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Fingerprinting of the Higgs boson couplings as a probe of new physics models

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### Fingerprinting of the Higgs boson couplings as a probe of new physics models

Yagyu, Kei (柳生 慶)

National Central U.

Collaboration with

Shinya Kanemura and Mariko Kikuchi (U. of Toyama)

Physics Letters B731, 27-35 (2014), arXiv:1401.0515 [hep-ph]

Academia Sinica, Mar. 7, 2014

- In the end of 19th century, people thought that physics has already been completed by Newton’s dynamics and Maxwell’s electromagnetism.
- However, there were a few phenomena which couldn’t be explained by classical physics such as the spectrum of cavity radiation.

Rayleigh-Jeans

Low

Exp.

Wien’s Low (1896)

Wien’s Low

Rayleigh-Jeans Low (1900)

- In the end of 19th century, people thought that physics has already been completed by Newton’s dynamics and Maxwell’s electromagnetism.
- However, there were a few phenomena which couldn’t be explained by classical physics such as the spectrum of cavity radiation.

Rayleigh-Jeans

Low

Exp. ~ Planck’s Low

Planck’s Low (1905)

Wien’s Low

Early 20th century

Classical Theory

Quantum Theory

Cavity Radiation

- Nuclear Physics

- Particle Physics, …

-Newton Dynamics

-Maxwell Electromagnetism

Planck’s Low

Einstein’s

Light Quantum Hypothesis

Cavity Radiation gave a “Bridge” connecting

Classical Theory and Quantum Theory.

We have the Standard Model.

Higgs mechanism

Higgs Sector

Yukawa interaction

Gauge interaction

Gauge Sector

G, W, Z, γ

Matter Sector

Quarks & Leptons

We have the Standard Model.

Higgs mechanism

Higgs Sector

Yukawa interaction

Gauge interaction

Gauge Sector

G, W, Z, γ

Matter Sector

Quarks & Leptons

Well tested before the LHC

We have the Standard Model.

Higgs mechanism

Higgs Sector

Yukawa interaction

Gauge interaction

Gauge Sector

G, W, Z, γ

Matter Sector

Quarks & Leptons

We have the Standard Model.

Higgs mechanism

Higgs Sector

Yukawa interaction

Gauge interaction

Gauge Sector

G, W, Z, γ

Matter Sector

Quarks & Leptons

The LHC has found a Higgs boson with 126 GeV

We have the Standard Model.

Higgs mechanism

Higgs Sector

Yukawa interaction

Gauge interaction

Gauge Sector

G, W, Z, γ

Matter Sector

Quarks & Leptons

However, still there are unclear things in the Higgs sector.

Today

New Physics

EWSB

Standard Model

Higgs Sector

Higgs Physics could give a next “Bridge” connecting

the Standard Model and New Physics!

What is the true structure of the Higgs sector?

-Minimal or Non-minimal?

What is the dynamics behind the Higgs sector?

- Weak coupling or Strong coupling

How is the Higgs sector related to the phenomena

beyond the SM?

- Neutrino oscillation, Dark matter, and Baryon asymmetry.

What is the true structure of the Higgs sector?

-Minimal or Non-minimal?

What is the dynamics behind the Higgs sector?

- Weak coupling or Strong coupling

How is the Higgs sector related to the phenomena

beyond the SM?

- Neutrino oscillation, Dark matter, and Baryon asymmetry.

Singlets

Doublets

Triplets…

Minimal

(1 doublet)

Extra

Explained

EW data,

Flavor, …

126 GeV Higgs

Neutrino mass, Dark matter and Baryon asymmetry

Introduce

Non-MinimalHiggs sectors

Singlets

Doublets

Triplets…

Minimal

(1 doublet)

Extra

Explained

EW data,

Flavor, …

New Physics Models

126 GeV Higgs

Neutrino mass, Dark matter and Baryon asymmetry

Determine

Non-MinimalHiggs sectors

Singlets

Doublets

Triplets…

Minimal

(1 doublet)

Extra

Determine

EW data,

Flavor, …

126 GeV Higgs

Higgs prop.

Neutrino mass, Dark matter and Baryon asymmetry

Determine

Non-MinimalHiggs sectors

Singlets

Doublets

Triplets…

Bottom up Approach!

Minimal

(1 doublet)

Extra

Determine

EW data,

Flavor, …

New Physics Models

126 GeV Higgs

Higgs prop.

2. Indirect search

1. Direct search

Measuring effects

on the 126 GeV Higgs boson

Energy

Discovery

Energy

H++,

H+,

H,

A, ...

h

h

126 GeV

H++, H+,

H, A, …

126 GeV

Studying both ways is important to determine

the structure of the Higgs sector.

2. Indirect search

1. Direct search

Measuring effects

on the 126 GeV Higgs boson

Energy

Discovery

Energy

H++,

H+,

H,

A, ...

h

h

126 GeV

H++, H+,

H, A, …

126 GeV

Studying both ways is important to determine

the structure of the Higgs sector.

