SO(5)xU(1) Gauge-Higgs Unification

(1)

BSM and the Origin of Higgs Kobe Univ. 14 March 2012

Yutaka Hosotani

SO(5)xU(1)

Gauge-Higgs Unification

(2)

125 GeV,

but with non-SM couplings,

gauge-Higgs unification

2 not seen at LHC

as it is stable,

or

If the Englert-Brout-Higgs boson is

(3)

∪

4D Higgs fields

H

extra-dim. component A

_y

3

4-dim. components A

_µ

4D gauge fields

γ , W , Z

∪

EW symmetry breaking

Hosotani mechanism Aharonov-Bohm phase

Gauge-Higgs unification

A M in 5 dim.

(4)

e

ⁱ^θ^ˆ^H^(x)

∼ P exp

� ig

�

C

dyA

_y

Higgs boson as an AB phase in extra dim �

θ ˆ

_H

(x) = θ

_H

+ H (x) f

_H

θ

_H

= � Higgs �

f

_H ^■

masses for

quarks/leptons/W,Z

�

■

symmetry breaking

4

C y

θ H ∼ θ H + 2π differs from SM.

(5)

in Randall-Sundrum warped space SO (5) × U (1)

ds

²

= e

⁻^2k^|^y^|

dx

_µ

dx

^µ

+ dy

²

0 ≤ | y | ≤ L = πR

Planck brane TeV brane

AdS Λ = − 6 k

²

SO (5) × U (1)

g

_A

g

_B

brane scalar

brane fermions quarks, leptons

YH, Oda, Ohnuma, Sakamura 2008 YH, Noda, Uekusa 2009

5

Agashe, Contino, Pomarol, 2005

� A

_µ

A

_y

�

(x, − y) = P

₀

� A

_µ

− A

_y

�

(x, y)P

₀^†

� A

_µ

A

_y

�

(x, πR − y ) = P

₁

� A

_µ

− A

_y

�

(x, π R + y)P

₁^†

Orbifold BC

y = 0 y = πR

(6)

P₀ = P₁ =







−1

+1







4D gauge bosons and Higgs

φ₁ φ₂ φ₃ φ₄ A_y ∼













Higgs

4D Higgs doublet

A_µ ∼



 





 



W Z γ

θ

_H

� = 0 → U (1)

_EM

6

� = SU (2)

_L

× U (1)

_Y

SO(5) → SO (4) � SU (2)

^�_L

× SU (2)

^�_R

brane scalar SO(4) × U (1) → SU (2)

^�_L

× U (1)

^�

(7)

RS:

fermions

k , z

_L

= e

^kL

g

_A

, g

_B

One free parameter z L

parameters

quark/lepton masses

α

_w

, sin

²

θ

_W

m

_Z

inputs

7

(8)

Warped space

Planck scale Weak scale

m W

8

TeV scale m KK

output ☺

m

_KK

= πke

⁻^kL

∼ π √

kL m

_W

kL = 30 ∼ 40 for z_L = 10¹³ ∼ 10¹⁷

EW Symmetry breaking

☺

output

input

(9)

Eﬀective interactions

L eﬀ ∼ − � 1 2 gf

^H

sin ˆ θ

^H

�

²

� W

^µ^†

W

^µ

+ 2 cos 1

₂

θ

W

Z

_µ

Z

^µ

�

− y

_f

f

_H

sin ˆ θ

_H

ψ

_f

ψ

_f

θ ˆ

_H

= θ

_H

+ H

f

_H

f

_H

= 2

√ kL

m

_KK

π g

9

cos θ

_H

WWH ×

Yukawa ZZH = SM

f

_H

sin ˆ θ

_H

→ v + H

in SM

θ

_H

∼ θ

_H

+ 2π

(10)

YH, Oda, Ohnuma, Sakamura 2008 YH, Noda, Uekusa 2009

Planck brane TeV brane

� T ˆ

_R

B ˆ

_R

�

� U ˆ

_R

D ˆ

_R

�

� X ˆ

_R

Y ˆ

_R

�

(

¹₂

, 0)

SO(5) × U (1)

Leptons



 



ν

_τ

τ L

_1X

L

_1Y

τ

^�



 



−1



 



L

_2X

L

_2Y

L

_3X

L

_3Y

ν

_τ^�



 



0

Matter content

�Lˆ_1XR Lˆ_{1Y R}

�

Quarks 

 

 U D X Y b

^�



 



−1 3



 

 T B

t b t

^�



 



