Transcript CUSTODIAL SYMMETRY IN THE STANDARD MODEL AND …

CUSTODIAL
SYMMETRY IN THE
STANDARD MODEL
AND BEYOND
V. Pleitez
Instituto de Física Teórica/UNESP
Modern Trends in Field Theory
João Pessoa ─ Setembro 2006
OUTLINE
 What is the Custodial Symmetry?
 Standard Model
 3-3-1 Models
 ...
 Conclusions
Automatic or Accidental (Global) Symmetry,
are not imposed, consequence of:




Lorentz invariance
Gauge invariance
Renormalizability
Representation content of the model
Examples: Baryon number, Lepton number,
and approximate chiral symmetries:
SU (2)  SU (2)
L
R
SU (3)  SU (3)
L
R
STANDARD MODEL’s THREE GENERATIONS:
QL ~ (3,2,1 / 3);
u 
Q1L    ;
 d L
uR ;
dR
c
Q2 L    ;
 s L
cR ;
sR
t 
Q3L    ;
 b L
tR ;
bR
uR ~ (3,1,4 / 3);
d R ~ (3,1,2 / 3)
The fermion mass problem:
 Why do weak isospin partners have
different masses?
 Why are quark and lepton masses split?
 Why there is a mass hierarchy between
generations, and
 Why is there a mixing angle hierarchy in
quarks but not in leptons?
Weak isospin
partners
u
mu  2
MeV
mc  1400
MeV
mt  174000
d
md  5
MeV
ms  100
MeV
mb  4500
MeV
MeV
PDG 2004
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.
u 
  ;
 d L
Before SSB:
After SSB:
mu  md  0
mu  md  0
uR ;
dR
u,d generic quarks
mu  md  0 ?
-parameter in the SM
M 2W
 2
1
2
c WM Z
  1  
(At the tree level)
(Radiative corrections)
  1  a few percent
How the following experimental facts
mu  md
  1  a few percent
can be made compatible ?
The first is a clear violation of isospin
The second one is a consequence of isospin [SU(2)] conservation
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:
SU(3)C  SU(2) L U (1)Y
SSB
SU (3)C  U (1)Q
  
H   0  ~ (1,2,1)
 
SSB: ONE SCALAR DOUBLET
SCALAR POTENTIAL:
V (H H )   H H  (H H )

2


2
2-doublet:
~
1

( H , H ) ~ (2,2)
2

~
H  H

L  Tr[(D) D ]   Tr   [Tr ]

2


2
'




g
g
D        i W    i B  3 
2
2


L :
  L,
Global and local:
g’=0 (sinW=0)
Global
  e
i
3
2
SU (2) L U (1)Y
SU(2) L  SU(2) R
g’=0
g   

D        i W   
2


U (1)Y :   e
i
3
2
 SU(2) R :
SU(2)L  SU(2)R :
1 v
   
2 0
  R 
  LR

0
  L     ,    R   
v
SU(2) L  SU(2) R

SU(2) L R
SU(2) L 
SU(2) R 
SU(2) L  SU(2) R  SU(2) L R
(broken)
(conserved)
L    L   
*

MW  M Z
W1,W2,W3Z are in a triplet of SU(2)L+R
When g’≠0
M 2W
MW  M Z cosW    2
1
2
c WM Z
At the tree level this is a zero order correction: g0,g’0
  1  
Fermion loops
g2
 | fermions 
64M 2W
2
2
2
2
2
 2



2
m
m
m
3
g
m
t
b
t
t
2


m

m

ln

b
 t
2
2
2 
2
2

m

m
m
64

M
t
b
W
 b 

This correction vanishes in the limit mt=mb
Radiative correction due to gauge and Higgs bosons are
proportional to g’2 (or sin2W). For instance, loops of Higgs
2

