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!
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