Top Yukawa Deviation in Extra Dimension ( ) ( ) ( ) - - PowerPoint PPT Presentation

Top Yukawa Deviation in Extra Dimension

• ✁

( ) ( )

( ) arXiv:0904.3813 [hep-ph] Contents

• 1. Introduction
• 2. Bulk Higgs with Brane Potential

3.

4.

• 1. Introduction

Large Hadron Collider (LHC)

• ✁
• ✁

!

⇓

[ (SM)]

[

(BSM)]

[

(BSM)]

• 1. Introduction

Large Hadron Collider (LHC)

• ✁
• ✁

!

⇓

[ (SM)]

[

(BSM)]

[

(BSM)]

• ✂

• Brane localized

• ✁

• 1. Introduction

Large Hadron Collider (LHC)

• ✁
• ✁

!

⇓

[ (SM)]

[

(BSM)]

[

(BSM)]

• ✂

• Brane localized

• ✁

• Brane localized
• ✁

• ✆

• ✟

⇒T op Y ukawa Deviation

• LHC
• ☛

• ☛

• ✠

• ✟

• ✆

• ☛

• LHC
• ☛

• ☛

• ✠

• ✟

• ✆

• ☛

T op Y ukawa Deviation

• LHC
• ☛

• ☛

• ✠

• ✟

• ✆

• ☛

T op Y ukawa Deviation −L(SM)

t

⊃ mt¯ tt + ytH¯ tt + h.c. = ytv¯ tt + ytH¯ tt + h.c. yt = mt v = [

• ✟

• ✝

(yH¯

tt)]

• LHC
• ☛

• ☛

• ✠

• ✟

• ✆

• ☛

T op Y ukawa Deviation −L(SM)

t

⊃ mt¯ tt + ytH¯ tt + h.c. = ytv¯ tt + ytH¯ tt + h.c. yt = mt v = [

• ✟

• ✝

(yH¯

tt)]

[Non-standard

] yt=mt

v = [

• ✟

• ✝

(yH¯

tt)]

“T op Y ukawa Deviation”

Top Yukawa deviation

Top Yukawa deviation

• ✁

MSSM

• multi-Higgs doublet
• ✆

. MSSM: Hu and Hd −L(MSSM)

t

⊃ ytH0

u¯

tRtL + h.c. ⇒ yt = √ 2mt/vu H0

u

H0

d

• =

1 √ 2

• vu

vd

• +
• cos α sin α

− sin α cos α h0 H0

• + iRβ0
• G0

A0

• −L(MSSM)

t

⊃ ytcos α h0 √ 2 ¯ tt + h.c. = √ 2mt vu cos α h0 √ 2 ¯ tt + h.c. ⇒ yh0¯

tt = (

√ 2mt/vu) cos α = yt

Top Yukawa deviation

Top Yukawa deviation

• ✁

MSSM

• multi-Higgs doublet
• ✆

. MSSM: Hu and Hd −L(MSSM)

t

⊃ ytH0

u¯

tRtL + h.c. ⇒ yt = √ 2mt/vu H0

u

H0

d

• =

1 √ 2

• vu

vd

• +
• cos α sin α

− sin α cos α h0 H0

• + iRβ0
• G0

A0

• −L(MSSM)

t

⊃ ytcos α h0 √ 2 ¯ tt + h.c. = √ 2mt vu cos α h0 √ 2 ¯ tt + h.c. ⇒ yh0¯

tt = (

√ 2mt/vu) cos α = yt [One-Higgs-doublet ]

• SO(5) × U(1)

• ✆

(

• ✝

)

Hosotani and Kobayashi, PLB 674 (2009) 192

• Brane-localized

• ✁

( )

Haba, Oda and RT, arXiv:0904.3813 [hep-ph]

• 2. Bulk Higgs with Brane Potential

Haba, Oda and RT, arXiv:0904.3813 [hep-ph]

