M. Zubkov ITEP Moscow 2007 10 Tev monopoles and topology of the Standard Model.

M. ZubkovM. ZubkovITEP Moscow 2007ITEP Moscow 2007

10 Tev monopoles and topology 10 Tev monopoles and topology of the Standard Model of the Standard Model

22

AbstractAbstract

Standard Model may be defined with the gauge Standard Model may be defined with the gauge groupgroupss

We show, thatWe show, that, , if the Unification is achieved at if the Unification is achieved at TevTev (it could be in PUT or ETC), in the cases (it could be in PUT or ETC), in the cases

monopoles with masses of the order of 10 Tevmonopoles with masses of the order of 10 Tev shouldshould appear, which may become the lightest appear, which may become the lightest topologically stable monopoles. topologically stable monopoles. The idea is illustrated The idea is illustrated by consideration of by consideration of Petite Unification modelsPetite Unification models..

6/)1()2()3( ZUSUSU 3/)1()2()3( ZUSUSU

)1()2()3( USUSU 3/)1()2()3( ZUSUSU 6/)1()2()3( ZUSUSU 2/)1()2()3( ZUSUSU

33

The lattice model for qualitative investigation of this phenomenon based on the Petite Unification Theory is presented

CTT CTT

10 Tev monopoles

monopoles

TevTC 1

We expect the percolation transition is present

Early Universe

44

The additional discrete symmetry in the Standard Model

C.Gardner, J.Harvey, Phys. Rev. Lett. 52 (1984) 879Tanmay Vachaspati, Phys.Rev.Lett. 76 (1996) 188-191Hong Liu, Tanmay Vachaspati, Phys.Rev. D56 (1997) 1300-1312

6/)1()2()3()5( ZUSUSUSU

1. SU(5) GUT

2. STANDARD MODEL B.L.G.Bakker, A.I.Veselov, and M.A.Zubkov, Phys. Lett. B 583, 379(2004)

The additional symmetry in the fermion and Higgs sectors of the SM

6Z

55

)1(),exp(

)2(),exp(

)3(),exp(

uBdxBiPe

suAdxAiPU

suCdxCiP

l

i

l

l

Quark, lepton, and Higgs Parallel transporters, and Wilson loops

Ue

e

H

e

ed

ueu

Uee

Ued

u

i

R

R

ijRi

Rjij

Ri

i

L

ij

L

i

i

i

i

i

i

2

3

2

3

4

3

1

5,4,3,2,1,0

3

2

326

N

eee

UeU

e

ZZZ

iNii

Ni

iN

66

TevSU 1210)5(

*202

321

321

3312

2213

1123

321

3

2

0

0

0

0

0

)5(0

0

uiuiu

eddd

euuu

duuu

duuu

duuu

eddd

SUUe

e

Tc

L

c

c

cc

cc

cc

L

ссс

i

i

5,4,3,2,1,0

3

2

326

N

eee

UeU

e

ZZZ

iNii

Ni

iN

77

RR

Rjij

Ri

Rjij

Ri

L

i

LL

j

jij

L

i

i

i

i

eee

dedueu

eUe

ed

uUe

d

u

SUUe

e

i

ii

i

2

3

2

3

4

3

;;

;;

:

)5(0

03

2

88

STANDARD MODEL WITH THE GAUGE GROUP :

Fermion ang Higgs sectors are the same

The gauge group is

6/)1()2()3( ZUSUSU

)1();2();3(

)exp(

)exp(

)exp(

)exp(

)exp(

)exp( 3

2

uBsuAsuC

dxBiPe

dxAiPe

dxCiPe

dxBiP

dxAiP

dxCiP

l

Nil

Nil

iN

l

l

l

The following elements of represent the same element of the gauge group

with N = 0,1,2,3,4,5

)1()2()3( USUSU

6/)1()2()3( ZUSUSU

99



The gauge group is

3/)1()2()3( ZUSUSU

)1();2();3(

)exp(

)exp(

)exp(

)exp(

)exp(

)exp( 3

2

uBsuAsuC

dxBiPe

dxAiPe

dxCiPe

dxBiP

dxAiP

dxCiP

l

Nil

Nil

iN

l

l

l


with N = 0,2,4

)1()2()3( USUSU

3/)1()2()3( ZUSUSU

1010



The gauge group is

2/)1()2()3( ZUSUSU

)1();2();3(

)exp(

)exp(

)exp(

)exp(

)exp(

)exp( 3

2

uBsuAsuC

dxBiPe

dxAiPe

dxCiPe

dxBiP

dxAiP

dxCiP

l

Nil

Nil

iN

l

l

l


with N = 0,3

)1()2()3( USUSU

2/)1()2()3( ZUSUSU

1111

THE CONVENTIONAL STANDARD MODEL )1()2()3( USUSU

xdBg

xdAAiATrg

xdCCiCTrg

S 42][2

1

42][2

2

42][2 4

1,

2

1,

2

1

212

3

22

21

2

22

21

12

22

21

1

22

21

2

213

3

12

~

2;

