review of gauge-higgs unification models
DESCRIPTION
Review of gauge-Higgs unification models. TIS2005, Taiwan, 6/10/2005. Naoyuki Haba ( 波場直之 ). (Tokushima Univ.). Plan of talk. 1. models of gauge-Higgs unification. 2. electro-weak symmetry breaking (1). 3. electro-weak symmetry breaking (2). 4. Higgs phenomenology. - PowerPoint PPT PresentationTRANSCRIPT
Review of gauge-Higgs unification models
Naoyuki Haba ( 波場直之 )
TIS2005, Taiwan, 6/10/2005
(Tokushima Univ.)
Plan of talk
1. models of gauge-Higgs unification
2. electro-weak symmetry breaking (1)
3. electro-weak symmetry breaking (2)
4. Higgs phenomenology
5. summary & discussion
Q: Can origin of Higgs be extra component of gauge field? → gauge invariance guarantees the smallness of “Higgs” mass (against quantum c)!A: Yes, we can do it in the extraD gauge theory. → 5th component of gauge field (A5) = 4D scalar in eff. theo. ⇒ Regard “Higgs”!
5 24A
1S
regard it adjoint Higgs which breaks SU(5) GUT
4D
5 (5)D SU GUT
( 0~ , )53MA
(Hosotani, etal)
μ
(ex)
What we want is not Σ but SM Higgs doublet which breaks SU(2)×U(1) today.
( radi:10-29mm ( 1016 GeV) )
4D
5 (3), (6)D SU SU
( 0~ , )53MA
12/S Z
5 8,35( )DH A
5 55 5cD Dg A
4D
⇒ origin of “Higgs doublet” (zero mode)
⇒ origin of Yukawa interactionR L
μ
Gauge-Higgs unification
“Higgs doublet” mass is finite. ( ~ 1/R)
5D gauge symmetry
(ex)
( radi:10- 16 mm ( 1TeV) )
( ) ( )1
( , )2
niR
n
n yx x e
Ry
4 1(1) : M S
0y
4D
R
: ( , 2 ) ( , )x y R yT xT
[ ( )]T U N
preparation ( notation )
,0
( )
( )
0
1
cos( )
sin(
1( , )
2
1( ( ) )
(
, )
)n
n
n
n
n
nyy
R
n
Rx x
xR
yy
Rx
42
1(2) : /M S Z
0y
4D
: ( , ) ( , )P Px y x y
y y
y R
4D
0y y R
2 2[ 1 ( ) ( ) ( )]P y P y P y
preparation ( notation )
,0
( )
( )
0
1
cos( )
sin(
1( , )
2
1( ( ) )
(
, )
)n
n
n
n
n
nyy
R
n
Rx x
xR
yy
Rx
42
1(2) : /M S Z
0y
4D
: ( , ) ( , )P Px y x y
y y
y R
4D
0y y R
2 2[ 1 ( ) ( ) ( )]P y P y P y
5 5
( , ) ( , )
( , ) ( , )
( , ) ( , )
( , ) ( , )
L L
R R
P P
P P
A x y A x y
A x y A x y
x y x y
x
P
y yP x
[ ( , ) ( , )]yx y Pi x y 55 : ( , )MD i
preparation ( notation )
,0
( )
( )
0
1
cos( )
sin(
1( , )
2
1( ( ) )
(
, )
)n
n
n
n
n
nyy
R
n
Rx x
xR
yy
Rx
42
1(2) : /M S Z
0y
4D
: ( , ) ( , )P Px y x y
y y
y R
4D
0y y R
2 2[ 1 ( ) ( ) ( )]P y P y P y
perparation ( notation )
zero mode (remaining field in the low energy )
E
1/ R
0
2/ R
3/ R
,0
( )
( )
0
1
cos( )
sin(
1( , )
2
1( ( ) )
(
, )
)n
n
n
n
n
nyy
R
n
Rx x
xR
yy
Rx
42
1(2) : /M S Z
0y
4D
: ( , ) ( , )P Px y x y
y y
y R
4D
0y y R
2 2[ 1 ( ) ( ) ( )]P y P y P y
preparation ( notation )
E
1/ R
0
2/ R
3/ R
1. models of gauge-Higgs unification
(1). SU(3)×SU(3) model(2). SU(6) model
cos( )ny
R
1 1
1 1
1 1
P T
A
5A
sin( )ny
R
(1). SU(3)c×SU(3)W model
in base of(3) (2) (1)W L YSU SU U
(Kubo,Lim,Yamashita,Hall,Nomura,Smith,Burdman,Nomura,….)
