Yutaka Hosotani

“素粒子物理学の進展 2017”京大基研, July 31 - August 4, 2017

YH, N. Yamatsu, arXiv:1706.03503

Gauge-Higgs seesaw mechanismin six-dimensional grand unification

Gauge-Higgs unification

� , W , Z

�AyAµ

AM

�Aharonov-Bohm phase

✓H

Higgs

2

Finite Higgs massgenerated.

Gauge-hierarchy problemis solved.

Hosotani mechanism

DynamicalEW sym breaking

UV brane IR brane

AdS � = �6 k2

SO(5) � U(1)

ds

2 = e

�2k|y|dx

µdxµ + dy

2

EW: SO(5)xU(1) GHU in Randall-Sundrum

✓Aµ

Ay

◆(x, yj � y) = Pj

✓Aµ

�Ay

◆(x, yj + y)P †

j

(y0, y1) = (0, L)

3

Agashe, Contino, Pomarol 2005YH, Sakamura 2006

YH, Oda, Ohnuma, Sakamura 2008Funatsu, Hatanaka, YH, Orikasa, Shimotani 2013

Medina, Shah, Wagner 2007

0 L

SO(5) ⇥ SO(4) ⇤ SU(2)L � SU(2)R

4D gauge bosons and Higgs

P0 = P1 =

�

�����

�1�1

�1�1

+1

�

�����

4

Aµ �

�

⇧⇧⇤

⇥

⌃⌃⌅W Z �

Ay �

�

�����

�

�����

Higgs

ei✓H(x) ⇠ P exp

n

ig

Z

dy Ay

o

Nearly the same as SM

5

At low energies

gauge couplings of quarks/leptons~ SM(✓H = 0.115)

W to ` ⌫ , ud , cs

gGHU/gSM

1.00019t b 0.9993

WWZ 0.9999998

Higgs couplings to W, Z, quarks/leptons ~ (SM) ⇥ cos ✓H

cos ✓H ⇠ 0.995 for ✓H = 0.1

Higgs decays:

corrections due to KK modes < 0.2%�(H ! ��), µ(H ! ��) ⇠ (SM) ⇥ cos

2 ✓H

Z(1)R , Z(1), �(1)

q

q

e� µ�

e+ µ+

Z0

6

ATLAS-CONF-2017-027(9 April 2017)p

s = 13TeV, 36.1 fb�1

no event for > 3000 GeV

✓H < 0.1

Z0 ! e+e�

SM

10�5

✓H = 0.115

✓H = 0.0737

14 TeV LHC

6TeV

SM

10�5

W 0 ! t b

W 0 ! µ ⌫

✓H = 0.115

6TeV

LHC

Predictions

Funatsu, Hatanaka, YH, Orikasa, 1612.03378 (PRD)

7

100 500 1000

0.2

0.4

0.6

0.8

1.0

1.2

1.4

s [GeV]

σ GHU/σSM(qq)

a

b

c

d

�GHU

�SM

(qq) 0.115

0.0737

Pe↵ = 0.946

Pe↵ = 0

100 200 500 1000 2000-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

s [GeV]

AFB(μ

+ μ- )

a

b

c

de

f

AFB(µ+µ�)

0.115

0.0737

SM

Pe↵ = 0.946

Distinct

deviations

Funatsu, Hatanaka,YH, Orikasa, 1705.05282

-1.0 -0.5 0.0 0.5 1.0

-0.20

-0.15

-0.10

-0.05

0.00

Peff

(AFBGHU-A

FBSM)/A

FBSM(μ

+ μ- )

AGHUFB

ASMFB

(µ+µ�) � 1

0.0737

0.115

250GeV

500GeV

Pe↵

Pe↵ =Pe� � Pe+

1 � Pe�Pe+

Z(1)R , Z(1), �(1)

e� µ�

e+ µ+e+

e� Z , �u d c s b

u d c s b

ILC

Next

Grand unification

9

Aµ :

0

B@

1

CA(+,+)

(+,+)

(�,�)(+,�)

(�,+)

SO(4)

SO(6)

Ay :

0

B@

1

CA(+,+)

(�,�)

(�,�)

(+,�)

(�,+)

Higgs doublet

Gauge-Higgs grand unification in 5d RSYH, Yamatsu, 1504.03817 (PTEP)

Furui, YH, Yamatsu, 1606.07222 (PTEP)

