Kei Yagyu - Osaka University · 2019. 6. 19. · Kei Yagyu 2019, 18thJune, Osaka U Collaboration with S. De Curtis, L. DelleRose (U. of Florence), S. Moretti (U. of Southampton),

Strong dynamics as an origin of the light Higgs boson and BSM phenomena

Kei Yagyu

2019, 18th June, Osaka U

Collaboration with S. De Curtis, L. Delle Rose (U. of Florence),

S. Moretti (U. of Southampton), R. Nagai (ICRR → U. of Padua)

1

Meet Joe Black

A story about a Death (死神)

Directed by Martin Brest, 1998

People knows his name, voice and face,

but does not really know “who he is”….

2

Meet Higgs boson

We know the mass, spin and parity

of the Higgs boson, but do not know

“who Higgs is”.

In 2012

In the Standard ModelThe Higgs boson is introduced as an elementary scalar field Φ(x).

Assuming μ2 < 0 and λ > 0, we obtain the

“wine bottle” type potential.

In the Standard ModelThe Higgs boson is introduced as an elementary scalar field Φ(x).

Assuming μ2 < 0 and λ > 0, we obtain the

“wine bottle” type potential.

ｙψL

ψR

v

g2V

V

v

v

λh

h

v

v

The SM Higgs sector works well to describe

the origin of masses,

but it is just a parametrization of the EWSB

in the economical way….

Questions in the SM Higgs sector

What is the origin of the negative μ2?

What is the origin of Yukawa couplings?

What is the true structure of the Higgs sector?

Questions in the SM Higgs sector

What is the origin of the negative μ2?

What is the origin of Yukawa couplings?

What is the true structure of the Higgs sector?

Why can the Higgs boson be so light?

Energy

100 GeV 1019 GeV

Higgs boson mass

mh

Planck

Λ = 1 TeV → c = 1 (say 100 %)

Λ = 10 TeV → c = 0.01 (1 %)

Λ = 1019 GeV → c = 10-32 (10-30 %)

EW

Energy

100 GeV 1019 GeV

Higgs boson mass

mh MP

103-4 GeV

BSM（No Λ2）

Scalar boson (Supersymmetry) : Chiral Symmetry

Fermion (Compositeness) : Chiral Symmetry

Gauge boson (Gauge-Higgs Unification): Gauge Symmetry

Higgs is

To know “who is the Higgs boson” is to know what is the BSM!!

Plan of Talk

I. Introduction

II. Composite Higgs Models

- Higgs as a pseudo Nambu-Goldstone boson (pNGB)

- Minimal Composite Higgs Model

III. CHMs with Non-Minimal Higgs Sectors

IV. Summary

Nambu-Goldstone bosons

Global symmetry breaking︓G → H

G

H

Rotation:

Broken generators︓

Nambu-Goldstoneʼs theorem:

One broken generator corresponds to

one massless NG boson Rotation by UNGB

Are there any NGBs as physical degrees of freedom in Nature?

Energy

Λ=4πf

f

q q

π

ρ1 GeV

0.1 GeV

9/35

Pion and Composite Higgs Georgi, Kaplan (1984)Contino, Nomura, Pomarol (2003)

QCD（no scalar）

G = SU(2)L × SU(2)R

H = SU(2)V

Non-pert. effects

Energy

Λ=4πf

f

q q

π

ρ1 GeV

0.1 GeV

×1000

9/35

Pion and Composite Higgs

QCD（no scalar）

Georgi, Kaplan (1984)Contino, Nomura, Pomarol (2003)

