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Exceptional Exceptional SupersymmetricSupersymmetricStandard Models and Discrete Standard Models and Discrete NonNon--AbelianAbelian Family SymmetryFamily Symmetry

The Origin of Mass Singlet SUSY Models, Dark MatterThe Quest for Unification E6SSMThe Flavour Problem TBM and discrete family symmetryGUT Relations Mixing angle predictions and sum rules

E6SSM with 27 Proton decay suppression

Steve King, National Seminar on High Energy Physics, NIKHEF, Amsterdam, 21st November, 2008

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21/11/2008 Steve King, Amsterdam 2

1. The origin of mass - the origin of the weak scale, its stability under radiative corrections, and the solution to the hierarchy problem (most urgent problem of LHC). Origin of mass in the Universe dark matter.

2. The quest for unification - the question of whether the three known forces of the standard model may be related into a grand unified theory (GUT), and whether such a theory could also include a unification with gravity.

3. The problem of flavour - the problem of the undetermined fermion masses and mixing angles (including neutrino masses and mixing angles) together with the CP violating phases, in conjunction with the observed smallness of flavour changing neutral currents and very small strong CP violation.

Standard Model PuzzlesStandard Model Puzzles

Attempts to address these questions are typically based on extra symmetry:1Supersymmetry (SUSY) 2 GUTs3 Family Symmetry


FERMIONS BOSONS

Supersymmetry (SUSY)

BOSONS FERMIONS


b

t

cs

ud

ee

GUTs and Family Symmetry


22 2 246Hm v GeV

Origin of mass in SM Origin of mass in SM

Tree-level min cond

Including rad corr 22 2 246H Hm m GeV

2

22 2 2

2

3( ) 100

12

H F tm top loop G m GeVTeV

Fine-tuning is required if the cut-off 1 TeV

�Hierarchy problem new physics at » TeV

�No hint in precision LEP measurements SUSY?

H H3LQ

Rt

2 42 12HV m H H


Stabilising the Hierarchy in SUSYStabilising the Hierarchy in SUSY

2 2 22

3( )

8

H tm top

2 2 22

3( )

8

H tm stop

2 2 22

9ln

8H t tt

m mm

SUSY stabilises the hierarchy providing 1tm TeV

Quadratic divergence cancels leaving

Cancel


MSSMMSSM u dW H H0

0

u du d

u d

H HH H

H H

Min conds at low energy 2

2 2 2

2

u u

ZH H

Mm m

A nice feature of MSSM is radiative EWSB Ibanez-Ross

0ZM GUTM

2 2

uHm (s)top loops drive negative

2

uHm

H H3LQ

Rt

2 2 2 22

3ln ~ (1)

4

u

GUTH t stop stop

Mm m O m

Q

Naturalness requirement is MZ » mHu » mstop

But MZ ¿ mstop One per cent fine tuning

Also no reason why should be any particular value ( problem)


To solve the problem and reduce fine tuning consider:

W= SHuHd where singlet <S> »

But leads to weak scale axion due to global U(1) PQ symmetry

Need to remove axion somehow

In NMSSM we add S3 to break U(1) PQ to Z3 � but this results in cosmological domain walls (or tadpoles if broken)

In USSM we gauge the U(1) PQ symmetry to eat the axionresulting in a massive Z� gauge boson � but not anomaly free

In E6SSM the anomalies of the USSM are cancelled by three complete 27�s of E6 at the TeV scale with U(1) PQ 2 E6

Singlet SUSY ModelsSinglet SUSY Models

MSSM Neutralino Dark Matter

MSSM u d YukW H H W Neutralino mass matrix

1

2

0

0

M

M

3 d uB W H H 1 1 2 3 4d uN B N W N H N H

32 0

2

1DM

P annih

Th C

M v

1

1

W

W

1

1 ,A hb

b

1

Z

1

1

f

f

f

Bulk Focus Funnel Co-annihilation

1fm m Higgsino LSP 1, 2A hm m

1m m

R-parity is conserved 1 is stable, but can annihilate

USSM Neutralino Dark Matter(1)USSM u d Yuk gaugeW SH H W U MSSM states S Z

1

2

1

0

0

0 Z

Z

M

M

s

s

M

M M

3 d uB W H H

H

,S B H

,b t

,b t

S B 1 1 2 3 4 5 6d uN B N W N H N H N S N B

New

How can a singlino LSP annihilate? Via SHH and Z� couplings

S

S

H

H

HS

S

Z f

f

1M 2

1

0Z

S

MM

M

mini-see-saw gives singlinoLSP as M1�1

de Carlos, Espinosa, Cvetic, Demir, Everett, Langacker; Barger, Lewis, McCaskey,Shaughnessy, Yencho, Kalinowski, SFK, Roberts