S =

• d4x

L dy[−|∂MΦ|2 − V(Φ) −δ(y − L)VL(Φ) − δ(y)V0(Φ)] L : Compactification length V0(Φ) V(Φ) VL(Φ) y = 0 Φ(x, y) y = L 4D y → z ≡ y − L 2

• 2. Bulk Higgs with Brane Potential

Haba, Oda and RT, arXiv:0904.3813 [hep-ph]

S =

• d4x

+L/2

−L/2

dz[−|∂MΦ|2 − V(Φ) −δ(z − L/2)V+(Φ) − δ(z + L/2)V−(Φ)] L : Compactification length V−(Φ) V(Φ) V+(Φ) z = −L

2

Φ(x, z) z = +L

2

4D y → z ≡ y − L 2

: V(Φ) = 0, Real Φ S =

• d4x

+L/2

−L/2

dz[−(∂MΦ)2 − δ(z − L/2)V+(Φ) −δ(z + L/2)V−(Φ)] V−(Φ) = λ 4(Φ2 − v2)2 V−(Φ) = V+(Φ) V− V+ V+(Φ) = λ 4(Φ2 − v2)2

: V(Φ) = 0, Real Φ S =

• d4x

+L/2

−L/2

dz[−(∂MΦ)2 − δ(z − L/2)V+(Φ) −δ(z + L/2)V−(Φ)] V−(Φ) = λ 4(Φ2 − v2)2 V−(Φ) = V+(Φ) V− V+ V+(Φ) = λ 4(Φ2 − v2)2 Φ(x, z) = Φc(x, z) + φ(x, z) ∂2

zΦc(z) = 0 ±∂zΦc+ ∂V+ ∂Φ

• Φ=Φc = 0

(± for z = ±L/2)

Kaluza-Klein ∂2

zfn = −k2 nfn, φ(x, z) =

• n=0

fn(z)φn(x)

• ±∂z+ ∂2V+

∂Φ2

• Φ=Φc
• fn(z)
• z=±L/2

= 0

• ✁

∂2

zΦc(z) = 0

± ∂zΦc + ∂V+ ∂Φ

• Φ=Φc = 0

(± for z = ±L/2) ⇒ Φc(z) = A + Bz ⇒ ±B + λ

• A ± BL

2 2 − v2 A ± BL 2

• = 0

⇒ Φc(z) = v :

• ✁

∂2

zΦc(z) = 0

± ∂zΦc + ∂V+ ∂Φ

• Φ=Φc = 0

(± for z = ±L/2) ⇒ Φc(z) = A + Bz ⇒ ±B + λ

• A ± BL

2 2 − v2 A ± BL 2

• = 0

⇒ Φc(z) = v :

• ✂
• ✁

• ☞
• ✁

• Φc(z) = v.
• ✂
• ✁

and/or V+(Φ) = V−(Φ)

• ✁

• ✝

• ✟

• ✁

(

• Z

W

) ⇒V(Φ) ∼ 0 and V+(Φ) = V−(Φ)

Kaluza-Klein ∂2

zfn(z) = −k2 nfn(z)

⇒ fn(z) = αn cos(knz) + βn sin(knz)

• ±∂z + ∂2V+

∂Φ2

• Φ=Φc
• fn(z)
• z=±L/2

= 0 ⇒ tan knL 2

• =
• 4λv2

kn

: fn(z) = αn cos(knz) [KK even] − kn

4λv2 : fn(z) = βn sin(knz) [KK odd]

Kaluza-Klein ∂2

zfn(z) = −k2 nfn(z)

⇒ fn(z) = αn cos(knz) + βn sin(knz)

• ±∂z + ∂2V+

∂Φ2

• Φ=Φc
• fn(z)
• z=±L/2

= 0 ⇒ tan knL 2

• =
• 4λv2

kn

: fn(z) = αn cos(knz) [KK even] − kn

4λv2 : fn(z) = βn sin(knz) [KK odd]