5 5
( , ) ( , )
( , ) ( , )
A x y A x y
A
P P
Px y A x y P
cos( )ny
R
1 1
1 1
1 1
P T
A
sin( )ny
R
in base of(3) (2) (1)W L YSU SU U
(3) (2) (1)W L YSU SU U
Higgs doublet
Higgs doublet
5A
(Kubo,Lim,Yamashita,Hall,Nomura,Smith,Burdman,Nomura,….)
(1). SU(3)c×SU(3)W model
cos( )ny
R
1
1
1
1
1
1
P
A
sin( )ny
R
1
1
1
1
1
1
T
(2). SU(6) model
(Hall,Nomura,Smith, Burdman,Nomura)
in base of (6)SU
5A
1
1
1
1
1
1
P
A
1
1
1
1
1
1
T
(6)
(3) (2) (1) (1)
SU
SU SU U U
Higgs doublet
Higgs doublet
(Hall,Nomura,Smith, Burdman,Nomura)
in base of (6)SU
5A
(2). SU(6) model
2. electro-weak symmetry breaking (1)
-“Higgs doublet” can really take VEV or not?-
(1). SU(3)×SU(3) model(2). SU(6) model(3). Introduction SUSY
NH, Y. Hosotani, Y. Kawamura and T. Yamashita, Phys.Rev.D70:015010, 2004 NH and T. Yamashita, JHEP 0402:059,2004
2 2 4( ) | | | |V m
0 2462
mVGeV
wanted potential is (at least) up to λ2 、 λ4
5( )V A
5A
at tree level
However, since it is originally gauge field,
Let’s estimate quantum corrections !
(0) (0) (0) (0)5, , /A A q l
(method )Sum of infinite# of diagram ( KK ) → obtain
→ search the vacuum of → whether “Higgs”
(0)5( )effV A
(0)5A (0)
5A
( ) ( ) ( ) ( )5, , /n n n nA A q l
(0)5 0, 0A or
’s 1 loop quantum corrections(0)5 ( )A
(0)5( )effV A
effective potential (gauge contribution ) :
6 4
3
32C
R
(0)5
1
2gR
a
A
a
51
3 1[cos(2 ) cos( )]
2gauge
effn
V C na nan
( / 2)C no symmetry breaking!
(1).SU(3)c×SU(3)W model
a
4 55 5
6 75 5
5
4 5 6 75 5 5 5
2
2
2 2
A iA
A iAA
A iA A iA
(0 2)a / 2 R
a=1 is acceptable if life timeof universe is long enough?
is physical d.o.f. ?(0)5A
5exp( )CW P ig dA y [ , ] [ , ] 0a C aU T U PW
(0) (0)5 5
† †(0)5 ( ) ( ) (' ( ) )yA Ay y
gy y
iA
(0)5
1
2a
RA T
g
2( )y
i a TRy e
(0)
5
1
20a T
gRA
†( 2' ) ( )y RT T yT ( )2 2
y yi a T i a T
R Re T e
†( )' ( )P Py PP y
Q: ( cf. is not! It is gauged away (would-be NG) )( )5
nA
: Wilson line phase
(05
05
) ( ) 0 '0A base wit A base wit Th T h
is the order parameter of symmetry breaking
A:
remaine!.
(0 1)a
more accurately, gauge symmetry which satisfies
(Abe, NH, Matsunaga etal)
If the vacuum exist at a=1,
(2) (1) (1) (1)SU U U U
5
2
0
0 0 1 1 0 01
exp exp 2 0 0 0 0 1 02
1 0 0 0 0 1
R
CW ig dy ig RgR
T AT
'
1 1 1 1
1 , 1 1 , 1
1 1 1 1
'W WTP P T
1
1
1
P
mean the remaining gauge symmetry is ( although <A5>≠0 )
(0)5
1
2
a
A
agR
It is no good!
base also shows(0)5 0A
0a 1a
region is good order parameter. Since “Higgs doublet” picture (STU) is good & 246 GeV ≪ 1/R is consistent.