Solves problem of MSSM Plus extra states for anomaly cancellation (see later)


Neutralino masses Dark matter abundance

Spin-independent proton cross-section (atto-barn)

Spin-dependent proton cross-section (atto-barn)

WMAP

M1� M1Kalinowski, SFK, Roberts

MSSM

CP-odd Higgs

CP-even Higgs

MSSM

MSSM

Higgsinos

Singlino


E6

(5) (1)SU U (3) (3) (3)C L RSU SU SU

(4) (2) (2)PS L RSU SU SU

(3) (2) (2) (1)C L R B LSU SU SU U

(3) (2) (1)C L YSU SU U

(5)SU

(10)SO

GGUTE6 is the largest GUT group usually considered


EE66SSMSSM SFK, Moretti, Nevzorov

15 14 4(1) (1) (1) NU U U

(10) (5) (1)SO SU U 6 (10) (1)E SO U

E6 ! SU(5)£U(1)N MGUT

TeV U(1)N broken, Z� and triplets get mass, term generated

27',27'

To achieve GUT scale

unification we need to add vector lepton

doublets

Quarks, leptons

Triplets and Higgs

Singletsand RH s

L4,L4-bar

MW SU(2)L£ U(1)Y broken

Right handed neutrinos are neutral under:

! SM £ U(1)N

RH masses

M1

M2

M3

E6 broken via SU(5) chain

Unification at MUnification at MGUTGUT in Ein E66SSMSSM

3

2

1

250 GeV

1.5 TeV

Blow-up of GUT region2 loop, 3(MZ)=0.118

SFK, Moretti, Nevzorov

162 10

XM

GeV


Minimal EMinimal E66SSM: no vector leptonsSSM: no vector leptonsHowl, SFK

(10) (4) (2) (2)PS L RSO SU SU SU6 (10) (1)E SO U

MGUT

TeV U(1)X broken, Z� and triplets get mass, term generated

MPlanck

Quarks, leptons

Triplets and Higgs

Singlet

MW SU(2)L£ U(1)Y broken

E6! SU(4)PS£ SU(2)L £ SU(2)R

SU(4)PS£ SU(2)L £ SU(2)R £ U(1)! SM £ U(1)X

(4,2,1) (4,1,2) (6,1,1) (1,2,2) (1,1,1) 27

Three families of 27�s survive to low energy (minus the RH �s)

£ U(1)

Extra U(1)X survives to TeV scale

RH masses

M1

M2

M3

E6 broken via Pati-Salam chain

N.B. No L4,L4-bar now


String scale unification in MEString scale unification in ME66SSMSSM

Low energy (below MGUT) three complete families of 27�s of E6

High energy (above MGUT» 1016 GeV) this is embedded into a Pati-Salam model and additional heavy Higgs are added.

Howl, SFK


Low energy matter content of ELow energy matter content of E66SSMSSM��s s

Exotic D,D-bar

Three families of Higgs Singlets

Quarks and Leptons

27i

. .

4 4L L

Right-handed neutrinos (heavy)

Vector leptons from 27�+27�bar (absent in ME6SSM)


Yukawa couplings of EYukawa couplings of E66SSMSSM��s s

SDD HSH FF D FH FW

, ,

, , , , ,

i i

c c c ci i i i i i

D D D

F Q L U D E N

,

,

i

u di i

S S

H H H

Singlet-Higgs-Higgs couplings includes effective term

Singlet-D-D couplings includes effective D mass terms

Yukawa couplings but extra Higgs give FCNCs. Need to have suppressed Yukawas involving extra Higgs

DQQ, DQL allows D decay but also proton decay. Need to: � either forbid one of DQQ or DQL - or allow both with Yukawas » 10-12

We need a theory of Yukawa couplings a.k.a. the flavour problem


The Constrained EThe Constrained E66SSMSSM

, ,

, ,

i u i d i i i i

j u d u d

t u b d d

W SH H SD D

f S H H h S H H

h QH t h QH b h LH

Assume universal soft masses m0, A, M1/2 at MGUT

In practice, input SUSY and exotic threshold scale S then select tan andsinglet VEV <S>=s and run up third family Yukawas from S to MGUT

Then choose m0, A, M1/2 at MGUT and run down gauge couplings, Yukawas and soft masses to low energy and minimise Higgs potential for the 3 Higgs fields S, Hu, Hd (even under Z2)

EWSB is not guaranteed, but remarkably there is always a solution for sufficiently large to drive mS

