : (2 (1)(

(1

)

))

)3

(3

YC

C

L

em

S UUU

SU U

S

SM model of EW interactions ~ Matter: 3 gen. quarks & leptons

That's all the matter we have? (additions, extensions?)

Dark Matter:

Dominant part (~85% ) of total matter is unknown – Dark Matter

Dark matter is EM neutral, interacting gravitationally.

Strong evidence of physics beyond the SM. The SM fails to explain DM.

The ‘Whirlpool galaxy’ - "M51"

Rotational velocity remains constant,

or "flat", with increasing distance

away from the galactic center.

Distance to M51 is 9 Mpc (30 million light yrs)moving away from us at 500 km/s.

Based on Newton's law, the velocity would steadily decrease for stars further away from the galactic center,

since the rotation speed satisfies v^2=GM/r

Atmospheric & Solar Neutrino Data

● Origin of these scales and mixings?

Unexplained in SM/MSSM

Third mixing angle: 13 0.2

Unknown phase: lept

are of great importance for leptonic CP viol.

Evidences for New Physics:

1) Cosm. Observation -- Dark Matter (DM):

Dominant part (~85% ) of total matter is unknown – DM

DM is EM neutral, interacting gravitationally.

Evidences for New Physics:

Additional strong evidences of physics beyond SM

2) Baryon Asymmetry 1010B

How this asymmetry is generated?

Big puzzles of particle physics models.

No explanation within SM/MSSM.

● Charged fermion masses & mixings

With λ=0.2

Observed Noticeable Hierarchies:

What is origin of these hierarchies?Is there any relation or sum rule?

Why three families?

Within SM no answer to these questions…

Each SM State SUSY Partner

, ,

, , ,

e u d

W Z G

H

SUSY: Symmetry between Bosons & Fermions

, , (sfermions)

, , , (gauginos)

, (Higgsinos)

e u d

W Z G

H Hu d

SM Scale ~ 100 GeV SUSY Scale: Not far above

few TeV

SUSY Breaking scale & br.patternare very important…

SUSY solves some problems/puzzles

● Solution of Hierarchy problem

● SUSY “Zoo” near TeV…

● Automatic coupling unification

GUT is revamped!

Low scale SUSY insures all order quantum stability of the construction.

Due to Bose Fermi symmetry all unwantedQuantum corrections cancel out.

SUSY Unification vs. non-SUSY

MSSMSM

● Neutral Higgs

is accompanied by neutral SUSY partners

0H

0 0 0, , ,H W Z

Lightest (LSP) Neutralino is stabile ~ 100 GeV

● Good Dark Matter candidate!

(mass ~ 100 GeV)

● Matter Unification

SUSY Grand Unification

offers more solutions to some problems/puzzles

And interesting asymptotic relations [in SO(10)]:

, ...Dt b tm m

SO(10) νR

Neutrino masses via see-saw

Oscillations

Leptogenesis

m

M

(1, 1,0)c N

l N H M N N

SM singlet

Δ L=2 Lepton number viol.

0 H

H M

2

Hm

M

NM M

SUSY GUT

● Charge Quantization,Unification of multiplets

● Neutrino Masses (via νR of SO(10)); L-violation

● Successful Coupling Unification

● Stab. Hierarchy (Light Higgs) low SUSY scale

● Dark Matter Candidate (LSP)

● Baryogenesis via Leptogenesis

● Prediction: B-violation proton decay

16 (10)of SO

SUSY GUT puzzles:

● GUT Symmetry Breaking? (flat directions/goldstones)

● Doublet-Triplet Splitting

● How/why mu-Term ~ 100 GeV ? (harder in GUT)

● Proton Stability (especially d=5 decay)

● Fermion Masses & Mixings (flavor problem)(Discussed Below)

● SUSY FCNC (sflavor problem)

● Minimal & Economical System- Calculability of GUT Threshold Corrections

- Perturbativity all the way up to MPlanck

Unless Unified solution is found, none of the predictions can be trusted..

All these issues are closely related and

Within SUSY & GUT, the problem of flavor remains unsolved.

Flavor symmetry GF acting between families can help to explain hierarchies

Simplest possibility: GF=U(1)F (Froggatt, Nielsen’79)

Models with gauged U(1)F are highly constrained(anomaly cancellation conds.)

-- Anomalous U(1)F (of string origin); GS mechanism for anomaly cancellation.

-- Alternatively: Anomaly free U(1)F

Within GUTs become more non-trivial [multiplet charges related]

Challenge to find simple anom. free U(1)F x GGUT

New SUSY SU(5) x U(1)Flavor

Models

U(1)Flavor : Non-Anomalous Flavor Symmetry

SU(5) Matter: 10i , 5i*

U(1)Flavor Charge: Q[10i] , Q[5i*]

SU(5) Scalars: H(5) , H*(5*) , Σ(24)

Charge: Q[H] , Q[H*] , 0

Extra matter : Only SU(5) Singlets (# = or < 3)For anomaly cancellation & RH Neutrinos

Flavons: X[q] , X*[-q] For U(1)Flavor Breaking

Search for Economical Setup..

