Fingerprinting of the Higgs boson couplings as a probe of new physics models The 11 th LHC Physics Monthly Meeting, KIAS, Feb. 18, 2014 Kei Yagyu (National

Fingerprinting of the Higgs boson couplings

as a probe of new physics models

The 11th LHC Physics Monthly Meeting,

KIAS, Feb. 18, 2014

Kei Yagyu (National Central U.)

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3

Congratulation!

이 상화

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Figure Skating (20th and 21st)

김 연아 浅田真央

126 GeV Higgs

Explained

Minimal (1 doublet)

EW data,Flavor, …

5

Extended Higgs sectors

ExtraSingletsDoubletsTriplets…

126 GeV Higgs

Explained

Minimal (1 doublet)

EW data,Flavor, …

6

126 GeV Higgs

Introduce



Minimal (1 doublet)

Beyond the SM

Neutrino mass, Dark matter and Baryon asymmetry

Explained

EW data,Flavor, …

7

126 GeV Higgs

Determine

Higgs prop.

Determine



Minimal (1 doublet)

Beyond the SM


EW data,Flavor, …

8

126 GeV Higgs

Beyond the SM


Determine

Higgs prop.

Determine



Minimal (1 doublet)

Bott

om

up

Ap

pro

ach

!

EW data,Flavor, …

9

126 GeVh

H++, H+, H, A, ...h

2. Indirect search1. Direct search

H++, H+, H, A, …

Discovery

Studying both ways is important to determine

the structure of the Higgs sector.

Bottom up Approach

126 GeV

Energy

Energy

10

Measuring effects

on the 126 GeV Higgs boson

126 GeVh

H++, H+, H, A, ...h

2. Indirect search1. Direct search

H++, H+, H, A, …

Discovery

Measuring effects

on the 126 GeV Higgs boson

Studying both ways is important to determine

the structure of the Higgs sector.

Bottom up Approach

126 GeV

Energy

Energy

11

Indirect Search

Patterns of deviation in various Higgs couplings

strongly depend on the structure of the Higgs sector.

Indirect search = Precision test of Higgs couplings

hbb

hττ

hcc

hγγ

hVV

hhh

Make a “Fingerprint” from precise measurements.

Minimal

Singlet Models

2HDMs

Triplet Models

etc…

Compare

12

Experiments Theory

The hZZ coupling can be measured by 1 % accuracy

at the ILC(250) !

Higgs coupling measurementsILC, TDRILC, Higgs White Paper, arXiv: 1310.0763

(300/fb)

13

The hVV and hff couplings can be measured by 1 % accuracy

at the ILC(500) !!

Higgs coupling measurements

(300/fb)

ILC, TDRILC, Higgs White Paper, arXiv: 1310.0763

14

The hVV and hff couplings can be measured by 1 % accuracy

at the ILC(500) !!

Higgs coupling measurements

(300/fb)

ILC, TDRILC, Higgs White Paper, arXiv: 1310.0763

15

　 Contents

Introduction

- Bottom up approach (Indirect search)

Deviations in the Higgs boson couplings in various Higgs sectors

- The hVV and hff couplings at the tree level

Higgs boson couplings in the 2HDMs

- Tree level

- One-loop level

Summery

16

1. Electroweak rho parameter

　 Basic Constraints

There are two guidelines to restrict Higgs sectors.

ρexp = 1.0004 -0.0004

+0.0003

Models with ρtree = 1 seems to be a natural choice. T Y

1 0

1/2 1/2

3 2

… …Alignment of (exotic) VEVs Ex. Model with doublet (Y=1/2) + triplet (Y=1) + triplet (Y=0)

(Georgi-Machacek model)

Satisfy the relation

if 17

2. Flavor Changing Neutral Current (FCNC)

Tree level FCNC process should be absent.

In general, multi-doublet extensions cause FCNC at the tree level



18

B0 Φ0

B0

B0 Φ0

B0

2. Flavor Changing Neutral Current (FCNC)

Tree level FCNC process should be absent.