2 3

(

¹₂

,

¹₂

) ⊕ (0, 0)

vector rep

L

R

L L L

R

L L L L

R

L L L L

R

L L L L

Φ ˆ (0,

¹₂

)

Brane scalar

� Φ ˆ � � = 0

Ψ(x, −y) = P₀γ⁵Ψ(x, y)

Ψ(x,πR − y) = P₁γ⁵Ψ(x,πR + y)

10

Anomaly

cancelation

(11)

11

m

_H

= 135 GeV (z

_L

= 10

¹⁵

)

θ

_H

= π

2 SU (2) � L × U (1) � → U (1) EM

EW Symmetry breaking

Hosotani mechanism

z

_L

= 10

¹⁵

0.5 1.0 1.5 2.0

0.5 U

-

0.5 0

-

1.

-

1.5

-

2.0

-

2.5

θ /π

H

gauge

total

fermions (top)

V

_eﬀ

(θ

_H

)/m

⁴_KK

(12)

H : −

all other SM particles : +

Stable Higgs

12

YH, Ko, Tanaka, 2009 YH, Tanaka, Uekusa, 2010

π

2 + H

f

_H

− π

2 − H f

_H

π

2 − H f

_H

H parity at θ H = 1 2 π

mirror sym period π

(13)

Agashe, Contino, Da Rold, Pomarol 2006

T parameter Zb ¯ b

H parity

13

{ T

^α

} = { T

^a^L

, T

^a^R

, T

^a^ˆ

, T

^ˆ⁴

}

SO(5)/SO(4) SO(5) : SO(4) � SU (2)

^�_L

× SU (2)

^�_R

T

^ˆ⁴

→ − T

^ˆ⁴

P H : SU (2)

^�^L

↔ SU (2)

^�^R

(14)

SO (5) × U (1) X

Where is SU(2) x U(1) in SO(5) x U(1) ?

L Y

� = SU (2)

_L

× U (1)

_Y

→ SU (2)

^�_L

× U (1)

^�

Brane scalar

� Φ ˆ � � = 0

→ SO(4) × U (1)

_X

� SU (2)

^�_L

× SU (2)

^�_R

× U (1)

_X

B.C.

→ U (1)

_EM

θ

_H

� = 0

14

(15)

YH, Sakamura 2007 Contino, Marzocca, Pappadopulo, Rattazzi 2011

Hatanaka, YH, Shimotani

SO(5) { T

^L^a

, T

^R^a

, T ˆ

^a

, T ˆ

⁴

}

SU (2)

^�_L

× SU (2)

^�_R

{ I

_L^a

, I

_R^a

, I ˆ

^a

, I ˆ

⁴

}

SU (2)

_L

× SU (2)

_R

� I

_L^a

I

_R^a

�

= 1 ± cos θ

_H

2 T

_L^a

+ 1 ∓ cos θ

_H

2 T

_R^a

∓ sin θ

_H

√ 2 T ˆ

^a

Note: T

_L^a

+ T

_R^a

= I

_L^a

+ I

_R^a

: custodial SU (2)

_V

15

Q

_EM

= I

_L³

+ I

_R³

+ Q

_X

= T

_L³

+ T

_R³

+ Q

_X

I

^α

(θ

_H

) = ΩT

^α

Ω

⁻¹

Ω = e

ⁱ^√^2θ^H^T ^ˆ⁴

W

^±

couples to I

_L¹

± iI

_L²

(16)

YH, Sakamura 2007

Hatanaka, YH, Shimotani

W

^±

I

_L¹

± iI

_L²

Higgs I ˆ

⁴

= ˆ T

⁴

Z c

^W

I

^L³

− s

^W

I

^Y

I

_Y

= s

_φ

I

_R³

+ c

_φ

T

_X

, s

_φ

= t

_W

γ s

_W

I

_L³

+ c

_W

I

_Y

I

^α

(θ

_H

) = ΩT

^α

Ω

⁻¹

Ω = e

ⁱ^√^2θ^H^T^ˆ⁴

SU(2) rotates in SO(5). L

16

(17)

W

_µ^±



 Z

_µ

γ

_µ





Z ˜

_µ

�

SU (2)

_R

SU (2)

_L

U (1)

_X

� W

_µ⁽ⁿ⁾

(x) �

C (z ; λ

⁽ⁿ⁾_W

)I

_L⁺

(θ

_H

) − sin θ

_H

√ 2 [ ˆ S (z ; λ

⁽ⁿ⁾_W

) − C (z ; λ

⁽ⁿ⁾_W

)] ˆ T

⁺

�

To be precise

All KK modes participate.

