National Central UniversityAcademia Sinica

National Center for Theoretical Sciences

Cheng-Wei Chiang

PHENOMENOLOGY OF

HIGGS BOSONS IN THE

GEORGI-MACHACEK MODEL

November 3, 2015LCWS2015 @ Whistler, Canada

CWC and K Yagyu, JHEP 1301 (2013) 026 CWC, AL Kuo and K Yagyu, JHEP 1310 (2013) 072CWC, S Kanemura and K Yagyu, PRD 90 (2014) 115025CWC and K Tsumura, JHEP 1504 (2015) 113CWC, S Kanemura and K Yagyu, arXiv:1510.06297 [hep-ph]CWC, AL Kuo and T Yamada, to arXiv:1511.xxxxx [hep-ph]1

QUICK OVERVIEW OF THIS TALK

• Georgi-Machacek Model• Higgs decay pattern• Constraints from LHC data

• SM-like Higgs, like-sign W, extra neutral Higgs searches

• ILC phenomenology• Summary

2

WHY HIGGS TRIPLETS?

• Higgs triplet models have the following intriguing features:• type-II seesaw for Majorana neutrino mass, generated by the

VEV of the new scalar (automatically induced by EWSB);• existence of a doubly-charged Higgs boson, leading to like-sign

LNV and possibly even LFV processes at tree level;➠ a link between neutrino and LHC physics

• SM-like Higgs possibly with stronger couplings with weak bosons;

• existence of a H±W∓Z vertex at tree level through mixing (only loop-induced in models such as 2HDM).

All models are wrong, but some are useful.--- George E.P. Box

3

GEORGI-MACHACEK MODEL

• The Higgs sector includes SM doublet field φ (2,1/2) and triplet fields χ (3,1) and ξ (3,0)

transformed under SU(2)L×SU(2)R as Φ → UL Φ UR† and Δ → UL Δ UR† with UL,R = exp(i θL,Ra Ta) and Ta being corresponding SU(2) generators.

� =

✓�0⇤ �+

�� �0

◆, � =

0

@�0⇤ ⇠+ �++

�� ⇠0 �+

��� ⇠� �0

1

A

Georgi, Machacek 1985Chanowitz, Golden 1985

SU(2)LSU(2)R

4

GEORGI-MACHACEK MODEL

• The Higgs sector includes SM doublet field φ (2,1/2) and triplet fields χ (3,1) and ξ (3,0)

transformed under SU(2)L×SU(2)R as Φ → UL Φ UR† and Δ → UL Δ UR† with UL,R = exp(i θL,Ra Ta) and Ta being corresponding SU(2) generators.

• Take vχ = vξ ≡ vΔ (aligned VEV).➠ SU(2)L×SU(2)R → custodial SU(2)V ➠ ρ = 1 at tree level

Georgi, Machacek 1985Chanowitz, Golden 1985

� =

✓v� �+

�� v�

◆, � =

0

@v� ⇠+ �++

�� v� �+

��� ⇠� v�

1

A

5

VACUUM EXPECTATION VALUE

• The VEV’s are subject to the constraint

with two mixing angle definitions seen in the literature:

• One could attribute EWSB entirely to vΔ (≃ 87 GeV) while keeping vφ = 0.

• Perturbativity of top Yukawa coupling demands vΔ ≲ 80 GeV.➠ other constraints later

Georgi, Machacek 1985Chanowitz, Golden 1985

6

v2 = v2� + 8v2� =1p2GF

= (246 GeV)2

tan ✓H =

2

p2v�v�

or tan� =

v�2

p2v�

CUSTODIAL SU(2) CLASSIFICATION

CP-even

CP-even

CP-odd

∆: 3 ⊗ 3 Φ: 2 ⊗ 2

5 ⊕ 3 ⊕ 1 3 ⊕ 1

SU(2)L ⊗ SU(2)R

SU(2)V

H5 ⌘

2

66664

H++5

H+5

H05

H�5

H��5

3

77775

H3 ⌘

2

4H+

3

H03

H�3

3

5H1 ⌘

⇥H0

1

⇤

�3 ⌘

2

4w+

z0

w�

3

5h

mixing angle αmixing angle β or θH

(125 GeV)

mH5

mH3mH1

mh

mass degeneracy within each representation as a result of custodial symmetry

7

NEUTRAL HIGGS COUPLINGS

• Normalize all couplings to those for SM Higgs boson(V = W,Z; F = quarks):

gauge-phobic

quark-phobic

Higgs F V

hcos↵

sin�sin� cos↵�

r8

3cos� sin↵

H01

sin↵

sin�sin� sin↵+

r8

3cos� cos↵

H03 i⌘f cot� 0

H05 0 W = �cos�p

3and Z =

2 cos�p3

⌘f = +1 for up-type quarks and �1 for down-type quarks and charged leptons.