0 1a V
Anyhow, only the gauge contribution is not enough for the suitable vacuum.!
4D 4D
0y y R
( ) ( ) ( ), ,a f sN N N
5 5
( , ) ( , )
( , ) ( , )
( , ) ( , )
( , ) ( , )
(
( , ) ( ,
)
)
( )
( )
L L
R R
P P
P P
A x y A x y
A x y A x y
x y x y
x y x y
P
s x y s x y
P
fermion (adj. & fund.) scalar (fund.)
☆ let us introduce extra bulk fields.
term is added.
effective potential: (0)5( ) gauge
eff effV A V
a
a
( ) ( ) ( ) ( ) ( ) ( )2, 8, 4, 2, 0a f s s a fN N N N N N
effective potential:
a
a
(ex)
(0)5( ) gauge m
eff eff effV A V V
( ) ( ) ( ) ( ) ( ) ( )2, 8, 4, 2, 0a f s s a fN N N N N N
effective potential:
a
a
(ex)
(0)5( ) gauge m
eff eff effV A V V
a
effective potential:
a
(0)5( ) gauge m
eff eff effV A V V ( ) ( ) ( ) ( ) ( ) ( )2, 8, 4, 2, 0a f s s a fN N N N N N (ex)
effective potential:
a
(0)5( ) gauge m
eff eff effV A V V ( ) ( ) ( ) ( ) ( ) ( )2, 8, 4, 2, 0a f s s a fN N N N N N (ex)
1(1)O TeV
R
a
OK !
effects of extra bulk field
(0)5
4
2
/ 2 246
R A
a g R GeV
(2) (1) (1)emSU U U 2
2 24 0.0582
2 2 244
( ) |
0.031( ) (130 )
effa
Vm g R
a
gg GeV
R
4( / 2 )g R g
1
1
1
1
1
1
P
1
1
1
1
1
1
T
(2). SU(6) model
51
3 1[cos(2 ) 2cos( ) 6cos( ( 1))]
2gauge
effn
V C na na n an
2 2(3) (2) (1) (4) (1)SU SU U SU U
not good! → introduction extra bulk field
0a 1a
E
1/ 2R
1/ R
0
3/ 2R
effective potential (gauge contribution ) :
V
,0
( )
0
( )
0
( )
1
( )
1
1( , ) ( ) ( )
2
1( , ) ( ) ( )
1( , ) ( ) ( )
1(
1/
, ) ( ) ( )
cos
cos
sin
2
2
s
1/
in
n
n
n
n
n
n
n
n
n
nyx y x
RR
nx y x y
RR
nx y x y
RR
nx y x y
RR
2
0
exp2
1
1
11exp 2
12
1
1
R
C
aW ig dy
gR
ig RgR
T T
T
( ) ( ) 2, 0a fN N other Ns
a
effective potential:(0)5( ) gauge m
eff eff effV A V V
(ex)
( ) ( ) 2, 0a fN N other Ns
a
effective potential:(0)5( ) gauge m
eff eff effV A V V
(ex)
1(1)O TeV
R
22 2 2 2
4 0.072 42( ) | (130 )eff
a
Vm g R g GeV
a
(3). Introduction of SUSY
A
5( )iA
L c
RL
cR
h
5D N=1 SUSY
odd dim.=vector-like
⇔ 4D N=2 SUSY
V
L
R
.5
5
4
2
4 [ ( )
{ ( ( ) ) . .}]
hyp V VR LD R
L
L
R y
S d xd
cd
y d
hg
e e
Yukawa interaction
( g ~ ytop ~ 0.7 when 1/R ~ GUT)
motivation of introducing SUSY : ☆ write all couplings by gauge coupling ☆ dark matter☆ forbidden dangerous higher order operators (Yukawa among extra bulk fields)
SUSY: introducing particles which have the same masses but different spin as 1/2 (ex.) gauge (1) ⇔ gaugino (1/2), Higgs (0) ⇔ higgsino (1/2), quark (1/2) ⇔ squark (0), ・・・
if SUSY is not broken, potential is flat → Scherk-Schwarz SUSY breaking
4 5 4 5 6 7 6 75 5 5 5
4 5 4 5 6 7 6 75 5 5 5
/ 2 (1/ 2)( ,( ) ( ))
/ 2 (1/ 2)( ,( ) ( ))
u
d
H A i A A i A
H A i A
R
A AR i
4 55 5
6 75 5
5
4 5 6 75 5 5 5
2
2
2 2
A iA
A iAA
A iA A iA
4 5
6 7
4 5 6 7
2
2
2 2
i
i
i i
☆ Higgs doublets: SUSY requires 2 HD (anomaly cancellation, holomorphy)
2 2 25 5 5[ , ] ( [ , ])treeL g tr A ig A
4( )2
gg
R
V
uH
dH
at tree level
A
5( )iA
L c
RL
cR
h
twist of SU(2)R as exp(2πiβσ2)
2 2( ) | |R
2R
1 loop effective potential → EWSB is not realized only by gauge contributionalso in SUSY case → introduction of extra bulk fields (hyper-multiplet) can do (ex.)