11GF M Z sin W
mh
 |higgs  
ln 2
2
24 2
m Z
2
2



Due to unbroken SU(2)L+R in the limit g’→0 (sin2W=0) the
custodial symmetry protects the tree level relation =1.
Quark masses in the SM (Yukawa couplings)
~
 LY  (QiL iju jR  LaL  ab bR ) H  (QiL d ij d jR  LaL l ablbR ) H

u
~
H  H *
i, j  1,2,3;
q  e, ,
(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.
Extending the custodial symmetry to the Yukawa sector
Defining the 2-doublets: in the quark sector

Qij  (QiLd jR
QiLu jR ) ~ (2,2) :
SU (2) L  SU (2) R
and in the lepton sector

Lij  (LaLlbR
LaL bR ) ~ (2,2):
SU(2) L  SU(2) R
Right-handed neutrinos are needed
The Yukawa interactions are now, manisfestly
invariant under SU(2)LSU(2)R,


 LY  habTr ( Lab )  gijTr (Qij)
1 v
   
2 0
SU(2) L  SU(2) R

mu  md ,
0

v

SU(2) L R
ml  mD
This is a consequence of the custodial SU(2)L+R symmetry
g’≠0 (sinW≠0), i.e, turn on the electromagnetic interactions
2
W
M
 2
1
2
c WM Z
and, as usual
~
 LY  (QiL iju jR  LaL  ab bR ) H  (QiL d ij d jR  LaL l ablbR ) H
u

or
Assume that
mu  md ,
ml  mD
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 ):
New Physics:
 New quark singlets of SU(2)LU(1)Y (generalized
seesaw mechanism)
 Multi-Higgs doublet extensions
 Radiative corrections of a Z’ vector boson
 The seesaw mechanism for neutrinos is
mandatory
(for details see hep-ph/0607144 )
generalized seesaw mechanism
Multi-Higgs doublet extensions
Radiative corrections of a Z’ vector boson
Breaks the deneracy of charged lepton and neutrino masses
And ...
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 ...
(1,2,1 / 2), (8,2,1 / 2),
(Glashow-Weinberg)
(1,3,0)
Added for unification at 1015 GeV
Manohar & Wise, hep-ph/0606172
BEYOND THE STANDARD
MODEL
Among other open problems, the SM does not
give an answer to the questions:
Why three generations?
Why sin2W is near ¼?
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 sin2W is a completely arbitrary parameter
There are only three active sequential generations (LEP):
The history of the value of sin2W until 1989
PDG 2004
sin2W(MZ)=0.231
20(15)
Just an accident?
If sin2W 1/4 is not na accident there must be an SU(3)
symmetry at the TeV scale sin2W(µ)=1/4 but
sin2W(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)CSU(2)LU(1)Y  SU(3)CSU(3)LU(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 also
Z’ prime has a mixing with Z of the SM

v at the TeV scale
Goldberger-Treimam Relation valid in the m2=0 (chiral limit)
2GAmn  g NN f
3-3-1 models have an approximate SU(2)L+R custodial symemtry
1  2 sin 2 W
g

MW
cos W
2
v
D&M&P: PRD73, 113004 (2006);
PL B637, 85 (2006)
vGF at the Fermi scale (weak interactions)
Ths condition is valid if, and only if,
sin   0
At the tree level
Z1  cosZ  sin Z '
Z2   sin Z  cosZ '
Z1  Z ,
Z2  Z '
sin   0  v  
(v>1 TeV), sin<<1
1  2 sin 2 W
g

MW
cos W
2
v
?
ILC e+e-  H1H2 (Cieza Montalvo-Tonasse, PRD71, 095015)
SU(3) L  SU(3) R

1
( )
3
Little 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)LSU(2)R
and left-right symmetries can be used to make the tree
level contributions to the T parameter and the anomalous
couplings of the b-quark to the Z very small...
M. Carena, et al., hep-ph/0607106
Conclusions
 The difference on the weak isospin
partners’s masses may be a signal of
NEW PHYSICS
 Right-handed neutrinos have to added
 The seesaw mechanism have to be
implemented
 Custodial symmetry is important, both in
the SM and beyond
Muito obrigado!