Yutaka Hosotani

第６回日大理工・益川塾連携シンポジウムキャンパスプラザ京都, 15 October 2016

New dimensions

from gauge-Higgs unification

SM is successful at low energies.SU(3)C ⇥ SU(2)L ⇥ U(1)Y

��Dµ���2 � V [�]

yjk j� k

�1

2TrGµ⌫G

µ⌫ �1

2TrFµ⌫F

µ⌫ �1

4Bµ⌫B

µ⌫

ji�µDµ j

Beautiful

No principle

LHiggs

LYukawa

+

+

+

Lgauge

Lfermion

2

LHiggs

LYukawa

+

+

Lgauge

Lfermion

Standard Model Gauge-Higgs Unification

L5dgauge

L5dfermion

gauge principle

3

Finite Higgs mass generated.

Solves the gauge-hierarchy prob.

Gauge-Higgs unification

� , W , Z

�AyAµ

AM

�Aharonov-Bohm phase

✓H

Higgs

Hosotani mechanism

dynamical

EW sym breaking

4

Planck brane TeV brane

AdS � = �6 k2

SO(5) � U(1)

ds

2 = e�2k|y|dxµdxµ + dy2

SO(5)xU(1) GHU in Randall-SundrumAgashe, Contino, Pomarol 2005YH, Sakamura 2006YH, Oda, Ohnuma, Sakamura 2008

Gauge-Higgs EW unification

Orbifold BC : P0 , P1

✓Aµ

Ay

◆(x, yj � y) = Pj

✓Aµ

�Ay

◆(x, yj + y)P

†j

(y0, y1) = (0, L)

5

SO(5) ⇥ SO(4) ⇤ SU(2)L � SU(2)R

Aµ �

�

⇧⇧⇤

⇥

⌃⌃⌅

W Z �

4D gauge bosons and Higgs

P0 = P1 =

�

�����

�1�1

�1�1

+1

�

�����

�1�2�3�4

Ay �

�

�����

�

�����

HiggsSU(2)L doublet

6

AB phaseei✓̂H(x) ⇠ P exp

n

ig

Z

dy Ay

o

Gauge principle for Higgs boson

Success

Dynamical EW sym. breaking

No vacuum instabilityVe↵ (✓H + 2⇡) = Ve↵ (✓H)

generated at 1 loop, and finitemH :Gauge-hierarchy prob. solved.

Almost SM at low energies for ✓H < 0.1

7

Higgs decay : µ ⇠ µSM · cos2 ✓H

Funatsu, Hatanaka, YH, Orikasa, Shimotani 1301.1744 Funatsu, Hatanaka, YH, 1510.06550

H �

�

W (n)X

n

H �W(n)

ZW (m)W (m)R

X

n,m: finite

Predictions

Universality mKK(✓H), mZ(1)(✓H), �H3 (✓H), �H4 (✓H)

deviation from SM

✓H

SM!!

!!

""

"

"

## # # ##

##

#

$$$ $ $$

$$

$

0.0 0.5 1.0 1.5"5

0

5

10

15

20

25

30

ΘH

Λ 3!GeV

"

$ nF%9# nF%3" nF%1! nF%0! SM

0.1

�Higgs3

0.0 0.5 1.0 1.5

2000

4000

6000

8000

10000

ΘH

mZ!1"#Ge

V$

nf"0

!!!!

"""

""

"

"

"

"

###

##

#

#

#

#

0.0 0.5 1.0 1.5

2000

4000

6000

8000

10000

ΘH

mZ!1"#Ge

V$

# nF"6" nF"3! nF"1

nF"0

mZ(1)

✓H 8

3000 4000 5000 6000 7000 8000 900010!10

10!8

10!6

10!4

MΜΜ!GeV"

dΣ#dM ΜΜ

!fb#GeV"

14 TeV LHCSM

✓H = 0.114

✓H = 0.073

µ+µ�e+e�

Z(1)R , Z(1), �(1)

q

q̄

e� µ�

e+ µ+

Z0

FHHOS 1404.2748

✓H = 0.114 ✓H = 0.073

Z0

Z(1)RZ(1)

�(1)

m (TeV) m (TeV)� (GeV) � (GeV)

5.73

6.07

6.08

482

342

886

8.00

8.61

8.61

553

494

1040

9

Gauge-Higgs grand unification in 5d

Planck brane TeV brane

P0 =

✓I10

�1

◆P1 =

✓I4

�I7

◆YH, Yamatsu, 1504.03817!

