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

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

Academia Sinica, Mar. 7, 2014

Yagyu, Kei ( 柳生慶 ) National Central U.

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

Collaboration with Shinya Kanemura and Mariko Kikuchi (U. of Toyama)

2

Cavity Radiation

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.

Wien’s Low (1896)

Rayleigh-Jeans Low (1900)

Exp.

Wien’s Low

Rayleigh-Jeans Low

3

Cavity Radiation

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.

Exp. ~ Planck’s Low

Wien’s Low

Rayleigh-Jeans Low

Planck’s Low (1905)

4

Paradigm Shift

Classical Theory

-Newton Dynamics-Maxwell Electromagnetism Planck’s Low

Einstein’s Light Quantum Hypothesis

Early 20th century

Cavity Radiation gave a “Bridge” connecting Classical Theory and Quantum Theory.

Quantum Theory

- Nuclear Physics- Particle Physics, …

Cavity Radiation

5

Gauge SectorG, W, Z, γ

Matter SectorQuarks & Leptons

Higgs SectorHiggs mechanism Yukawa interaction

Today

Gauge interaction

We have the Standard Model.

6




Today

Gauge interaction


Well tested before the LHC

7




Today

Gauge interaction


8




Today

Gauge interaction


The LHC has found a Higgs boson with 126 GeV

9




Today

Gauge interaction


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

10

Next Paradigm Shift

New PhysicsStandard Model

Higgs Sector

EWSB

Today

Higgs Physics could give a next “Bridge” connecting the Standard Model and New Physics!

11

Three Questions

1. What is the true structure of the Higgs sector?

-Minimal or Non-minimal?

2. What is the dynamics behind the Higgs sector?

- Weak coupling or Strong coupling

3. How is the Higgs sector related to the phenomena

beyond the SM? - Neutrino oscillation, Dark matter, and Baryon asymmetry.

12

Three Questions

1. What is the true structure of the Higgs sector?

-Minimal or Non-minimal?

2. What is the dynamics behind the Higgs sector?

- Weak coupling or Strong coupling

3. How is the Higgs sector related to the phenomena

beyond the SM? - Neutrino oscillation, Dark matter, and Baryon asymmetry.

126 GeV Higgs

Explained

Minimal (1 doublet)

EW data,Flavor, …

13

ExtraSingletsDoubletsTriplets…

126 GeV Higgs

Explained

Minimal (1 doublet)

EW data,Flavor, …

14

Non-Minimal Higgs sectors

126 GeV Higgs

Introduce



Minimal (1 doublet)

New Physics ModelsNeutrino mass, Dark matter and Baryon asymmetry

Explained

EW data,Flavor, …

15

126 GeV Higgs

Determine

Higgs prop.

Determine



Minimal (1 doublet)

Neutrino mass, Dark matter and Baryon asymmetry

EW data,Flavor, …

16

New Physics Models

126 GeV Higgs

New Physics ModelsNeutrino mass, Dark matter and Baryon asymmetry

Determine

Higgs prop.

Determine



Minimal (1 doublet)

Bott

om u

p Ap

proa

ch!

EW data,Flavor, …

17

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

EnergyEnergy

18

Measuring effects on the 126 GeV Higgs boson

126 GeVh

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

2. Indirect search1. Direct search

H++, H+, H, A, …

DiscoveryMeasuring 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

EnergyEnergy

19

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

hhhMake a “Fingerprint” from precise measurements.

Minimal Singlet Models2HDMsTriplet Modelsetc…

Compare

20

Experiments Theory

Higgs coupling measurements

21κV

κ F

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

Scaling factors

ATLAS-CONF-2013-034 CMS-PAS-HIG-13-005

Higgs coupling measurements

22κV

κ F

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

Scaling factors

ATLAS-CONF-2013-034 CMS-PAS-HIG-13-005

1

1.2

1.4

0.8

0.6The uncertainties for κF and κV are about ±40% and ±20%, respectively.

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)

23

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

24

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

25

　 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

26

1. Electroweak rho parameter

　 Basic ConstraintsThere 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 Y1 01/2 1/23 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 27

2. Flavor Changing Neutral Current (FCNC)Tree level FCNC process should be absent. In general, multi-doublet extensions cause FCNC at the tree level

　 Basic ConstraintsThere are two guidelines to restrict Higgs sectors.

28

B0 Φ0B0

B0 Φ0B0

2. Flavor Changing Neutral Current (FCNC)Tree level FCNC process should be absent. In general, multi-doublet extensions cause FCNC at the tree level

　 Basic Constraints

Only one Higgs doublet couples to each fermion.

29

There are two guidelines to restrict Higgs sectors.