UV brane IR brane

P0 =

✓I10

�1

◆P1 =

✓I4

�I7

◆SO(11)�16

h�16 iSO(4) ⇥ SO(6) ! SU(2)L ⇥ SU(3)C ⇥ U(1)Y

10

32 =

✓ 16

16

◆

16 = ✓ujL

djL

◆

✓⌫L

eL

◆0

BBBBBBBBBBB@

⌫ee⌫uj

dj

dj

uj

1

CCCCCCCCCCCA

16 =

0

BBBBBBBBBBB@

⌫0

e0

e0

⌫0

u0j

d0j

d0j

u0j

1

CCCCCCCCCCCA

✓⌫R

eR

◆

✓ujR

djR

◆

Quarks & Leptons

0

BBB@

E NN E

Dj Dj

S

1

CCCA 11 =

exotic light particles

32 11

unavoidable in 5d theory

ds

2 = e

�2k|y|(dxµdxµ + dv

2) + dy

2

5th dim6th dim

6d hybrid-warped space: compactified RS6 ⌘ RS6

v ⇠ v + 2⇡R6 y ⇠ y + 2L5

(�y,�v) ⇠ (y, v)

Gauge-Higgs grand unification in 6d

11

UV brane IR brane

AdS ⇤ = �10 k2

Einstein eqs. solved with 5d branes

x x

xx

0 1

2 3

2⇡R6

2L5

y

vParity around 4 fixed points

P0, P1, P2, P3

P3 = P1P0P2 = P2P0P1

No exotic light particles

12

m(5)KK = ⇡k e�kL5 ⌧

1

R66 - 10 TeV GUT scale

P0 = P1 =

✓I4

�I7

◆

P2 = P3 =

✓I10

�1

◆

SO(11) GHU in RS6

13

{�M ,�N} = 2⌘MN

�76d =

✓I4

�I4

◆= �5

4d (�i�5�6) �54d =

0

BB@

I2�I2

I2�I2

1

CCA

(x, yj � y, vj � v) = �i�5�6Pj (x, yj + y, vj + v)

�76d �5

4d

Chiral fermions in RS6

6d Weyl + orbifold BC chiral fermions

Action

14

I =

Z

d

6x

p

� detG n

�AEA

MDM + ic k �6o

bulk vector mass 32(x, y, v) , 11(x, y, v)

On the UV brane (y=0)

�32(x, v) SO(11) ! SU(5)

1(x, v) simplectic Majorana

Neutrinos

m⌫ ⌧ me

16

Seesaw mechanism in 4d

Lm ⇠i

2(⌫c†

L , ⌫†R)

✓0 mD

mD M

◆✓⌫L

⌫cR

◆+ h.c.

P. Minkowski, Phys. Lett. B67 (1977) 421

|mass| =

8<

:

m2D

M⇠ m⌫

M

17

6d bulk 32 ! ⌫L, ⌫0R

5d UV brane 1 ! ⌘ (simplectic Majorana)

resulting 4d effective theory

Lm ⇠i

2(⌫c†

L , ⌫0†R , ⌘c†

L )

0

@0 mD 0

mD 0 mB

0 mB M

1

A

0

@⌫L

⌫cR

⌘L

1

A + h.c.

|mass| =

8

>

>

>

<

>

>

>

:

m2DM

m2B

⇠ m⌫

12

n

p

M2 + 4m2B ± M

o

Gauge-Higgs seesaw

18

Simplectic Majorana conditionMirabelli, Peskin, PRD58 (1998) 065002

on the 5d UV brane at y=0

1(x, v) =

0

BB@

⇠R+

⌘L+

⇠R�⌘L�

1

CCA

orbifold BC 1(x, vj � v) = �i�5�6 1(x, vj + v)

(++)

(++)

simplectic Majorana C6d

1 = i�54d�

6 1 ( 5d spinor)

⇠R+ = ⌘cL�

19

Gauge-Higgs seesaw mechanism

Dirac mass

�(y)B

n

32�32 1 + h.c.o

Hosotani mechanismmD : ⌫ � ⌫0 g 32�5Ay 32

!mBp

k(�⌫0 + ⌫0�)|y=0

Majorana mass

mixing

�(y)1

2M 1 1 !

1

2M�� !

i

2M(⌘c†

L ⌘L � ⌘†L⌘

cL)

20

Neutrino mass

m⌫ = �m2

uMz2c+1L

(c + 12)m2

B

mu =p

4c2 � 1 kz�c�1

2L sin 1

2✓H

4d effective theory0

@0 mD 0

mD 0 mB

0 mB M

1

A m⌫ =m2

DM

m2B

Summary

21

SO(11) gauge-Higgs grand unificationin 6-dim hybrid warped space

Gauge-Higgs seesaw mechanism