In general, multi-doublet extensions cause FCNC at the tree level


Only one Higgs doublet couples

to each fermion.

19


Simple Extended Higgs Sectors

We consider the following simple Higgs sectors;

(with ρtree = 1 and no tree level FCNC)

1. Φ + S (Singlet)

2. Φ + D (Doublet)

3. Φ + Δ (Triplets or larger) [GM model, Septet model]

20

Hisano, Tsumura, PRD87 (2013)

Kanemura, Kikuchi, KY, PRD88 (2013)

Two mixing angles

Mixing between CP-even states

VEVs

where

T: isospin, Y:hypercharge

21

Yukawa

Gauge

Deviations in hff and hVV

Φ

f

f

φα

Yf = mf /<Φ> <φ> β

ΦV

V<Φ>

φ

V

V

<φ>

α

β

22

Yukawa

Gauge

Higgs Singlet Model (φ=S)

Φ

f

f

Sα

Yf = mf /<Φ> <S>

ΦV

V<Φ>

S

V

V

<S>

α

★ The singlet VEV

does not contribute

to the EWSB.

→ β=0 (<Φ>=246 GeV)

★ The hff and hVV

couplings are

universally

suppressed.

23

Yukawa

Gauge

Two Higgs Doublet Model (φ=D)

Φ (D)

f

f

D (Φ)α

Yf = mf /<Φ (D)> <D (Φ)>

ΦV

V<Φ>

D

V

V

<D>

α

β

β★ There are 2 patterns in κf

for each fermion f.

★ ξ = 1

24

Yukawa

Gauge

Model with a triplet (or higher) (φ=Δ)

Φ

f

f

Δα

Yf = mf /<Φ> <Δ>

ΦV

V<Φ>

Δ

V

V

<Δ>

α

β

β

★ The hff couplings are

universally suppressed.

★ ξ factor can be larger

than unity.

→ κV > 1

25

Ex.

GM model: ξ = 2*sqrt(6)/3

Septet model : ξ = 4

SM

26

SM

κF’

27

SM

κF’

κF = κF’

28

SM

κF’

κF = κF’

29

Gauge vs Yukawa

-π/4 < α < +π/4

0.1 < tanβ < 100

Singlet Model

2HDM (Type-I)

Georgi-Machacek Model

[ξ = 2*Sqrt(6)/3]

30

31

-π/4 < α < +π/4

0.1 < tanβ < 100

Tau vs Bottom

Singlet

2HDM (Type-I)


2HDM (Type-II)

2HDM (Type-X)

2HDM (Type-Y)

　 Contents

Introduction

- Bottom up approach (Indirect search)

Deviations in the Higgs boson couplings in various Higgs sectors

- The hVV and hff couplings at the tree level

Higgs boson couplings in the 2HDMs

- Tree level

- One-loop level

Summery

32

S. Kanemura, M. Kikuchi, KY, appear in PLB,

arXiv: 1401.0515 [hep-ph]

2HDMs

In general, Yukawa Lagrangian is given by

To avoid the tree level FCNC, one of the Yukawa couplings

should be forbidden.

Z2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977)

Z2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006)

S3 symmetry Kajiyama, Okada, KY, arXiv:1309.6234 [hep-ph]

U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012)

…

33

2HDMs with the softly-broken Z2 sym.

In general, Yukawa Lagrangian is given by

To avoid the tree level FCNC, one of the Yukawa couplings

should be forbidden.

Z2 symmetry (softly-broken) Glashow, Weinberg, PRD15 (1977)

Z2 symmetry (unbroken) Barbieri, Hall, Rychkov, PRD74 (2006)

S3 symmetry Kajiyama, Okada, KY, arXiv:1309.6234 [hep-ph]

U(1) symmetry Ko, Omura, Yu, JHEP1201 (2012)

…

There are four independent types of Yukawa interactions.34

Barger, Hewett, Phillips (1990), Grossman (1994)

u

d

Φ ２

e

Φ １

u

d

Φ ２

e

u

d

Φ ２

e

Φ １

Type-I Type-II (MSSM)

ud

Φ ２

e

Φ １

Type-X(Leptophilic)

Type-Y(Flipped)

Aoki, Kanemura, Tsumura, KY (2008)

Four Yukawa Interactions

Under the Z2 symmetry, two doublets are transformed as

Φ1 → +Φ1 and Φ2 → -Φ2.