independent of α

group factor that makes it possible for the entire factor to be greater than 1(mixing required)

8

F =g'FF

gSMhFF

, V =g'V V

gSMhV V

suppressed by α

DECAY PATTERN

• Decay rates of new Higgs bosons generally depend on their mass hierarchy, vΔ (or tanθH), and mixing angle α.

• Fix mh = 125 GeV and α = 0 to be specific.• Decay rates now depend upon vΔ, mH3 and the mass

splitting between 5-plet and 3-plet:

• General mass spectra without fixing α and consistent with current Higgs data and some other theoretical and experimental constraints have recently been worked out.

�m ⌘ mH3 �mH5

9

CWC, Kuo, Yamada, to appear

DECAYS OF H5 BOSONS

mH5 > mH3

mH5 = mH3

doubly-charged singly-charged neutral

vΔ is an important order parameter of the model.10

• In the case of small vΔ, both H±± and H± decay dominantly into leptonic final states, same as the simplest Higgs triplet model in phenomenology.

SIGNATURE FOR SMALL VΔ

(GeV)±±Hm200 300 400 500 600 700 800

)-1

Lum

inos

ity (f

b

-110

1

10

210

Discovery potential

3 lepton≥

4 lepton

550 GeV

600 GeV

Akeroyd, CWC, Gaur 2010

14-TeV LHC

11

CMS 2012

A general lower bound of 400 GeV from like-sign dilepton modes is given by both ATLAS and CMS. ATLAS 2012, 2014

PRODUCTION FOR LARGE VΔ

• For large vΔ, H±± couples dominantly to weak bosons.• VBF as dominant production processes for sufficiently

large vΔ and sufficiently large MH±±.CWC, Nomura, Tsumura PRD 2012

VBF process

an experimentally less explored scenario, and unique for GM12

CONSTRAINT FROM HSM

• Take MH5 = MH3 = MH1 = 300 GeV as an example.• Allowed region in mixing angle space

• signal strengths(~2013 summer)

• unitarity• vacuum stability• Rb

• S parameter• hVV coupling up

by ~1.3 allowed

chV V ⌘ gGMhV V /g

SMhV V

CWC, Kuo, Yagyu JHEP 2013

13

IMPORTANCE OF VBF PROCESSES

μVVGGF = 1.0 ± 0.1 κV contours κF contours• Enhancement (suppression) in BR(h→VV) due to κV > 1

(< 1) is compensated by suppression (enhancement) in gluon fusion cross section due to κF < 1 (> 1).➠ importance of studying the VBF processes in GM

14

0 100 200 300 400 500

MT [GeV]

1

10

100

# o

f E

ven

t /

bin

GM15

GM13

SM

0 100 200 300 400 500

MT [GeV]

1

10

100

# o

f E

ven

t /

bin

GM15

GM13

SM

0 100 200 300 400 500

MT [GeV]

1

10

100

1000

# o

f E

ven

t /

bin

GM15

GM13

SM

H5++

W + W+

W + W +

l+

l+

ν

ν

�

�

W+ W+

Z

Z

l+

l+

ν

l-

�

�

H5+

TRANSVERSE MASS DISTRIBUTION

h, H50

W+ W+

W-

W-

l+

l-

ν

ν

�

�

neutral singly-charged doubly-charged`±`±jj /ET`±`±`⌥jj /ET`±`⌥jj /ET

125 GeV 300 GeV 300 GeV

CWC, Kuo, Yagyu JHEP 2013

easier to determine H5±± mass than the other two14 TeV, 100 /fb

15

chVV = 1.3 with (θH,α) = (40°,55°) and MH5 = MH3 = MH1 = 300 GeV ➠ no mass hierarchy

CONSTRAINT FROM H5±±

• ATLAS data of same-sign di-boson events (20.3/fb, 8-TeV) can be used to limit the vΔ-mH5 plane:

• Results are independent of α.

