CUSTODIAL CUSTODIAL SYMMETRY IN THE SYMMETRY IN THE STANDARD MODEL STANDARD MODEL

AND BEYONDAND BEYONDV. PleitezV. Pleitez

Instituto de Física Teórica/UNESPInstituto de Física Teórica/UNESPModern Trends in Field TheoryModern Trends in Field TheoryJoão Pessoa João Pessoa ─ ─ Setembro 2006Setembro 2006

OUTLINEOUTLINE

What is the Custodial Symmetry?What is the Custodial Symmetry? Standard ModelStandard Model 3-3-1 Models3-3-1 Models ...... ConclusionsConclusions

Automatic or Accidental (Global) Symmetry, Automatic or Accidental (Global) Symmetry, are not imposed, consequence of:are not imposed, consequence of:

Lorentz invarianceLorentz invariance Gauge invarianceGauge invariance RenormalizabilityRenormalizability Representation content of the modelRepresentation content of the model

RLSUSU )2()2(

Examples: Baryon number, Lepton number,

and approximate chiral symmetries:

RLSUSU )3()3(

RR

L

L dud

uQ ;;1

RR

L

L scs

cQ ;;2

RR

L

L btb

tQ ;;3

STANDARD MODEL’s THREE GENERATIONS:

)3/2,1,3(~);3/4,1,3(~);3/1,2,3(~ RRL duQ

The fermion mass problem:The fermion mass problem:

Why do weak isospin partners have Why do weak isospin partners have different masses?different masses?

Why are quark and lepton masses split?Why are quark and lepton masses split? Why there is a mass hierarchy between Why there is a mass hierarchy between

generations, and generations, and Why is there a mixing angle hierarchy in Why is there a mixing angle hierarchy in

quarks but not in leptons?quarks but not in leptons?

MeVmu 2

MeVmd 5 MeVms 100

MeVmc 1400

MeVmb 4500

PDG 2004

MeVmt 174000

Weak isospinpartners

u

d

The SM answer: the gauge group permits a different Yukawa coupling constantto set each fermion mass and mixing angle.

The SM accomodates the problem but does not explain it. this suggests that it should be correlated with the breakdown of a larger symmetry.

Weak isospin partners have different masses because the left- and right-handed fields are not related by any symmetry.

RR

L

dud

u;;

Before SSB: 0 du mm

After SSB: 0 du mm0 du mm ?

u,d generic quarks

1

1 a few percent

122

2

ZW

W

Mc

M (At the tree level)

(Radiative corrections)

-parameter in the SM

1 a few percent

du mm

The first is a clear violation of isospinThe second one is a consequence of isospin [SU(2)] conservation

can be made compatible ?

How the following experimental facts

The accidental SU(2) (global) symmetry, for its protective functions is called: CUSTODIAL SYMMETRY. (It may, or not, be the isospin.)

STANDARD MODEL’s GAUGE SYMMETRIES:

YLC USUSU )1()2()3(

QU )1(

SSB

CSU )3(

)1,2,1(~0

HSSB: ONE SCALAR DOUBLET

22 )()( HHHHHHV

SCALAR POTENTIAL:

HHHH ~~

)2,2(~),(2

1

2-doublet:

22 ][])[( TrTrDDTrL

3

'

22 B

giW

giD

:L 23

,i

eL

YL USU )1()2( Global and local:

g’=0 (sinW=0)

RL SUSU )2()2( Global

W

giD

2

g’=0

RSUeU R

i

Y :)2(:)1( 23

RLSUSU RL :)2()2(

v

v

0

0

2

1 RL ,

RLRL SUSUSU )2()2()2(

RLRL SUSUSU )2()2()2(

RL SUSU )2()2(

*LL

(broken)

(conserved)

ZW MM

When g’≠0

122

2

ZW

W

Mc

M WZW MM cos

At the tree level this is a zero order correction: g0,g’0

W1,W2,W3Z are in a triplet of SU(2)L+R

1

W

t

b

t

bt

btbt

Wfermions M

mg

m

m

mm

mmmm

M

g2

2

2

2

2

2

22

2222

2

2

64

3ln

2

64|

Fermion loops

Radiative correction due to gauge and Higgs bosons are proportional to g’2 (or sin2W). For instance, loops of Higgs

Z

hWZFhiggs m

mMG2

2

2

22

ln224

sin11|

Due to unbroken SU(2)L+R in the limit g’→0 (sin2W=0) the custodial symmetry protects the tree level relation =1.

This correction vanishes in the limit mt=mb

Quark masses in the SM (Yukawa couplings)

HlLdQHLuQL bRabl

aLjRijd

iLbRabaLjRiju

iLY )(~

)(

,,;3,2,1,~ * eqjiHH

(we have omitted summation symbols)

If all Yukawa couplings ’s are different the generated Dirac masses in eachcharge sector (weak isospin partners) are different and arbitrary.