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]

30

Hisano, Tsumura, PRD87 (2013)Kanemura, Kikuchi, KY, PRD88 (2013)

Two mixing angles

Mixing between CP-even states

VEVs

where

T: isospin, Y:hypercharge

31

Yukawa

Gauge

Deviations in hff and hVV

Φ

f

fφ

α

Yf = mf /<Φ> <φ> β

ΦV

V<Φ>

φ

V

V

<φ>

α

β

32

Yukawa

Gauge

Higgs Singlet Model (φ=S)

Φ

f

fS

α

Yf = mf /<Φ> <S>

ΦV

V<Φ>

α

★ The singlet VEV does not contribute to the EWSB. → β=∞ (<Φ>=246 GeV)

★ The hff and hVV couplings are universally suppressed.

33

S

<S>

Yukawa

Gauge

Two Higgs Doublet Model (φ=D)

Φ (D)

f

fD (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

34

Yukawa

Gauge

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

Φ

f

fΔ

α

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

35

Ex. GM model: ξ = 2*sqrt(6)/3 Septet model : ξ = 4

SM

36

SM

κF’

37

SM

κF’

κF = κF’

38

SM

κF’

κF = κF’

39

40

Gauge vs Yukawa

Singlet Model2HDM (Type-I)Georgi-Machacek Model [ξ = 2*Sqrt(6)/3]

Gauge vs Yukawa

-π/4 < α < +π/4 0.1 < tanβ < 100

Singlet Model2HDM (Type-I)Georgi-Machacek Model [ξ = 2*Sqrt(6)/3]

41

　 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

42

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)

…

43

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.

44

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

u

d

Φ ２

e

Φ １

ud

Φ ２

e

u

d

Φ ２

eΦ １

Type-I Type-II (MSSM)

ud

Φ ２

eΦ １

Type-X(Leptophilic)

Type-Y(Flipped)

Aoki, Kanemura, Tsumura, KY (2008)

Four Yukawa InteractionsUnder the Z2 symmetry, two doublets are transformed as Φ1 → +Φ1 and Φ2 → -Φ2.

45

We define the Higgs basis by introducing β

tanβ = <Φ2>/<Φ1>

Mass Eigenstates

NG bosons Charged Higgs

CP-even Higgs CP-odd Higgs

SM-like Higgs boson w/126 GeV46

ξu ξd ξe

Type-I cotβ cotβ cotβType-II cotβ -tanβ -tanβType-X cotβ cotβ -tanβType-Y cotβ -tanβ cotβ

Yukawa/Gauge Interaction

hV

V= (SM) × sin(β-α)

h

f

f

= (SM) × [sin(β-α)+ξf cos(β-α)]

47

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

48

Φ = H±, A, H

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]

49

Decoupling/SM-like Limit

Excluded

by unitarity

(mH = mA = mH+= M =)

10% dev.

1% dev.

0.1% dev.

cos(β-α) > 0

cos(β-α) < 0

50

δ =


Excluded

by unitarity

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 =

51


Excluded

by unitarity

(mH = mA = mH+= M =)

10% dev.

1% dev.

0.1% dev.

cos(β-α) > 0

cos(β-α) < 0

δ =

52

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.

ud

cotβe

Type-I

ud

cotβe

-tanβType-II

ud

cotβe

-tanβType-X

ud

cotβ

e-tanβ

Type-Y

53

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.

ud

cotβe

Type-I

ud

cotβe

-tanβType-II

ud

cotβe

-tanβType-X

ud

cotβ

e-tanβ

Type-Y

54

Bottom vs Tau

κV2 = 0.99, 0.95,

(δ ~ 0.005, 0.02)cos(β-α) < 0

55

• 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

1-loop level

56

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.

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. 57

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

SMSM

SM

Top mass ： mt = ytv Scalar boson mass ： mφ

2 = 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.,

58

The hhh coupling @1-loop in the 2HDM

Φ = H, A, H±

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

59


Φ = H, A, H±

In the case with M2 >> λv2,

we can see the decoupling behavior.


0

60


Φ = H, A, H±


~1

In the case with M2 < λv2,

nondecoupling effects (quartic power of the masses)appear.

61

Renormalized hff vertices Renormalized hff vertex

Renormalized scale factor at on-shell

The counter term contribution

62

Parameter Shifts

Fermion masses and wave functions

CP-even Higgs sector and mixing angle β

The VEV


63

On-shell Renormalization Conditions

= 0h Hp2=mh2

h H p2=mH2=

h h p2 =mh2= 0

f f p2=mf2= 0 f 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).

64

1PI + C.T.

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

2-M2 = (300 GeV)2]

SM

Shinya Kanemura, Mariko Kikuchi and KY, PLB731, 2014

65

tanβ = 1tanβ = 3

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

66


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

67


Fingerprinting at the tree level

cos(β-α) < 0, tanβ = 1, 2, 3 and 4,

68


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.

69



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

stab.

70



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

stab.

Shinya Kanemura, Mariko Kikuchi and KY, arXiv: 1401.0515

71

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

72

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 κV can 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 2HDM by precisely measured hff couplings.

Summary

73

Documents

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