ATLAS 2014

100 200 300 400 500 600 700 800

mH5

, mH3

[GeV]

20

30

40

50

60

70

v∆ [

GeV

]

Excluded

at t

he 68%

CL

Allowed

Excluded

at t

he 95%

CLExcluded by R b

100 200 300 400 500 600 700 800 900 1000

mH5

, mH3

[GeV]

0

10

20

30

40

50

60

70

v∆ [

GeV

]

30 fb-1

100 fb-1

300 fb-1

3000 fb-1

Excluded by R b

most severe bound on vΔ at mH5 = 200 GeV

more improvement in high mass region

for mH5 ≲ 200 GeV, more events from 5-plet Higgses

are rejected by kinematic cuts

limit from 8-TeV LHC of 20.3 /fb 5σ reach at 14-TeV LHC

16

CWC, Kanemura, Yagyu PRD 2014

SEARCHES OF OTHER NEUTRAL HIGGSES

[GeV]Hm300 400 500 600 700 800 900 1000

BR

[pb]

× σ

95%

CL

Lim

it on

-310

-210

-110

1

10Obs. ggFExp. ggF

σ1 ±σ2 ±

BR× Thσ-1Ldt = 20.7 fb∫ = 8 TeV s

ATLAS Preliminary, NWAνµνe→WW→H

[GeV]Hm300 400 500 600 700 800 900 1000

BR

[pb]

× σ

95%

CL

Lim

it on

-310

-210

-110

1

10Obs. VBFExp. VBF

σ1 ±σ2 ±

BR× Thσ-1Ldt = 20.7 fb∫ = 8 TeV s

ATLAS Preliminary, NWAνµνe→WW→H

[GeV]Hm200 400 600 800 1000

BR

[fb]

× σ

95%

CL

limit

on

-110

1

10

210

310 PreliminaryATLAS

4l→ ZZ→H-1Ldt =20.7 fb∫

=8 TeVs

Obs ggFExp ggF

σ 1 ±

σ 2 ± BR× SMσ

ATLAS 2014

[GeV]Hm200 400 600 800 1000

BR

[fb]

× σ

95%

CL

limit

on

-110

1

10

210 PreliminaryATLAS

4l→ ZZ→H-1Ldt =20.7 fb∫

=8 TeVs

Obs VBF+VHExp VBF+VH

σ 1 ±

σ 2 ± BR× SMσ

[GeV]Xm60 70 80 90 100 200 300 400 500 600

BR

[fb]

⋅ fid

σ95

% C

L lim

it on

-110

1

10

210

ATLAS-1Ldt = 20.3 fb∫ = 8 TeV, s

ObservedExpected

σ 1 ±σ 2 ±

17

CONSTRAINT FROM H10

• Constraints from VBF channels are stronger than those from GGF mechanism.

• ZZ is more constraining than WW when MH1≲375 GeV as the former has a slightly better experimental sensitivity.

• The γγ mode (GGF+VBF) provides useful bounds on vΔ in the low-mass regime.

• All of them are sensitive to α.

CWC and Tsumura JHEP 2015

18

CONSTRAINT FROM H50

• Since H5 does not couple to SM quarks and charged leptons, it has only VBF ZZ, WW, and γγ channels.

• Constraints are generally weaker, but independent of α.• The WW mode does not provide a useful constraint.

19

CWC and Tsumura JHEP 2015

NO CONSTRAINT FROM H30 YET

• Signal strength of H30→ff is significantly enhanced in the mass range between 2MW and 2Mt:

• Use these modes to search for H30 or constrain the model.

hZ threshold tt threshold

µGGFFF [H3] = (H3

F )2FA1/2(MH3)

FS1/2(MH3)

⇥ BF

BSMF (MH3)

1�

4M2f

M2H3

!�1

20

CWC and Tsumura JHEP 2015

5-PLET AT ILC• Three types of production modes at ILC:

• Pair production (PP) processes

• Vector boson associated (VBA) processes

• Vector boson fusion (VBF) processes

e+e� ! Z⇤/�⇤ ! H++5 H��

5

e+e� ! Z⇤/�⇤ ! H+5 H�

5

e+e� ! Z⇤/�⇤/⌫⇤e ! H±±5 W⌥W⌥

e+e� ! Z⇤ ! H±5 W⌥ , H0

5Z

e+e� ! H±5 e⌥⌫e

e+e� ! H05e

+e� , H05⌫e⌫̄e

independent of vΔ dominant for small vΔ kinematically limited to √s/2

depending on vΔ dominant for large vΔ and mH5 up to √s − MW,Zinvolving H5±W∓Z vertex

depending on vΔ dominant for large vΔ and mH5 up to ~√sinvolving H5±W∓Z vertex

21

CROSS SECTIONS @ ILC

H5+H5−

PP

VBA

VBA

VBF

CWC, Kanemura, Yagyu 2015

100 200 300 400 500

mH5

[GeV]

10-1

100

101

102

103

σ [

fb]

Pair Productions

H5

++H

5

−−

H5

+H

5

−

100 200 300 400 500 600 700 800 900 1000

mH5

[GeV]

10-1

100

101

102

σ [

fb]

Vector Boson Associated Productions

v∆ = 50 GeV H

5

+W

− + c.c.

H5

0Z

H5

++W

−W

− + c.c.

100 200 300 400 500 600 700 800 900 1000

mH5

[GeV]

10-1

100

101

102

σ [

fb]

Vector Boson Fusion Productions

H5

+e

−ν + c.c.

H5

0νν

v∆ = 50 GeV

H5

0 e

+e

−

22

ps = 500 GeV (solid), 1 TeV (dashed)

independent of α

VBA CROSS SECTIONS @ ILCCWC, Kanemura, Yagyu 2015

100 150 200 250 300 350 400 450

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

e+e

− H

5

0Z

50 fb

20 fb

10 fb

5 fb

1 fb

→

100 150 200 250 300 350 400 450

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

e+e

− H

5

+W

− + c.c.

50 fb

20 fb

10 fb

5 fb

1 fb

→

100 150 200 250 300 350 400 450

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

e+e

− H

5

++W

−W

− + c.c.→

1 f

b

5 f

b

10 f

b

95% CL , 8 TeV, 20 fb-1

5σ , 14 TeV, 300 fb-1

5σ , 14 TeV, 3000 fb-1

0.5

fb

0.1

fb

100 200 300 400 500 600 700 800 900

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

10 fb

5 fb

1 fb

0.1 fb

100 200 300 400 500 600 700 800 900

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

1 fb

20 fb

10 fb

5 fb

0.1 fb

100 200 300 400 500 600 700 800 900

mH5

[GeV]

0

10

20

30

40

50

60

70

80

v∆ [

GeV

]

5 fb

1 fb

10 fb

0.1 fb

23

ps = 1 TeV

ps = 500 GeV

INVARIANT MASS DISTRIBUTIONS

• Invariant mass distributions for subsystems of the e+e−→ W+W−Z process including ISR with scale set at √s.

• Narrow peaks are due to H5± and H50, respectively.• Precise measurement of the H5±W∓Z vertex is possible.

CWC, Kanemura, Yagyu 2015

24

0 100 200 300 400 500M(WZ) [GeV]

0

0.1

0.2

0.3

0.4

fb/(

5 G

eV)

0 100 200 300 400 500M(WW) [GeV]

0

0.05

0.1

0.15

0.2

0.25

fb/(

5 G

eV)

ps = 500 GeV and v� = 30 GeV

mH5 = 200 GeV (black) and 300 GeV (red)

SUMMARY

• With SU(2)L×SU(2)R-symmetric Higgs potential and vacuum alignment, GM model preserves custodial symmetry, allows a large vΔ, and possibly has hVV couplings stronger than SM’s.

• There is an [approximate] mass degeneracy in each of the 3-plet, and 5-plet Higgs representations.

• For large vΔ, VBF processes are useful for searching for exotic GM Higgs bosons, verifying their mass spectrum, and extracting hVV couplings.

• Latest LHC data are employed to put constraints on the parameter space (vΔ vs mH5 or α).

• Synergy between searches of H5± and H50 at ILC and H5±± at LHC will make the 5-plet study more comprehensive.

25

Thank You!

26