35

In the Higgs basis, two doublets can be parameterized as:

tanβ = <Φ2>/<Φ1>

Mass Eigenstates

NG bosons Charged Higgs

CP-even Higgs CP-odd Higgs

SM-like Higgs boson w/126 GeV36

ξu ξd ξe

Type-I cotβ cotβ cotβ

Type-II cotβ -tanβ -tanβ

Type-X cotβ cotβ -tanβ

Type-Y cotβ -tanβ cotβ

Yukawa/Gauge Interaction

h

V

V

= (SM) × sin(β-α)

h

f

f

= (SM)

× [sin(β-α)+ξf cos(β-α)]37

Higgs Potential

The Higgs potential under the softly-broken Z2 sym. and CP-invariance

Mass formulae with sin(β-α) ~1

We have 8 parameters in the potential. They can be interpreted by

v (=246 GeV), mh (=126 GeV),

mH, mA, mH+, sin(β-α), tanβ, and M2

mh2 ~ λv2, mΦ

2 ~ M2 + λv2

38

SM-like/Decoupling Limit

SM-like limit: taking sin(β-α) → 1

All the Higgs boson couplings become the same value as

in the SM Higgs couplings at the tree level.

Decoupling limit: taking M2 (=mΦ2) → ∞

Decoupling limit can be taken

only when the SM-like limit is taken.

[mΦ2 ~ M2 + λv2]

39

Decoupling/SM-like Limit

Exclu

ded

by u

nita

rity

(mH = mA = mH+= M =)

10% dev.

1% dev.

0.1% dev.

cos(β-α) > 0

cos(β-α) < 0

40

δ =


Exclu

ded

by u

nita

rity

κV =

sin

(β-α

) → 1

(mH = mA = mH+= M =)

10% dev.

1% dev.

0.1% dev.

cos(β-α) > 0

cos(β-α) < 0

δ =

41


Exclu

ded

by u

nita

rity

(mH = mA = mH+= M =)

10% dev.

1% dev.

0.1% dev.

cos(β-α) > 0

cos(β-α) < 0

δ =

42

Patterns of Deviation in hff Couplings

h

f

f

= (SM) × [sin(β-α) + ξf cos(β-α)]

(SM) × [sin(β-α) + cotβ cos(β-α)]

(SM) × [sin(β-α) - tanβ cos(β-α)]

(SM) ×

(SM) ×

=

~For cos(β-α) > 0

cos(β-α) < 0 δ ≪ 1

δ = 1 - sin(β-α)

If κV ≠ 1 is found, several patterns of deviation in hff appear.

u

d

cotβ

e

Type-I

u

d

cotβ

e

tanβ

Type-II

u

d

cotβ

e

tanβ

Type-X

u

d

cotβ

e

tanβ

Type-Y

43

Patterns of Deviation in hff Couplings

h

f

f

= (SM) × [sin(β-α) + ξf cos(β-α)]

(SM) × [sin(β-α) + cotβ cos(β-α)]

(SM) × [sin(β-α) - tanβ cos(β-α)]

(SM) ×

(SM) ×

=

~For cos(β-α) > 0

cos(β-α) < 0 δ ≪ 1

δ = 1 - sin(β-α)

If κV ≠ 1 is found, several patterns of deviation in hff appear.

u

d

cotβ

e

Type-I

u

d

cotβ

e

tanβ

Type-II

u

d

cotβ

e

tanβ

Type-X

u

d

cotβ

e

tanβ

Type-Y

44

Bottom vs Tau

κV2 = 0.99, 0.95,

(δ ~ 0.005, 0.02)

cos(β-α) < 0

45

• How these predictions can be modified by taking

into account radiative corrections?

• The hff and hVV couplings can be measured with

O(1)% accuracy.