~

2

;sin22

;sin;cos

)~~

(2

1~;

~sin

~cos

~

;sin~

cos~1~

2~;

2~;

2~

)1();2();3(

iAAWg

WBAZgg

Z

ZBA

gg

gge

gg

g

gg

g

AiAWBAZ

ABAe

A

Bg

BAg

ACg

C

uBsuAAsuCC

Wem

WW

WW

WWemem

iiii

iiii

1212

There are 4 versions of the Standard Model

)1()2()3( USUSU

2/)1()2()3( ZUSUSU

3/)1()2()3( ZUSUSU

6/)1()2()3( ZUSUSU

1313

Is there any difference Is there any difference between the four versions between the four versions of the Standard Model? of the Standard Model?

On the level of perturbation On the level of perturbation theory they are identicaltheory they are identical

1414

The Standard Model does not The Standard Model does not work at E > 1 TEVwork at E > 1 TEV

TEV physics is described by the Unified theory with simply TEV physics is described by the Unified theory with simply connected gauge groupconnected gauge group

Standard Standard ModelModel

Standard Standard ModelModel

R = 1 R = 1 TEVTEV

-1-1

Unified theoryUnified theory

Standard Model fields are not Standard Model fields are not defineddefined

1515

222

44242][

2

)][2()();2(,

)(4

]],[[,8

14

;);1()2(

vHTrHVsuHA

xdHVxdHAiHTrxdAAiATrS

ggvUSU

T’Hooft – Polyakov monopoleT’Hooft – Polyakov monopole

An example: Georgi-Glashow modelAn example: Georgi-Glashow model

1||;

||2),(;0;

2

1),( 02

xx

xvtxHA

x

xtxA

a

a

i

aaij

i

M

1616

3

1

2

0

321

301

31

;)()()(),(

1||;

2),(;0;2),(

ii

jiji

dyxxyxtx

xv

txHAtxA

111

222

221

;

sinsin||;cossin||;cos||

323

HHAA

eee

xxxxxx

iii

1

2),(

),(

3

ii dxtxAi

ii

e

dxtxA

1717

10||

10||

/

L

L

L

L

HHGH

)/1,(

,1

HGH

G

L

L

LL

Standard ModelStandard Model(gauge group H)(gauge group H)

111

TevR

Parallel transporter within the Parallel transporter within the Unified theory along contour LUnified theory along contour L

Unification at Tev Unification at Tev occurs in PUT and some of Extended Technicolor occurs in PUT and some of Extended Technicolor

ModelsModels

Unified theory Unified theory (gauge group (gauge group G)G)

1818

)1(,)exp(

)2(,)exp(

)3(,)exp( 3

2

uBedxBiPe

suAedxAiPU

suCedxCiP

Ni

L

i

Ni

L

iN

L

L

331

32

])/)1()2()3(([

])/)1()2()3(/[(

ZZZUSUSU

ZUSUSUG


Standard ModelStandard Model

N = 0,2,4 N = 0,2,4

ANTI ANTI MONOPOLMONOPOLEE Unified Unified theorytheory

MONOPOLMONOPOLE E Unified Unified theorytheory

Tev

TevM

s

sZ

1

12.0

103

1919

)1(,)exp(

)2(,)exp(

)3(,)exp( 3

2

uBedxBiPe

suAedxAiPU

suCedxCiP

Ni

L

i

Ni

L

iN

L

L221

22

])/)1()2()3(([

])/)1()2()3(/[(

ZZZUSUSU

ZUSUSUG



N = 0,3 N = 0,3

MONOPOLMONOPOLEE Unified Unified theorytheory


128

1

1002

TevM Z

2020

)1(,)exp(

)2(,)exp(

)3(,)exp( 3

2

uBedxBiPe

suAedxAiPU

suCedxCiP

Ni

L

i

Ni

L

iN

L

L

ZUSUSU

USUSUG

)])1()2()3(([

)])1()2()3(/[(

1

2



N = 0 N = 0

ANTI ANTI MONOPOLE MONOPOLE UnifiedUnified theorytheory


128

1

100

TevM Z

2121

)1(,)exp(

)2(,)exp(

)3(,)exp( 3

2

uBedxBiPe

suAedxAiPU

suCedxCiP

Ni

L

i

Ni

L

iN

L

L

661

62

])/)1()2()3(([

])/)1()2()3(/[(

ZZZUSUSU

ZUSUSUG



N = N = 0,1,2,3,4,5 0,1,2,3,4,5

ANTI ANTI MONOPOLMONOPOLE E UnifiedUnified theorytheory


Tev

TevM

TevM

TevM

s

Z

Z

sZ

110

1;