Defining the 2-doublets: in the quark sector

RLjRiLjRiLij SUSUuQdQQ )2()2(:)2,2(~)(

RLbRaLbRaLij SUSULlLL )2()2(:)2,2(~)(

and in the lepton sector

Right-handed neutrinos are needed

Extending the custodial symmetry to the Yukawa sector

The Yukawa interactions are now, manisfestly invariant under SU(2)LSU(2)R,

)()( ijijababY QTrgLTrhL

D

ldu mmmm ,

v

v

0

0

2

1

RLRL SUSUSU )2()2()2(

This is a consequence of the custodial SU(2)L+R symmetry

g’≠0 (sinW≠0), i.e, turn on the electromagnetic interactions

122

2

ZW

W

Mc

M

and, as usual

HlLdQHLuQL bRabl

aLjRijd

iLbRabaLjRiju

iLY )(~

)(

oror

it is possible that the source of the breakdown of the SU(2)L+R symmetry in the gauge-Higgs bosons system is different from the breakdown of that symmetryin the fermion-Higgs sector. In the latter one, NEW PHYSIC may be at work.

M&P (hep-ph/0607144 ):

D

ldu mmmm ,

Assume that

New Physics:New Physics:

New quark singlets of SU(2)New quark singlets of SU(2)LLU(1)U(1)Y Y (generalized (generalized seesaw mechanism)seesaw mechanism)

Multi-Higgs doublet extensionsMulti-Higgs doublet extensions Radiative corrections of a Z’ vector bosonRadiative corrections of a Z’ vector boson The seesaw mechanism for neutrinos is The seesaw mechanism for neutrinos is

mandatorymandatory

(for details see (for details see hep-ph/0607144hep-ph/0607144 ) )

generalized seesaw mechanismgeneralized seesaw mechanism

Multi-Higgs doublet extensionsMulti-Higgs doublet extensions

Radiative corrections of a Z’ vector bosonRadiative corrections of a Z’ vector boson

Breaks the deneracy of charged lepton and neutrino masses

)0,3,1(),2/1,2,8(),2/1,2,1(

Also in the context of the SM, multi-Higgs extensions

The most general scalar structure which naturally (follows from the group structure and representation content ...

(Glashow-Weinberg) Added for unification at 1015 GeV

Manohar & Wise, hep-ph/0606172

And ...

BEYOND THE STANDARD BEYOND THE STANDARD MODELMODEL

In the context of the standard model:

No attempt is made to explain the number of fermion generations from the viewpoint of anomaly cancelation: each generation is anomaly free.

Also sin2W is a completely arbitrary parameter

Among other open problems, the SM does not give an answer to the questions:

Why three generations?

Why sin2W is near ¼?

There are only three active sequential generations (LEP):

PDG 2004

sin2W(MZ)=0.23120(15)

The history of the value of sin2W until 1989

Just an accident?

If sin2W 1/4 is not na accident there must be an SU(3) symmetry at the TeV scale sin2W(µ)=1/4 but sin2W(MZ)=0.23120(15)

By choosing appropriately the representation content of the model: The anomaly cancelation plus the property of asymptotic freedom of QCD the number of generations allowed is three and only three

Both problems have answers in the so called 3-3-1 models.

SU(3)CSU(2)LU(1)Y SU(3)CSU(3)LU(1)X

STANDARD MODEL 3-3-1 MODELS

SU(3)L symmetry at an energy scale v of the order of TeV

New quarks have masses proportional to v The neutral vector boson Z’ has a mass proportional to v and alsoZ’ prime has a mixing with Z of the SMv at the TeV scale

Goldberger-Treimam Relation valid in the m2=0 (chiral limit)

fgmG NNnA 2

WW

W Mv

g

cos

sin21

2

2

D&M&P: PRD73, 113004 (2006); PL B637, 85 (2006)

vGF at the Fermi scale (weak interactions)

3-3-1 models have an approximate SU(2)L+R custodial symemtry

Ths condition is valid if, and only if,

'sincos1 ZZZ

'cossin2 ZZZ

0sin At the tree level

', 21 ZZZZ

v0sin (v>1 TeV), sin<<1

ILC e+e- H1H2 (Cieza Montalvo-Tonasse, PRD71, 095015)

WW

W Mv

g

cos

sin21

2

2 ?

)(3

1 RL SUSU )3()3(

Little Higgs, 5D composite HiggsLittle Higgs, 5D composite Higgs

Higgsless models ,Little Higgs and 5D composite models:SU(2) that protects from radiative corrections can also protect the Zbbbar coupling.

Agashe et al. hep-ph/0605341.

...in a Randall-Sundrum scenarios the SU(2)LSU(2)R and left-right symmetries can be used to make the treelevel contributions to the T parameter and the anomalouscouplings of the b-quark to the Z very small...

M. Carena, et al., hep-ph/0607106

ConclusionsConclusions

The difference on the weak isospin The difference on the weak isospin partners’s masses may be a signal of partners’s masses may be a signal of NEW PHYSICSNEW PHYSICS

Right-handed neutrinosRight-handed neutrinos have to added have to added TheThe seesaw mechanism seesaw mechanism have to be have to be

implementedimplemented Custodial symmetry is important, both in Custodial symmetry is important, both in

the SM and beyondthe SM and beyond

Muito obrigado!Muito obrigado!