• In order to compare precision measurements, to

include radiative corrections are essentially

important!

Radiative Corrections

1-loop level

46

Radiative Corrections in the 2HDMs

There are papers for 1-loop corrections to

the Higgs boson couplings in 2HDMs.

Hollik, Penaranda, Eur. Phys. J. C23 (2002) [in the MSSM Higgs sector]

Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558, (2003);

Kanemura, Okada, Senaha, Yuan, PRD70 (2004).

hhh

hVV Kanemura, Okada, Senaha, Yuan, PRD70 (2004).

hff Guasch, Hollik, Penaranda, PLB515 (2001) [in the MSSM Higgs sector]

We discuss 1-loop corrections to the hff

couplings

in the four types of the 2HDM. 47

Decoupling/Nondecoupling

NP loop effects to the low energy obs. vanish when new particles are heavy.

Appelquist, Carazzone (1975)Decoupling theorem

1/Mn → 0 (M → ∞)

Violation of the decoupling theorem

SM

NP+SMM → ∞

SM

SM SM

SM

SM

SM

Top mass ： mt = ytv

Scalar boson mass ： mφ2 = λv2 + M2

(with λv2 > M2 )

If a particle mass is (mostly) given by the Higgs VEV,

the particle loop effect does not vanish even in rather large mass case.

E.g.,

48

The hhh coupling @1-loop in the 2HDM

Φ = H, A, H±

Kanemura, Kiyoura, Okada, Senaha, Yuan PLB558 (2003)

49


Φ = H, A, H±

In the case with M2 >> λv2,

we can see the decoupling

behavior.


0

50


Φ = H, A, H±


~1

In the case with M2 < λv2,

nondecoupling effects

(quartic power of the

masses)

appear.

51

Renormalized hff vertices

Renormalized hff vertex

Renormalized scale factor at on-shell

The counter term contribution

52

Parameter Shifts

Fermion masses and wave functions

CP-even Higgs sector and mixing angle β

The VEV


53

On-shell Renormalization Conditions

= 0h H

p2=mh2

h Hp2=mH2

= h h p2 =mh2

= 0

f f p2=mf2

= 0f f p2=mf2

= 0

G0 A p2=mZ2

= G0 A p2=mA2

= 0

δβ (and δCA)

δZh, δα and δCh

δmf and δZVf

The counter term δv

is determined from the

EW on-shell RCs.Hollik, Fortsch. Phys. 38, 165 (1990).

54

Decoupling [sin(β-α)=1, mH+=mA=mH (=mΦ) and mΦ

2-M2 = (300 GeV)2]

SM

Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515

55

tanβ = 1tanβ = 3

Nondecoupling

[sin(β-α)=1, mH+=mA=mH (=mΦ) and M2 = 0]


56

Nondecoupling

[sin(β-α)=1, mH+=mA=mH (=mΦ) and M2 = 0]


57

Fingerprinting at the tree level

cos(β-α) < 0,

tanβ = 1, 2, 3 and 4,


58

Fingerprinting at the 1-loop level

cos(β-α) < 0,

tanβ = 1, 2, 3 and 4,

mH+ = mA = mH (=mΦ),

100 GeV < mΦ < 1 TeV,

0 < M < mΦ,

Unitarity + Vacuum

stab.


59


cos(β-α) < 0,

tanβ: Scanned


100 GeV < mΦ < 1 TeV,

0 < M < mΦ,

Unitarity + Vacuum

stab.


60


cos(β-α) < 0,

tanβ: Scanned


100 GeV < mΦ < 1 TeV,

0 < M < mΦ,

Unitarity + Vacuum

stab.


61

One-loop corrected hZZ coupling

Even taking the maximal nondecoupling case (M2=0),

the amount of correction is less than 1%.

1 - sin2(β - α)


Tanβ = 2,mΦ = 300 GeV

62

Indirect Search = Comparing fingerprints of the Higgs couplings.