KK

• ✁

z = ±L/2

• ✆
• ✄
• ✁

V+ = V−

• ✟

• ±z

accidental

• ✁

fn(z) = fn(−z) [even] fn(z) = −fn(−z) [odd].

fn(z) = αn cos(knz), βn sin(knz) tan

• knL

2

• = 4λv2

kn , − kn 4λv2

Even Even Odd E0 E2 E4 E0 E2 E4 O1 O3 O5 O1 O3 O5 3 Π

5 Π 2

2 Π

3 Π 2

Π

• Π

2 Π 2

Π

3 Π 2

2 Π 3 Π

5 Π 2

knL2

KK

• ✁

/

• ✝

(λ → 0) + / n = 0

L2 L2

− / n = 1

L2 L2

+ / n = 2

L2 L2

. . . ⇒ KK

• ✁

/

• ✝

(λ → ∞) + / n = 0

L2 L2

− / n = 1

L2 L2

+ / n = 2

L2 L2

. . .

fn(z) =                                                  

• 1

L

0 mode

• 2

L cos

nπ

L z

• n : even
• 2

L sin

nπ

L z

• n : odd

[λ → 0]       

• 2

L

• 1+sin((n+∆n)π)

(n+∆n)π

cos

(n+∆n)π

L

z

• n : even
• 2

L

• 1−sin((n+∆n)π)

(n+∆n)π

sin

(n+∆n)π

L

z

• n : odd

[λ

• ]

    

• 2

L cos

(n+1)π

L

z

• n : even
• 2

L sin

(n+1)π

L

z

• n : odd

[ˆ λ → ∞] ∆n

• kn

nπ/L

• ✁

• ☎

(0 < ∆n < 1)

• ✁

Haba, Oda and RT, arXiv:0904.3813 [hep-ph]

S =

• d4x

+L/2

−L/2

dz[−|∂MΦ|2 − V(Φ) −δ(z − L/2)V+(Φ) − δ(z + L/2)V−(Φ)]

• V(Φ) ∼ 0
• V+(Φ) = V−(Φ)
• ✁

• Φc(z) = v
• V+(Φ) = V−(Φ)

• ±z

accidental

• ✁

(KK parity)

1.0 0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 2zL

⇐f0(z, λ = 0)

Φc = v ⇐

• λ

• ✝

• ✆
• ✁

⇐Brane localized

• f0(z)

3.

• ✝

• S =
• d4x

+L/2

−L/2

dz[−|∂MΦ|2 −δ(z − L/2)V+(Φ) − δ(z + L/2)V+(Φ)]

• Φ(x, z) ≡

     

∞

• n=0

fϕ+

n (z)ϕ+ n (x)

v +

1 √ 2 ∞

• n=0

[fn(z)φq

n(x) + ifχ n(z)χn(x)]

     

• Bulk fields

• Brane localized fields (t(x),,,) or Bulk fields

Bulk fields

• X(x, z) = fX

n (z)X(x), ∂zfX n (z)|z=±L/2 = 0,

fX

0 (z) =

, (X = A, W ±, Z,

)

KK

(

• v(z))
• Skin =
• d4x

+L/2

−L/2

dx|DMΦ|2 ⇒

• ∂2

z − v2(z)

2 (g2

5 + g′ 5 2)

• fZ

n (z) = −µ2 Z,nfZ n (z),

⇒

• ∂2

z − v2(z)

2 g2

5

• fW

n (z) = −µ2 W,nfW n (z),

∓ ∂zfZ,W

n

(z) = 0 ⇒ fZ,W (z) flat

• ✝

• ✝

M2

Z ≡

+L/2

−L/2

dyfZ

0 (y)

• v2(y)

4 (g2

4 + g′ 4 2)L−∂2 y

• fZ

0 (y),

M2

W ≡

+L/2

−L/2

dyfW

0 (y)

• v2(y)

4 g2

4L−∂2 y

• fW

0 (y)