(SS SUSY breaking parameter β=0.1) Nf
(±) (fund.) & Na(±) (adjo.)
4D 4D
0y y R
gauge
quarks/leptons
5exp" )" (Higg P A ys d
( ( 2 ) )ye e
( ) ( ) ( ) ( ) 24
( ) ( ) ( ) ( ) 24
(3) (3) : 2, 4, 0 ( 130 )
(6) : 2, 0, 10 ( 130 )
a a f f
a a f f
SU SU N N N N m g GeV
SU N N N N m g GeV
25 5 5[ ] . .cD DL h c
extra matters
We have seen (by introducing extra bulk field) A5 can play a role of
Higgs doublet, SU(2)×U(1)→U(1)emSo how about inducing Yukawa int. (g=y) ? (this is 2nd motivation)]
For this perpose, as suggests
quark/lepton must be in the bulk.
( ex. ) A5 can’t couple with 4 D brane field
If we set then it is possible (but in this case Higgs is non-local field.)
3. electro-weak symmetry breaking ( 2 )
-Can “Higgs” take VEV when quark/lepton are in bulk?-
show here example of SUSY SU(3)×SU(3) model
NH and T. Yamashita, JHEP 0404 (2004) 016
cos( )ny
R
A
5( )iA
sin( )ny
R
L c
R
L
cR
fund. rep. bulk field
3 → down-Yukawa 6 → up-Yukawa 10 → charged lepton-Yukawa 8 → ν-Yukawa
(Burdman-Nomura)
gauge sector
SU(3)c×SU(3)W model
25 5 5[ ] . .cD DL h c
Yukawa
h
quark/lepton’s contribution to the effective potential :
effective potential of gauge sector & quark/lepton :
(Ng: generation#)
2(2) (1) (1)L YSU U U 0a 1a
V
51
(0) (1)
14( ) (1 cos(2 (2 1) ))11 2
(0
2 1)
eff eff
ng
V V
C nn
N
not good! → extra bulk field in bulk
effective potential:
( ) ( ) ( ) ( )0, 45, 40a f a fN N N N 0.1 3gN
(0) /5( ) gauge q l m
eff eff eff effV A V V V
(ex)
effective potential:
( ) ( ) ( ) ( )0, 45, 40a f a fN N N N 0.1 3gN
(0) /5( ) gauge q l m
eff eff eff effV A V V V
(ex)
( ) ( ) ( ) ( )0, 42a f a fN N N N SU(6) model の例
4. Higgs phenomenology
(1). soft scalar mass(2). 3-point self coupling(3). Mass spectrum
NH, K.Takenaga and T.Yamashita, Phys.Rev.D71:025006,2005NH, K.Takenaga and T.Yamashita, hep-ph/0411250
2( ) 2
5
2( ) 2
5
1 (2 )[ , , , ] 1 1 2 cos(2 ) cos( )
3
1 (2 )[ , , , ] 1 1 2 cos(2 ) cos( ( 1))
3
zn
zn
znI a z n zn e n na
n
znI a z n zn e n n a
n
SU(3) × SU(3) model
We add soft scalar mass, m (z=mR) in addition to SS term as SUSY breaking.