2 <0 (c.f. large ht to drive mH2<0 )

Athron, SFK, Miller, Moretti, Nevzorov

Hu, Hd, S without indices are third family Higgs and singlet, Hu,, Hd,, S are non-Higgs

The Z2H allowed couplings


Characteristic spectrumCharacteristic spectrumFor a given low energy M1, M2, M3 need a larger M1/2 than in the MSSM

Lightest states are h10 and gauginos:

Generally m0>M1/2 heavy squarks,sleptons with

2Remaining gauginos, Higgs and Z� are much heavier(ignoring non-Higgs and non-Higgsinos)


A Benchmark Point A Benchmark Point

12 0700 , 1.6 , 1M GeV m TeV A TeV

1.4TeV

1.8TeV

2.2TeV

03,4 2,

02, ,H h A

0 05,6 3, ,h Z

tan 3, 6 , 0.7, 0.5s TeV

01

02 1, g

97GeV

174GeV

460GeV

01h120GeV

Athron, SFK, Miller, Moretti, Nevzorov

4.7TeV3D3D5TeV

1,2D1.5TeV

1,2D300GeV

1.4TeV 1t

2, , ,Q t b L 1.8TeV1.7TeV

Extra Higgsinos

extra-Higgs

??GeV


The lightest states are the The lightest states are the gauginosgauginos

01 1N

02 2 1 1,N C

g123 0.7M M

122 0.25M M

121 0.15M M

12

400 1000M GeV

» Wino

» Bino

Gluino


e

Le

L

L

Standard Model states

Neutrino mass states

1m2m

3m

Oscillation phase 3 masses + 3 angles + 1(3) phase(s) = 7(9) new parameters for SM

Atmospheric Reactor Solar

.

.

.

.

.

.

.

.

.

.

.

.

Majorana

Majorana phases1 2,

1

2

/ 213 13 12 12

/ 223 23 12 12

23 23 13 13

1 0 0 0 0 0 0

0 0 1 0 0 0 0

0 0 0 0 1 0 0 1

ii

iMNS

i

c s e c s e

U c s s c e

s c s e c

Three neutrino mass and mixing


Normal Inverted

Absolute neutrino mass scale?

Neutrino mass squared splittings and angles


Solar


Schwetz et al �08

Fogli et al

Fogli et al

Hint for cos = -1

Hint for 13 non-zero


12 2

12

3

13

3

23

134 1.4 ,

35 , 4

43 5 , 7 5

5 , 0 .

o o

Harrison, Perkins, Scott

Fogli et al

Current data is consistent with TBM

A clue to the choice of family symmetry comes from tri-bimaximal mixing (TBM)

c.f. Data


Diagonal charged lepton basis

3 2 1

0 0 0 1 1 1 4 2 2

0 1 1 1 1 1 2 1 12 3 6

0 1 1 1 1 1 2 1 1LL

m m mm

Consider the TB neutrino mass matrix in the flavour basis

Largest symmetry of TB neutrino mass matrix is S4/Z3

where the charged lepton sector is symmetric under Z3

mLL = GT m

LL G for G2 S4/Z3 i = GT I

In fact many discrete symmetries D can lead to TBM not only S4


GFami ly SU(3) is the largest family group usually consideredSU(3)

27

2 ( 7 )P S L

72Z Z

54 SO(3)

4A

4S

5D

3S

SU(2)

'T

4D

Many of these symmetries (or others) have been proposed as a family symmetry to give TBM


columnsSFKTBM from see-saw mechanism

T T T

LL

AA BB CCm

X Y Z See-saw I

Diagonal RH nu basis

c.f. TB matrix

Constrained Sequential Dominance

We need a model of Yukawa couplings with CSD enforced by a family symmetry


c ij ci j i jHL E H L E

�Renormalizable Yukawas requires extended Higgs H Hij

e.g. charged lepton fields carry family indices i,j

The family symmetry then generally forbids

�Alternatively allow non-renormalizable Yukawa terms involving the usual Higgs H plus SM singlet flavon fields

ijc c

i j i jHL E HL EM

,i ci j

i

L EE

2

i jc c

i j i jHL E HL EM

or

In constructing a model we must overcome the problem that the Yukawa couplings are forbidden by family symmetry

ci jHL E


Two basic possibilities for the underlying family symmetry :

1)1) ContinuousContinuous symmetry SO(3) or SU(3) discrete symmetry D in the (effective) neutrino sector which is broken completely in the charged lepton sector

2)2) DiscreteDiscrete symmetry D which is preserved in the neutrino sector (or possibly broken to a smaller discrete symmetry D�) but broken completely in the charged lepton sector