Indirect search = Precision test of Higgs couplings

Experiments

Theory

hVV

Minimal

Singlet Models

2HDMs

Triplet Models

etc…

hbb

hττ

Compare

hcc

hγγ

hhh

Make a “Fingerprint” from precise measurements.

- Patterns of deviation in various Higgs couplings strongly depend on the structure of the Higgs sector.

Scaling factors

κV = ghVV (exp)/ghVV (SM), κF= ghFF(exp)/ghFF(SM)

ATLAS-CONF-2013-034

CMS-PAS-HIG-13-005

κF

κV

1.4

Scaling factors

κV = ghVV (exp)/ghVV (SM), κF= ghFF(exp)/ghFF(SM)

1.2

ATLAS-CONF-2013-034

CMS-PAS-HIG-13-005

1

0.8

κF

0.6

The uncertainties for κF and κV are about

±40% and ±20%, respectively.

κV

ILC, TDR

ILC, Higgs White Paper, arXiv: 1310.0763

(300/fb)

The hZZ coupling can be measured by 1 % accuracy

at the ILC(250) !

ILC, TDR

ILC, Higgs White Paper, arXiv: 1310.0763

(300/fb)

The hVV and hffcouplings can be measured by 1 % accuracy

at the ILC(500) !!

ILC, TDR

ILC, Higgs White Paper, arXiv: 1310.0763

(300/fb)

The hVV and hffcouplings can be measured by 1 % accuracy

at the ILC(500) !!

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

Basic Constraints

There are two guidelines to restrict Higgs sectors.

1. Electroweak rho parameter

+0.0003

ρexp =1.0004

-0.0004

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

Satisfy the relation

Alignment of (exotic) VEVs

Ex. Model with doublet (Y=1/2) + triplet (Y=1) + triplet (Y=0)

(Georgi-Machacek model)

if

Basic Constraints

There are two guidelines to restrict Higgs sectors.

2. Flavor Changing Neutral Current(FCNC)

Tree level FCNC process should be absent.

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

B0

B0

Φ0

Basic Constraints

There are two guidelines to restrict Higgs sectors.

2. Flavor Changing Neutral Current(FCNC)

Tree level FCNC process should be absent.

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

B0

B0

Only one Higgs doublet couples

to each fermion.

Φ0

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]

Hisano, Tsumura, PRD87 (2013)

Kanemura, Kikuchi, KY, PRD88 (2013)

- Yukawa

f

★ The singlet VEV

does not contribute

to the EWSB.

→ β=∞ (<Φ>=246 GeV)

α

S

Φ

<S>

Yf = mf /<Φ>

f

<Φ>

V

★ The hff and hVV

couplings are

universally suppressed.

Φ

V

- Gauge

<S>

α

S

- Yukawa

f

★There are 2 patterns in κf

for each fermion f.

α

β

D (Φ)

Φ (D)

<D (Φ)>

Yf = mf /<Φ (D)>

f

V

★ξ = 1

<Φ>

V

D

Φ

V

V

- Gauge

β

<D>

α

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

- Yukawa

★The hff couplings are

universally suppressed.

f

α

β

Δ

Φ

★ξ factor can be larger

than unity.

→ κV > 1

V

<Δ>

Yf = mf /<Φ>

f

<Φ>

V

Δ

Ex.

GM model: ξ = 2*sqrt(6)/3

Septet model : ξ = 4

Φ

V

V

- Gauge

β

<Δ>

α

SM

-π/4 < α < +π/4

0.1 < tanβ < 100

Singlet Model

2HDM (Type-I)

Georgi-Machacek Model

[ξ = 2*Sqrt(6)/3]

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

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)

…

2HDMs with the softly-broken Z2sym.

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.

Φ２

Φ１

Φ２

- u

u

e

e

d

d

Φ２

Φ２

Φ１

u

e

u

e

d

Φ１

d

Under the Z2 symmetry, two doublets are transformed as

Φ1→ +Φ1 and Φ2→ -Φ2.

Type-I

- Type-II (MSSM)

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

- Aoki, Kanemura, Tsumura, KY (2008)

Type-X

(Leptophilic)

Type-Y

(Flipped)

We define the Higgs basis by introducing β

tanβ = <Φ2>/<Φ1>

Charged Higgs

NG bosons

CP-even Higgs

CP-odd Higgs

SM-like Higgs boson w/126 GeV

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

- 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

- Mass formulae with sin(β-α) ~1

mh2 ~ λv2, mΦ2 ~ M2 + λv2

Φ = H±, A, H

- 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) → ∞

[mΦ2 ~ M2 + λv2]

Decoupling limit can be taken

only when the SM-like limit is taken.

10% dev.

cos(β-α) > 0

Excluded

by unitarity

cos(β-α) < 0

1% dev.

δ =

0.1% dev.

(mH= mA= mH+= M =)

10% dev.

cos(β-α) > 0

Excluded

by unitarity

cos(β-α) < 0

1% dev.

κV = sin(β-α) → 1

δ =

0.1% dev.