Typical patterns of deviations in extended Higgs sectors at tree level

Points: CP-even Higgs mixing and VEV sharing

1. Higgs singlet model → κf and κV are universally suppressed.

2. Two Higgs doublet models → 4 patterns in κf’s.

3. Triplet models → κf are universally suppressed and κV can be larger than 1.

Radiative corrections to the Higgs boson couplings

Points: (Non)decoupling property of extra Higgs bosons

1-loop corrections from extra Higgs bosons to the hhh, hff and hVV couplings

can be maximally O(100)%, O(10)% and O(1)%, respectively.

If 1% deviation in the hZZ couplings is found at the ILC(250),

we can discriminate the four types of 2HDM by precisely measured

hff couplings at ILC(250) or ILC(500).

Summary

63

64

Vacuum stability + Unitarity

65

Unitarity bound for the Singlet Model

Kang, Park, arXiv:1306.6713 [Singlet]

66

Gauge vs Yukawa

-π/4 < α < +π/4

0.1 < tanβ < 100

Singlet Model

2HDM (Type-I)


[ξ = 2*Sqrt(6)/3]

Unitarity const.

w/ 300 GeV.


Kanemura, Okada, Senaha, Yuan,

PRD70 (2004) [2HDM]

Aoki, Kanemura, PRD77 (2008) [GM]

67

Gauge vs Yukawa

-π/4 < α < +π/4

0.1 < tanβ < 100

Singlet Model

2HDM (Type-I)


[ξ = 2*Sqrt(6)/3]

Unitarity const.

w/ 500 GeV.


Kanemura, Okada, Senaha, Yuan,

PRD70 (2004) [2HDM]

Aoki, Kanemura, PRD77 (2008) [GM]

68

Top Yukawa

69

Tanβ dependence

70

τ vs b

71

b vs c

72

τ vs c

73

IPI diagram Counter term Counter termIPI diagram2-pointfunction

3-pointfunction= =

++

Parameters shift: g → g + δg, g’ → g’ + δg’, v → v + δv,

Wμ → ZW1/2 Wμ , Bμ → ZB

1/2 Bμ

On-shell Renormalization Scheme

74

LHC: 14 TeV, 300 fb-1

ILC1: 250 GeV, 250 fb-1

ILC: 500 GeV, 500 fb-1

ILCTeV: 1 TeV, 1000 fb-1

Higgs coupling measurementsPeskin, 1207.2516[hep-ph]

75

　 Signal Significance @125 GeV

ATLAS CMS

γγ 7.4σ (4.3σ) [CONF-2013-012]

3.2σ (4.2σ)[PAS-HIG-13-1]

ZZ*→4l

6.6σ (4.4σ)[CONF-2013-013]

6.7σ (7.1σ)[PAS-HIG-13-2]

WW*→lvlv

3.8σ (3.8σ)[CONF-2013-030]

4.0σ (5.1σ)[PAS-HIG-13-3]

bb No excess1.4 (1.3)×SM exc.[CONF-2013-079]

2.1σ （ 2.2σ）[PAS-HIG-13-012]

τ τ 4.1σ (3.2σ)[CONF-2012-160]

2.9σ (2.6σ)[PAS-HIG-13-004]

Spin 1 is excluded

Higgs mechanism

Yukawa?

Obs. (Exp.) 7+8TeV, ~25/fb

There is no room for doubt that it is a Higgs boson.76

Gauge vs Yukawa

Singlet Model

2HDM (Type-I)


[ξ = 2*Sqrt(6)/3]For details, see Prof. Chiang’s talk

77

Fingerprinting (Gauge vs Fermion)

-π/4 < α < +π/4

Singlet Model

2HDM


[ξ = 2*Sqrt(6)/3]

78

Fingerprinting (Gauge vs Fermion)

-π/4 < α < +π/4

0.1 < tanβ < 100

Singlet Model

2HDM


[ξ = 2*Sqrt(6)/3]

79

Documents

Fingerprinting of the Higgs boson couplings as a probe of new physics models The 11 th LHC Physics Monthly Meeting, KIAS, Feb. 18, 2014 Kei Yagyu (National