KK

(

• v)
• Skin =
• d4x

+L/2

−L/2

dx|DMΦ|2 ⇒

• ∂2

z − v2(z)

2 (g2

5 + g′ 5 2)

• fZ

n (z) = −µ2 Z,nfZ n (z),

⇒

• ∂2

z − v2(z)

2 g2

5

• fW

n (z) = −µ2 W,nfW n (z),

∓ ∂zfZ,W

n

(z) = 0 ⇒ fZ,W (z) flat

• ✝

• M2

Z ≡

+L/2

−L/2

dyfZ

0 (y)

• v2(y)

4 (g2

4 + g′ 4 2)L−∂2 y

• fZ

0 (y),

M2

W ≡

+L/2

−L/2

dyfW

0 (y)

• v2(y)

4 g2

4L−∂2 y

• fW

0 (y)

Top Yukawa deviation (Brane localized

)

• ✝

• −Lt = y′

t,5

+L/2

−L/2

dz

• δ
• z − L

2

• + δ
• z + L

2

• ×
• v + f0(z)φq

0(x)

√ 2

• t(x)t(x) + h.c.

= yt,5

• v + f0(L/2)φq

0(x)

√ 2

• t(x)¯

t(x)⇒ f0(L/2) → 0

Top Yukawa deviation (Brane localized

)

• ✝

• −Lt = y′

t,5

+L/2

−L/2

dz

• δ
• z − L

2

• + δ
• z + L

2

• ×
• v + f0(z)φq

0(x)

√ 2

• t(x)t(x) + h.c.

= yt,5

• v + f0(L/2)φq

0(x)

√ 2

• t(x)¯

t(x)⇒ f0(L/2) → 0

1.0 0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 2zL

⇓ f0(L/2)

boundary coupling ⇓ λ

• ✆

⇓

• ne-Higgs doublet

• ⇓ sizable

top Yukawa deviation

⇓

• ☛

f0(z)

Top Yukawa deviation (Brane localized

)

• −Lt = yt,5
• v + f0(L/2)φq

0(x)

√ 2

• t(x)¯

t(x) mt = yt,5v, v ≡ 174GeV/ √ L, yt = mt/(v √ L), yH¯

tt = yt,5f0(L/2),

⇒ r ≡ yH¯

tt/yt = f0(L/2)

√ L

rWWH r

Λ ^ 1000 104 105 106 0.10 1.00 0.50 0.20 0.30 0.15 0.70

mKK ≡ π/L = 4TeV ˆ λ ≡ λΛ2 Λ = 10TeV ⇓ r = 1: Deviation

(ˆ λ = 0) r = 0.5: 50%

Deviation (ˆ λ ∼ O(105))

LHC

Gluon fusion W W fusion

• ✟

• ✝

• ☛
• λ

• ✠

• ✟

• Gluon fusion

|yH¯

tt|

LHC

W W H

• −LW W H =

emW 2 sin θW 1 2L +L/2

−L/2

dzf0(z)f W + f W − φq(x)W +(x)W −(x)

SM

W W H

• rW W H ≡

1 √ L +L/2

−L/2

dzf0(z)

1.0 0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 2zL

rWWH r

Λ ^ 1000 104 105 106 0.10 1.00 0.50 0.20 0.30 0.15 0.70

f0(z) W W H

• ✝

• ☛

• ✠
• r ≤ rW W H

LHC

Gluon fusion W W fusion SM

• σg(∼ 10σw)

> σW Our setup

• ✠
• ˆ

λ ≪ 1 σ5,g = r2σg > σ5,g = r2

W W HσW

• ˆ

λ ∼ O(106) σ5,g = 0.01σg < σ5,g = 0.85σW

Top Yukawa deviation

• −Lt = yt,5

L +L/2

−L/2

dz

• v + f0(z)ft

0ft

φq(x) √ 2

• ¯

t(x)t(x) r = yt¯

tH

yt = 1 √ L +L/2

−L/2

dyf0(z)= rW W H

Deviation

• (0.92 < rW W H < 1)