Furui, YH, Yamatsu, 1606.07222

SO(11) GHU in 5d RS

Aµ :

0

B@

1

CA(+,+)

(+,+)

(�,�)(+,�)

(�,+)

SO(4)

SO(6)

Ay :

0

B@

1

CA(+,+)

(�,�)

(�,�)

(+,�)

(�,+)

Higgs doublet

10

SO(4) ⇥ SO(6)

SU(2)L ⇥ U(1)Y ⇥ SU(3)C

U(1)EM ⇥ SU(3)C

SO(11)

P0 6= P1

�16

✓H

5d grand unification

SO(5) ⇥ U(1)X ⇥ SU(3)C

SO(4) ⇥ U(1)X ⇥ SU(3)C

SU(2)L ⇥ U(1)Y ⇥ SU(3)C

U(1)EM ⇥ SU(3)C

P0 = P1

�(1,2)

✓H

EW unification

BC

brane scalar

Hosotani mech.

11

32 11 011

32 =

✓ 16 16

◆

16 =zero modes✓ujLdjL

◆

✓⌫LeL

◆0

BBBBBBBBBBB@

⌫eê⌫̂ujdj

d̂jûj

1

CCCCCCCCCCCA

16 =zero modes

0

BBBBBBBBBBB@

⌫0

e0

ê0

⌫̂0

u0jd0j

d̂0jû0j

1

CCCCCCCCCCCA

✓⌫ReR

◆

✓ujRdjR

◆

Quarks & Leptons

0

BBB@

Ê NN̂ E

Dj D̂jS

1

CCCADjR D̂jR 11 =

0

BBB@

Ê0 N 0

N̂ 0 E0

D0j D̂0j

S0

1

CCCA D0jL D̂0jL 011 =

12

SO(10) inv. brane interactions

Mass splitting

Quark/lepton spectrum

13

P0 6= P1 in RS.

However, light exotic fermions appear.û, d̂, ê

✓H , cj (bulk scalar mass)

no proton decayN = 3 N = �1

p ! ⇡0 e+⇥

32 =

✓ 16 16

◆

16 =zero modes✓ujLdjL

◆

✓⌫LeL

◆0

BBBBBBBBBBB@

⌫eê⌫̂ujdj

d̂jûj

1

CCCCCCCCCCCA

16 =zero modes

0

BBBBBBBBBBB@

⌫0

e0

ê0

⌫̂0

u0jd0j

d̂0jû0j

1

CCCCCCCCCCCA

✓⌫ReR

◆

✓ujRdjR

◆

14

ds

2 = e�2k|y|(dxµdxµ + dv2) + dy2

5th dim6th dim

v ⇠ v + 2⇡R6 y ⇠ y + 2L5(�y,�v) ⇠ (y, v)

Gauge-Higgs grand unification in 6d

SO(11) GHU in 6d hybrid-warped spacework in progress, with N. Yamatsu

Planck brane TeV brane

AdS ⇤ = �10 k2

15

x x

xx

0 1

2 3

2⇡R6

2L5y

vParity around 4 fixed points

P0, P1, P2, P3

P3 = P1P0P2 = P2P0P1

m(5)KK = ⇡k e�kL5 ⌧

1

R66 - 10 TeV GUT scale

P0 = P1 =

✓I4

�I7

◆

P2 = P3 =

✓I10

�1

◆No exotic

light particles

16

6D-Weyl + orbifold BC zero modes : chiral

�54D =

0

BB@

I2�I2

I2�I2

1

CCA , �76D = �

54D�̄ =

0

BB@

I2I2

�I2�I2

1

CCA

(x,�y,�v) = P0�̄ (x, y, v) , �̄ = �i�5�6

Dirac eq. z = eky (0 y L5)⇢�µDµ + �

6Dv + �5Dz + i

c

z�6

�1

z5/2 = 0

bulk vector mass

Fermions in 6d hybrid warped space

17

18

6d grand unification5d grand unification

SO(4) ⇥ SO(6)

SU(2)L ⇥ U(1)Y ⇥ SU(3)C

U(1)EM ⇥ SU(3)C

SO(11)

P0 6= P1

�16

✓H

SO(4) ⇥ SO(6)

SU(2)L ⇥ U(1)Y ⇥ SU(3)C

U(1)EM ⇥ SU(3)C

SO(11)

✓H

SO(10)

�32

P0 = P1

P2 = P3BC

brane scalar

Hosotani mech.

Summary

Higgs phenomenology, Z’, W’ (KK modes)

SO(5)xU(1) gauge-Higgs EW unification

Extra dimensions5th dim : EW

6th dim : GUT

SO(11) gauge-Higgs grand unification

19