( ) ( ) ( ) ( ) ( )
1
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
2 { ( [2 , , , ] 2 [ , , , ])
( [2 , , , ] 2 [ , , , ])
[ , , , ] [ , , , ])}
mattereff adj adj adj
n
adj adj adj
fnd fnd fnd fnd
V C N I a z n I a z n
N I a z n I a z n
N I a z n N I a z n
( )GeVm φ can be heavy even the same matter content
(1). soft scalar mass
L c
RL
cR
( 例 )
SU(3) × SU(3) model
m (z=mR)
SU(6) model
O(1) # of extra bulk field can realize EWSB !
m (z=mR)
(ex)
tend to be small comparing to SM ( ~ 10%)
(2). 3-point self coupling
( motivation ): measurement of λis important to know the mechanism of EWSB, and deviation from the Standard Model can be significant.
e
e Z
e
e
WW
ILC 実験
☆ higher order operators
4
4
cos ( )n nV a a g RH
g R
a few TeV → suppression scale → suppressed enough
0
2 346 3
3
32a a
g V
R a
☆ effective 3-point coupling
deviation from SM
23,SM h
SMSM
m
v
tan 1
4 5 4 5 6 7 6 75 5 5 5
4 5 4 5 6 7 6 75 5 5 5
1( ( ), ( ))
21
( ( ), ( ))2
u
d
H A i A A i A
H A i A A i A
D-flat
h
NH, K.Takenaga,T.Yamashita, Phys.Rev.D71:025006,2005
0
45
4
: ( )
: ( )
A massless h
massless A
5 05
5
:
: ( )Z
A
M H
6,75
6,7
:
: ( )W
A
M H
(3). Mass spectrum
V
uH
dH
at tree levelat S1 case
,(100) , (100)Z Wh A O GeV H H M O GeV probably (radiative induced mass ~ O(100)GeV)
☆ gauginos mass~higgsinos mass ~ β/R
☆
(preliminary )
origin of Higgs : extraD component of extraD gauge field
5DH A → “doublet Higgs” 5 5 5cD DA → Yukawa int.
Higgs mass is finite (1/R) (← extraD gauge invariance)
1 loop effective potential of “Higgs doublets” (A5) in SU(3)×SU(3) model & SU(6) model (quark/lepton blane & bulk) ↓ EW DSB can be possible by extra bulk matters (suitable rep. & #)
,(100) , (100)Z Wh A O GeV H H M O GeV
☆ gauginos mass ~ higgsinos mass ~ β/R☆ 3-point self coupling: -10 % deviation from SM☆ extra bulk fields ~ O (100) GeV★ (mass spectrum (now calculating)) tanβ ~ 1
5 . summary & discussion
problems(1): SU(6) model ☆ how to break extra U(1) ? ☆ how to forbid rapid proton-decay when 1/R ~ TeV? ← U(1)B
(2): SU(3)×SU(3) model ☆Winberg angle
5 2 25 5 5 4 4
1 12 ( ) ( 3 ) |
4 2 2 2a a a a b c
bc
Bdy F F dy A igf A A ig W i g H
5D gauge kinetic term→4D Higgs kinetic term
(g4 ~ O(1), (M*R)1/2 1 (≫ M* 1≫ /R))
23 sin 3 / 2Y Wg g
● wall-localized kinetic terms,2 2
0(0) , ( )F R F
g42 > λ-1, (we take g4 ~ 1), and expect 2
4 4
( , ) ( , ).3
Yg gW B W B
g g
:[ (6) : sin 3/8]Wcf SU
● introduction of additional U(1)’, extending U(3)×U(3), etc.
(SU(3) symmetry 無い )
12/S Z ☆ gauge-Higgs unification in E6, E7 GUTs on
( good point ): don’t need many representation to obtain quark/lepton Yukawa ints.
E6: bulk matters adjoint & fund.⇒ E7: bulk matters adjoint ⇒
quark/lepton favor structure ← effects of brane-localized extra fields
(NH and Y. Shimizu, Phys.Rev.D67:095001,2003,
Erratum-ibid.D69:059902,2004)
related work ( 1 )
4D 4D
0y y Rgauge
extra matters
quark/lepton
cf. 3,6,10,8 rep. are needed in SU(3)×SU(3) model
2 2, , , 0u dh hM m m m m B
gaugino mass ⇔ higgsino mass
at tree level at 1/R
Analyze radiative breaking (EWSB) is possible or notincluding SGGRA effects.(Choi, N.H., Jeong, Okumura, Shimizu, Yamaguchi, JHEP 0402:037,2004)
releted works (2)
☆ RGE analyses ( analyses of MSSM with boundary condidtion )
mass2
logE 2
uHm
2
dHm