We first discuss option 1) then go on to option 2)


SO(3) or SU(3)

SO(3) real vacuum alignment Barbieri, Hall, Kane, Ross; Antusch, SFK

For CSD we need e=-f, a=b=c from additional vacuum alignment �possible but difficult in SO(3) or SU(3) SFK, Ross, Varzelias

Symmetry broken by triplet flavons 3 , 23 , 123

2

2

2 3

1

1

0

0

0 i

iLR

i

i

i i

ee

fe

Y

he

ae

be

ce

123

a

b

c

23

0

e

f

3

0

0

h

123. RF h 2

123. RF h 33. RF h

LH triplets, RH singlets

or3 23

(3) (2) 0

SU SU

3LH triplets, RH triplets

SFK, Ross; Velasco-Sevilla; Varzelias;,Malinsky


Varzielas, SFK, Ross; SFK, Malinsky

Discrete Family SymmetryWe can replace SO(3) and SU(3) by their discrete subgroups:

4 27(3) (3)A SO SU

A4 is similar to the semi-direct product

Same invariants as A4

2=12+2

2+32 ,

3 =1 2 3

Altarelli, Feruglio

2 ' 20 123 0 123 1 0 3w M g g 123

1

1

1

3

0

0

1

23

0

1

1

F-term Vacuum AlignmentVarzielas, SFK, Ross


Radiative Vacuum AlignmentVarzielas, SFK, Ross, Malinsky

0

(s)top loops drive negative

A nice feature of MSSM is radiative EWSB Ibanez-Ross

ZM GUTM

2 2

uHm

2

uHm

H H3LQ

Rt

Similar mechanism can be used to drive flavon vevs using D-terms

Leads to desired vacuum alignment with discrete family symmetry A4 or 27

negative

for negative m3/2

for positive m3/2

23 (0,1, 1)T v

3

123

for positive 123


EE66SSM with SSM with 2727 family symfamily sym Howl, SFK


Dirac type Yukawa couplings

Majorana type Yukawa couplings

Suppressed proton decay


..

.. 12

12 3 3e

dC

.

.

.

GUT relations and Sum Rules

Georgi-Jarlskog

If m is of the TB form we predict 13» 3o and sum rule: SFK, Antusch, Masina


r = reactor s = solars = solar a = atmospheric

SFK; see also Pakvasa, Rodejohann,Wyler; Bjorken, Harrison, Scott, Parke,�

It is useful to consider the following parametrization of the PMNS mixing matrix in terms of deviations from TBM

For a list of oscillation formulae in terms of r,s,a see SFK arXiv:0710.0530


�

1 ( / 3) 0

( / 3) 1 0

0 0 1

2 10

3 31 1 1

6 3 21 1 1

6 3 2

L L

i

E iMNSU V

e

V e

Tri-bim

aximal

Cabibbo-like = Wolfenstein

Deriving the Sum Rule

s r

2 1 11 ( / 6)cos 1 ( / 3)cos / 3

3 3 21 1 1

1 (2 / 3)cos 1 ( / 3)cos6 3 2

1 1 1

6 3 2

i

MNS

e

U

unaffected

Leads to s = r cos with r= /3


In terms of deviation parameters Sum Rule becomes

Including RG corrections (leading log)

Antusch, SFK, Malinsky

RG corrections to sum rules have also been studied numerically

Boudjema, SFK


Testing the sum rule 12 1335.3 coso Bands show

3 error for an optimized

neutrino factory determination

of 13cos .

.

Antusch, Huber, SFK,

Schwetz

12=33.8o§ 1.4o

(current value)


Conclusion Hierarchy problem suggests SUSY Mu and fine tuning problems suggest singlet SUSY models U(1) PQ problems of singlet models suggests gauged U(1) Gauged U(1) anomalies + see-saw suggests E6SSM New possibilities for dark matter Neutrino mixing is consistent with TBM This suggests a non-Abelian family symmetry which can

give a discrete group like S4 in the effective neutrino sector The see-saw mechanism can give TBM via CSD CSD can be achieved using flavons with vacuum alignment

from non-Abelian family symmetry Discrete family symmetries like A4 or 27 are preferred 27 family symmetry in E6SSM suppresses proton decay GUT scenarios lead to sum rule predictions due to charged

lepton corrections to TBM - RG corrections calculated Sum rules may be tested at a neutrino factory

Documents

Amsterdam king.ppt - pdfMachine from Broadgun Software ... · Low energy matter content of E6SSM™s Exotic D,D-bar Three families of Higgs Singlets Quarks and Leptons 27i. . L4 L4