128

1

100

100

10

2

3

2222

6

3

/)1()2()3(

/)1()2()3(

ZUSUSU

ZUSUSU

)1()2()3(

/)1()2()3( 2

USUSU

ZUSUSU

100 TEV MONOPOLES

10 TEV MONOPOLES

2323

Petite UnificationPetite Unification

TevNSUSU kPS 1)()4(

)3()4( : PUT

)2()4( : PUT

)2()4( : PUT

23.0) M(sin;12.0) (M ;128

1)(

22

31

40

Z2

ZS

SUSU

SUSU

SUSU

M

PS

PS

PS

WZ

Andrzej J. Buras, P.Q. Hung, J.D.Bjorken Phys.Rev.D25:805,1982; A.Buras, P.Q. Hung Phys.Rev. D68 (2003) 035015; A. Buras, P.Q. Hung, Ngoc-Khanh Tran, Anton Poschenrieder, Elmar Wyszomirski, Nucl.Phys. B699 (2004) 253

2424

)(

1)2()4( PUT 40

eKtodueexcluded

TevSUSU

L

PS

;2,1,1,1,4;1,2,1,1,4

;1,1,2,1,4;1,1,1,2,4

0

0

0

0

0

0

321

321

321

321

321

321

321

321

3

RL

RL

R

i

i

L

R

i

i

L

PS

i

i

E

N

E

N

eddd

uuu

eddd

uuu

e

eU

e

eU

e

e

2525

RRRR

Rjij

Ri

Rjij

Ri

L

i

LL

j

jij

L

i

i

R

i

i

L

R

i

i

L

PS

i

i

eee

dedueu

eUe

ed

uUe

d

u

e

eU

e

eU

e

e

i

ii

i

2

3

2

3

4

3

;

;;

;;

:

0

0

0

0

0

03

2626

1Ni

L

i

Ni

L

iN

L

R

i

i

L

R

i

i

L

PS

i

i

edxBiPe

NedxAiPU

edxCiP

e

eU

e

eU

e

e

)exp(

3,0;)exp(

)exp(

0

0

0

0

0

0

3

2

3

24 /)1()2()3()2()4( ZUSUSUSUSU PS

TevMmonopoleZ 1002

2727

TevSUSU PS 1)2()4( PUT 31

*202

,,

2

2

2

3

2

;2,1,1,4,;1,1,2,4,

;2,2,1,4,,,

;1,2,2,4,,,

0

0

0

0

0

0

uiuiu

L

N

D

U

L

N

D

U

eL

N

D

U

d

ui

eL

N

D

U

d

ui

e

e

e

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e

Tc

RL

i

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iR

LL

i

iс

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iL

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H

i

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i

i

2828

1Ni

L

i

Ni

L

iN

L

R

i

i

H

i

i

L

PS

i

i

edxBiPe

NedxAiPU

edxCiP

e

e

e

eU

e

e

)exp(

4,2,0;)exp(

)exp(

0

0

0

0

0

0

3

2

2

3

2

33 /)1()2()3()2()4( ZUSUSUSUSU PS

TevMmonopoleZ 103

2929

TevSUSU PS 1)3()4( PUT 22

*202

2

2

12

222

2

222

11

122

2

3

2

3

2

3

4

3

2

3

2

3

2

)(,~

~,)(,)(

,~

~,)(,)(

,)(,)(,)~~

(

)(,,)(,)~~

(

)(,,)(,)(

,,)(,)(

)3,3,4()3,3,4(

00

00

00

0

0

0

0

uiuiu

le

dD

Ui

ee

UD

Ui

NL

Niu

d

ui

lL

Nid

d

ui

LL

Nid

d

ui

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D

Ui

e

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с

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LicT

с

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i

i

3030

1Ni

L

i

Ni

L

iN

L

H

i

i

i

L

i

i

PS

i

i

edxBiPe

NedxAiPU

edxCiP

e

e

e

e

Ue

e

e

)exp(

3,0;)exp(

)exp(

00

00

00

0

0

0

0

3

2

3

2

3

2

3

4

3

2

3

2

3

2

22 /)1()2()3()3()4( ZUSUSUSUSU PS

TevMmonopoleZ 1002

3131

U

U D

1

20

1 TevR

11 TevR

TevifTevEnergyeverythingMMpps

ZZ 1202

;33

g

Energy scale not far from LHC upper bound

6

3

/)1()2()3(

/)1()2()3(

ZUSUSU

ZUSUSU

U D

U

p

p

jets

monopole

anti monopole

3232

1

200

1 TevR

11 TevR

everythingMMee ZZ 22

_

E ~ 200 Tev

2/)1()2()3( ZUSUSU

e _

e

jets

6/)1()2()3( ZUSUSU

+

monopole

anti monopole

3333

1

200

1 TevR

11 TevR

everythingMMee ZZ

E ~ 200 Tev

)1()2()3(

/)1()2()3( 2

USUSU

ZUSUSU

e

+

e

jets

6

3

/)1()2()3(

/)1()2()3(

ZUSUSU

ZUSUSU

_

3434

T

CTT CTT

monopoles monopoles

CT

PERCOLATION TRANSITION

Early Universe

3535

TCTT

CTT

Nambu monopoles

Nambu monopoles

GevTC 100200~

Electroweak Transition

Early Universe

B.L.G.Bakker, A.I.Veselov, and M.A.Zubkov, Phys. Lett. B642 (2006) 147-152

3636

21332

2

3

;);(sin22

sin4

)2(,,2

iAAWBAZBABA

NdxdxA

suAAZNNdxZdxA

Wem

Wem

ii

LL

L

vН

0

Standard Model Standard Model

GevR

TevM

200

1

1

NAMBU MONOPOLES (unitary gauge)

Z string

NAMBU MONOPOLE

NAMBU MONOPOLE

3737

Percolation of Nambu monopoles near the Electroweak transition

Monopole density and percolation probability for the monopole clusters. The temperature is decreased with increasing of

T

3838

H

i

i

i

L

i

i

PS

i

i

e

e

e

e

Ue

e

e

ZUSUSUSUSUSU

3

2

3

2

3

4

3

2

3

2

3

2

2

00

00

00

0

0

0

0

/)1()2()3()3()3()4(

L

i

i

e

Ue

ZUSUSU

3

2

3

2

0

0

/)1()2()3(

Simplified lattice model

H

i

i

i

L

i

i

e

e

e

e

Ue

ZUSUSUSU

3

2

3

2

3

4

3

2

3

2

00

00

00

0

0

/)1()2()3()3(

3939

)3(

)3(

suH

SU

8

23

222

2min)(

)54

()()(

HHV

DetHTrHHV xx

Fields1. Lattice gauge field (defined on links)

2. Adjoint Higgs field (defined on sites)

sitesx

linksxyxxyy

plaquettesplaquette HVHHTrTrS )()(Re

3

11 2

Lattice action

Higgs condensate

8

23

222

2min)(

)54

()()(

HHV

DetHTrHHV xx

4040

linksplaquettesplaquette

linksxyxy

plaquettesplaquette

Tr

TrTrS

))||1(2|||(|Re3

11

)2(Re3

11

)(

233

223

213

88

At low energies

L

i

i

e

Ue

ZUSUSU

3

2

3

2

0

0

/)1()2()3(

London limit

4141

2

3;

2

3

2

3:)1(

||||;

||||:)2(

33

212

211

312

12212

211

311

11

ArgU

eU

eUSU

ii

233* mod Argddj

MONOPOLE WORLDLINE

Electroweak fields

2Z

4242

CONDENSATION OF MONOPOLES

Expected phase diagram (at finite temperature)

low temperature

high temperature

4343

)1()2()3(

/)1()2()3(

/)1()2()3(

/)1()2()3(

2

3

6

USUSU

ZUSUSU

ZUSUSU

ZUSUSU

0. Four versions of the Standard Model with the gauge groups

are indeed different if the space-time has nontrivial topology.

1. Nontrivial topology appears around the worldlines of monopoles of the unified model. If unification is achieved at Tev (ETC or PUT) and the Standard Model has the gauge group or

then such monopoles may appear with masses about 10 Tev. 3. Those topologically stable monopoles may be created during high energy collisions (probably, at the next generation of colliders, or even at LHC) and may be condensed in the early Universe at high temperature.

3

6

/)1()2()3(

/)1()2()3(

ZUSUSU

ZUSUSU

M. Zubkov ITEP Moscow 2007 10 Tev monopoles and topology of the Standard Model.

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Transcript of M. Zubkov ITEP Moscow 2007 10 Tev monopoles and topology of the Standard Model.