17

W

_Lµ¹

, W

_Lµ²





W

_Lµ³

B

_µ^X

W

_Rµ³





S, T : need reexamination.

SU(2) rotates in SO(5). L

(18)

Collider signatures

18

No single-Higgs production Higgs pair production

H parity

Cheung, Song, 1004.2783, Alves, 1008.0016 YH, Tanaka, Uekusa, 1103.6076

Higgs = missing energy, momentum hard to conﬁrm at LHC/ILC

Stable Higgs

(19)

sin

²

θ

_W

χ

²

(AF B ) χ

²

(Z decay )

No. data

6 8

SM

0.2312 10.8 13.6

z

_L

: 10

¹⁵

z

_L

: 10

¹⁰

z

_L

: 10

⁵

YH, Tanaka, Uekusa, 2011

Gauge couplings

precision measurements

◊ Z-decay branching fractions

◊ Forward-backward asymmetry in e

⁺

e

⁻

→ Z → � � ¯ , q q ¯

z

_L

≥ 10

¹⁵

0.2309

6.3

0.2303 6.4

0.2284 7.1 16.5 37.7 184.5

19

(20)

Large widths

Strong couplings for right-handed quarks and lepton

KK Z (1) & γ (1)

m Γ z

_L

in GeV

γ (1)

10

¹⁵

1144 1959 10

⁵

678 446 m

Γ z

_L

in GeV

Z (1)

10

¹⁵

1130

422 10

⁵

653 104

20

Not seen at LHC, so far. ☹

(21)

W W Z W W Z

⁽¹⁾

W W Z

⁽²⁾

W W Z

⁽³⁾

W W Z

⁽⁴⁾

W W Z

⁽⁵⁾

0.999 85

− 0.0343

2.07 × 10

⁻⁵

− 1.25 × 10

⁻³

− 1.38 × 10

⁻⁵

− 2.04 × 10

⁻⁴

g

_{W W Z}⁽ⁿ⁾

/g

e

_L

e

_R

u

_R

u

_L

t

_L

t

_R

0.0311

− 0.0400

− 0.2058 2.516

− 1.656

− 1.467

Z (1) couplings

ν

_eL

e

_L

ν

_µL

µ

_L

u

_L

d

_L

t

_L

b

_L

u

_R

d

_R

t

_R

b

_R

1.0053 1.0053 1.0053 0.9816

− 5 × 10

⁻¹²

− 0.0009

couplings

W

21

(22)

z

_L

m

_H

10

⁵

10

¹⁰

10

¹⁵

108 135

72 GeV

Stable Higgs Dark Matter

20 30 40 50 60 70 80 90 100

Higgs mass (GeV) 0

0.1 0.2

7 Hh2

semi-analytic micrOMEGAs WMAP

WMAP

Gauge-Higgs

m H

Ω

_H

h

²

Relic abundance

WMAP data

m

_H

= 70 ∼ 75 GeV

22

YH, Ko, Tanaka, 2009

(23)

Collider signatures z

_L

> 10

¹⁵

m

H

= 135 GeV Dark matter m

_H

= 70 ∼ 75 GeV z

_L

∼ 10

⁵

23

SUSY exact m

^H

= 0

broken 70 ∼ 75 GeV

Hatanaka, YH, 1111.3756

� t

m

_n

�

W, Z, Higgs

� m

_n

�

t ˜

� m ˜

_n

= �

m

²_n

+ Λ

²_stop

� W , ˜ Z, ˜ Higgs ˜

˜

m

_n

= �

m

²_n

+ Λ

²_gh

(24)

24

0 500 1000 1500 2000 2500

0 200 400 600 800 1000

�

_gh

� GeV �

�

stop

� GeV �

m_h�120GeV

m_h�75GeV

m_h�70GeV Phase transition

No EWSB

z_L = 10¹⁵ z_L = 10¹⁷

m

_h

= 120 GeV

m

_h

= 75 GeV

m

_h

= 70 GeV

Λ

_stop

= 250 − 275 GeV Λ

_gh

< 100 GeV

for m

_h

= 70 ∼ 75 GeV

300 - 320 GeV stop

neutralino < 100 GeV

gluino > 1 TeV

(25)

25 125 GeV with non-SM couplings,

or

(extra dimensions).

gauge-Higgs

If the Englert-Brout-Higgs boson is

not seen at LHC (as it is stable),

Summary