(mH= mA= mH+= M =)

10% dev.

cos(β-α) > 0

Excluded

by unitarity

cos(β-α) < 0

1% dev.

δ =

0.1% dev.

(mH= mA= mH+= M =)

Patterns of Deviation in hff Couplings

-tanβ

cotβ

- cotβ

e

u

u

e

d

d

- -tanβ

- cotβ

- cotβ

u

u

e

e

d

d

- -tanβ

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

= (SM) × [sin(β-α) + ξf cos(β-α)]

f

(SM) × [sin(β-α) + cotβcos(β-α)]

(SM) × [sin(β-α) - tanβcos(β-α)]

h

=

f

(SM) ×

(SM) ×

δ = 1 - sin(β-α)

Type-I

Type-II

For cos(β-α) > 0

cos(β-α) < 0

Type-Y

~

δ ≪ 1

Type-X

Patterns of Deviation in hff Couplings

-tanβ

cotβ

- cotβ

e

u

u

e

d

d

- -tanβ

- cotβ

- cotβ

u

u

e

e

d

d

- -tanβ

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

= (SM) × [sin(β-α) + ξf cos(β-α)]

f

(SM) × [sin(β-α) + cotβcos(β-α)]

(SM) × [sin(β-α) - tanβcos(β-α)]

h

=

f

(SM) ×

(SM) ×

δ = 1 - sin(β-α)

Type-I

Type-II

For cos(β-α) > 0

cos(β-α) < 0

Type-Y

~

δ ≪ 1

Type-X

1-loop level

If α is the same order of the EM coupling, the correction is at most O(0.1)%.

However, it can be larger than 1% due to nondecoupling effects

of extra Higgs boson loops.

How these predictions can be modified by taking into account radiative corrections?

The hff and hVV couplings can be measured with O(1)% accuracy.

Radiative Corrections in the 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.

- There are papers for 1-loop corrections to

the Higgs boson couplings in 2HDMs.

Decoupling theorem

Appelquist, Carazzone (1975)

1/Mn→ 0 (M → ∞)

SM

SM

NP+SM

SM

M → ∞

Violation of the decoupling theorem

SM

SM

SM

SM

- 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.,

Top mass：mt= ytv

Scalar boson mass：mφ2 = λv2 + M2

(with λv2 > M2 )

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

The hhh coupling @1-loop in the 2HDM

Φ = H, A, H±

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

The hhh coupling @1-loop in the 2HDM

Φ = H, A, H±

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

0

In the case with M2 >> λv2,

we can see the decoupling behavior.

The hhh coupling @1-loop in the 2HDM

Φ = H, A, H±

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

~1

In the case with M2 < λv2,

nondecoupling effects

(quartic power of the masses)

appear.

- Renormalized hff vertex

- Renormalized scale factor at on-shell

- The counter term contribution

- Fermion masses and wave functions

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

- CP-even Higgs sector and mixing angle β

- The VEV

On-shell Renormalization Conditions

= 0

= 0

1PI + C.T.

δmf and δZVf

f

f

f

f

p2=mf2

p2=mf2

= 0

=

= 0

δZh, δα and δCh

h

H

h

h

G0

h

A

H

p2 =mh2

p2=mH2

p2=mZ2

p2=mh2

The counter term δv

is determined from the

EW on-shell RCs.

=

= 0

A

G0

p2=mA2

Hollik, Fortsch. Phys. 38, 165 (1990).

δβ (and δCA)

[sin(β-α)=1, mH+=mA=mH(=mΦ) andmΦ2-M2 = (300 GeV)2]

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

tanβ = 1

tanβ = 3

SM

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

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

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

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

Fingerprinting at the tree level

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

- cos(β-α) < 0,
- tanβ = 1, 2, 3 and 4,

Fingerprinting at the 1-loop level

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

- 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.

Fingerprinting at the 1-loop level

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

- cos(β-α) < 0,
- tanβ: Scanned
- mH+ = mA = mH(=mΦ),
- 100 GeV < mΦ < 1 TeV,
- 0 < M < mΦ,
- Unitarity + Vacuum stab.

Fingerprinting at the 1-loop level

Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515

- cos(β-α) < 0,
- tanβ: Scanned
- mH+ = mA = mH(=mΦ),
- 100 GeV < mΦ < 1 TeV,
- 0 < M < mΦ,
- Unitarity + Vacuum stab.

One-loop corrected hZZ coupling

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

Tanβ = 2,

mΦ = 300 GeV

1 - sin2(β - α)

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

the amount of correction is less than 1%.

- Higgs Physics = “Bridge” connecting the SM and New Physics.
- Indirect Search = Comparing fingerprints of the Higgs couplings.
- Typical patterns of deviations in extended Higgs sectors at tree level

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 κVcan be larger than 1.

- Radiative corrections to the Higgs boson couplings

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

can be maximally O(100)%, O(5)% and O(1)%, respectively.

- If 1% deviation in the hZZ couplings is found, we can discriminate

four types of 2HDMby precisely measured hff couplings.

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