LHC

• −LW W H =

emW 2 sin θW 1 2L +L/2

−L/2

dzf0(z)f W + f W − φq(x)W +(x)W −(x),

• rW W H ≡

1 √ L +L/2

−L/2

dzf0(z),

• Brane localized

⇒σg

σW r2

W W H

• verall

S =

• d4x

+L/2

−L/2

dz[−|∂MΦ|2 −δ(z − L/2)V+(Φ) − δ(z + L/2)V+(Φ)] Φ0(x, z) = v + 1 √ 2

∞

• n=0

[fn(z)φq

n(x) + ifχ n(z)χn(x)]

m2

H = −

+L/2

−L/2

dzf0(z)∂2

zf0(z) = k2

0 mode 1st mode 2nd mode Λ ^ 500000

• 1. 106

1.5106

• 2. 106

2.5106

• 3. 106

200 400 600 800 1000 1200 1400 mHGeV

[λ → 0] m2

H → 0

[

• λ]

m2

H ≃ 4λv2

EWm2

KK/π2

[λ → ∞] m2

H → m2 KK

Even Even Odd E0 E2 E4 E0 E2 E4 O1 O3 O5 O1 O3 O5 3 Π

5 Π 2

2 Π

3 Π 2

Π

• Π

2 Π 2

Π

3 Π 2

2 Π 3 Π

5 Π 2

knL2

[λ → 0 (kn → nπ/L)] m(n)

H

→ nmKK [λ → ∞ (kn → (n + 1)π/L)] m(n)

H

→ (n + 1)mKK

m(n)

X

= m(0)

X + nmKK

NG

3

• 4

0 mode ΛHΧΧ vEW ΛH vEW ΛHHΧΧ ΛHH ΛHHH vEW ΛHHHH Λ ^ 1106 2106 3106 100 500 100 500 mH0GeV selfcouplingin4D ΛΧΧΧΧ ΛΧΧ Λ 2nd mode 1st mode 0 mode Λ ^ 1106 2106 3106 500 1000 1500 2000 1000 2000 mHnGeV selfcouplingin4D

• Boundary coupling λ

• ✝
• ✆

boundary

• ✁

• ✂

• ✝

• λHHHH
• λHHH
• λHHχχ
• λHHϕ+ϕ−

(

boundary

)

• λHχχ

λHϕ+ϕ−

• NG

boundary coupling

• mH > 140GeV
• W W

dominant

• mH < 140GeV
• H → b¯

b dominant

Γ(H → WLWL) ∼ λHϕ+ϕ−vEWGF mH 2 √ 2 ∼ GF m2

KKmH

2 √ 2π

0 mode mKK 2TeV H WLWL mKK 2TeV 0 mode mKK 500GeV H WLWL mKK 500GeV Λ ^ 1106 2106 100 500 1000 GeV

• mKK

TeV

• ΓHWLWL > mH

• ✠

• ✠

(

)

4.

S =

• d4x

+L/2

−L/2

dz[−|∂MΦ|2 − V(Φ) −δ(z − L/2)V+(Φ) − δ(z + L/2)V−(Φ)] L : Compactification length V− V V+ z = −L/2 Φ(x, z) z = +L/2 4D

• Brane localized
• ✁

• ✆

• V(Φ) ∼ 0
• V+(Φ) = V−(Φ)
• ✁

• Φc(z) = v

4.

S =

• d4x

+L/2

−L/2

dz[−|∂MΦ|2 −δ(z − L/2)V+(Φ) − δ(z + L/2)V+(Φ)] Brane localized fermion Bulk fermion Top Yukawa deviation sizable (r → 0.1) tiny (> 0.92)

Gluon fusion 1% of SM 85% of SM W W fusion 85% of SM (Dominant) 85% of SM

• ✆

• Higher KK

⇒ Haba, Oda and RT, arXiv:0904.3813 [hep-ph] ⇒ LHC

ILC

• ☛