Anomaly Cancellation

Singlets

Vanishes with:

Minimal Setup: No states beyond min. SUSY SU(5)

i.e. Three 10’s + four 5* ’s + one H(5) + one

Search for Anomaly Free Economical Setup

Finding I. Try to find embedding of SU(5)xU(1)F (matter) inAnomaly free non-Abelian G

Example:

[Vertical embedding]

Finding II. Embed U(1)F in anomaly free non-Abelian GF (Babu’2011)

Example:[Horizontal embedding]

*With and ‘minimal flavon’ setup, no realistic model emerges

We follow Finding I. However, if other possibilities [without G, GF

embeddings of U(1)F] exist, worthwhile of searching & makingclassification of realistic models.

Finding I: Embeddings

I.a.

I.b.

SO(10)SU(5)xU(1)’: 16= 10[1] + 5*[-3]+1[5]

(Flipped SU(5) type) 10=5[2q]+ 5*[-2q] (q=-1)

U(1)’ charges in brackets

E6->SO(10)xU(1)’’SU(5)xU(1)’’:

(Flipped SO(10) type)

27= 16[1] + 10[-2]+1’[4]=

(10+ 5*+1)[1]+(5+5’*)[-2]+1’[4]

I.c.

Anomaly free:

With ‘flips’:

Three family of (anomaly free):

All other G findings, such as E7, E8, SU(N>7) give extra SU(5) states and are rejected

-- Possible to build superpositios of U(1)s:

With , is anomaly free

is automatically anomaly free

(I)

(II)

Other superpositions are also possible..

ABB BBB DABC BBC

Four classes of U(1)F assignment emerge:

Many combinations.. , but restrictions – no extra `exotics’

Give 6 combined options:

Or with

Three family SU(5) GUT!

For example, ABB: 100+5*0

10α +5*-3 α+15 α

10α' +5*-3 α’+15 α’

Hq+H*-q

Some selection rules (‘guide’):

AAB: rejected because of two 10’s same 0-chage (no hierarchical up-Yukawas)

ACC: rejected for extra 5-plets

In case of ABB, α and α’ should be relatedα/α’=m/n, to avoid two U(1)s

Classify acceptable up type quark mass matrices...

ABB: 100+5*0

10α +5*-3 α+15 α

10α' +5*-3 α’+15 α’

ABB Scenario includes GF case of O(3) isotriplet:

For a’=-a=1 we obtain horizontal embedding:

Up Quark Mass Matrices

U(1)Flavor breaking:

Higher operators are suppressed by powers of and

3 Sub-Cases (giving different down sector):n=0 U1; n=3 U5; n=1 U7

3 Sub-Cases (giving different down sector):n=0 U3; n=1 U4; n=1 U9

3 Sub-Cases (giving different down sector):n=0 U2; n=-1 U6; n=-3 U8

Content:

Make selection & identification(s):

Three Family SU(5)xU(1)F -

Mass matrices

Is a Good choice

For charged fermion mass hierarchies & CKM

Naturally large mixing:

Neutrino sector needs more detailed study..

● Discussed problem of hierarchies between fermionmasses and mixings within SUSY SU(5) GUT

● New SUSY SU(5)xU(1)Flavor models are built:Non-anomalous flavor sym. with economical setup

● Successful charged fermion mass patterns emerged within three family SU(5)xU(1)Flavor model

(more cases/details in: )

● Neutrino sector may discriminate some scenarios(?)

Thank You

Summary

hep-ph/1109.2642

Backup Slides:

U(1)F Breaking

Flavon(s) needed for U(1)F Breaking & for generating Yukawacouplings

Tempting to use singlet(s) (1 or/and 1’) responsible for anomaly cancellation.-However, no realistic model has been found.

-- Introduce flavons – Minimal flavon setup

In SU(5)x U(1)F , the FI-term is allowed

D-term:

& superpotential:

*Without S, higher order superpotential/Kahler terms may do the job

U(1)F Breaking (contd.)

All F’s & D =0 unique solution (no degeneracy) fixed VEVs:

a)

b)

c)

ExpansionParameters:

Two Favorite models

Content:

With selection

and identification =

We get down quark/ch. Lepton mass matrices:

Is a Good choice

Charged fermionmass hierarchies:

CKM mixings:

Large neutrino mixing:

Neutrino sector needs more detailed study..

Content and charge assignment:

Make selection:

With identification:

Mass matrices

For n=-2/5:

Is a Good choice

For obtaining Charged fermionmass hierarchies and CKM mixings

Naturally large mixing:

Neutrino sector needs more detailed study..