Energy

1 TeV

0.1 TeV

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

×1000

9/35


H

Non-pert. effects

G

QCD（no scalar）


Energy

1 TeV

0.1 TeV

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

×1000

No discovery, Exc. by EWPT

☹

9/35


QCD（no scalar）


H

Non-pert. effects

G

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

×10000

9/35


10 TeV

1 TeV

Too heavy

☹Heavy enough

☺

QCD（no scalar）


H

Non-pert. effects

G

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ

QCD（no scalar）

1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

×10000

9/35


10 TeV

1 TeV

0.1 TeV v ~ f/4π

Vacuum Misalignment


H

Non-pert. effects

G

Mrazek et al, NPB 853 (2011) 1-48

G [dim] H [dim] Higgs sector

SO(5) [10] SO(4) [6] Φ

SO(6) [15] SO(5) [10] Φ + S

SO(6) [15] SO(4)×SO(2) [7]SU(5) [24] SU(4)×U(1) [16] Φ + ΦʼSp(6) [21] Sp(4)×SU(2) [13]

SU(5) [24] SO(5) [10] Φ + Δ + Setc

Agashe, Contino, Pomarol (2005)

16/35

G

H

G

f

vEM

The structure of the Higgs sector is determined by the coset G/H.

H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry.

The number of NGBs (dimG-dimH) must be 4 or lager.

Explicit breaking of G must be introduced.

Basic Rules for the Construction

sm

Minimal Composite Higgs Model

G/H = SO(5)/SO(4): 4NGBs SO(4) ≃ SU(2)L × SU(2)R

SU(2)L × SU(2)R

TΦ transforms as the SU(2) bidoublet

10 SO(5) generators:


10 6

NGB Matrix

Linear Rep.

Minimal Composite Higgs Model

Kinetic Lag.

Higgs couplings

Gauge boson mass

Custodial symmetry!


Higgs Potential

Due to the shift symmetry of the NGB, the Higgs potential is 0 at any order of perturbation. → Higgs boson is massless.

We need to introduce an explicit breaking of G. → Higgs becomes pseudo-NGB with a finite mass.

Explicit breaking can be introduced via partial compositeness mechanism.Kaplan, PLB365, 259 (1991)

Elementary sector（SM particles） Strong sector particles

Linear mixing

Potential =

Vacuum misalignment

The Higgs potential is written as

Vacuum condition (Vʼ = 0)

GeV4

Vacuum missalignment

The Higgs potential is written as

Vacuum condition (Vʼ = 0)

Higgs Mass (Vʼʼ)

The light Higgs boson is naturally explained by an O(1) coefficient.

α and β can be predicted from strong dynamics.

Structure of the CHMs

Elementary Sector Strong Sector

Mixing

Partial CompositenessGsm = SU(2)L×U(1)Y

G → H

Integrate ρ and ψ out

G

SM particles are embedded

SO(5)×U(1)X Model︓Fermion SectorDe Curtis, Redi, Tesi, JHEP04 (2012) 042


Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X SO(5)×U(1)X

SO(4)×U(1)X

Σ

We take SO(5) ５-plet for the fermion representation.

X=2/3X=2/3

4=2×2

1

4=2×2

1



Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X SO(5)×U(1)X

SO(4)×U(1)X

Σ


X=2/3X=2/3

(+ LL-term + RR-term)

2-site model

Effective Lagrangian︓Fermion Sector

The Higgs potential can be calculated as

Effective Potential

(+ LL-term + RR-term)

Higgs boson mass

Lightest extra fermion mass [GeV]

f = 800 GeV, mρ = 2.5 TeV

De Curtis, Redi, Tesi, JHEP04 (2012) 042

Plan of Talk

I. Introduction

II. Composite Higgs Models

- Higgs as a pseudo Nambu-Goldstone boson (pNGB)

- Minimal Composite Higgs Model

III. CHMs with Non-Minimal Higgs Sectors

IV. Summary

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ

QCD（no scalar）

1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

9/35


10 TeV

1 TeV

0.1 TeVv ~ f/4π


SO(4)

SO(5)

SU(2)V

SU(2)L × SU(2)R

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ

QCD（no scalar）

1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

9/35


10 TeV

1 TeV

0.1 TeVv ~ f/4π


K, η

SO(4)

SO(5)

SU(3)V

SU(3)L × SU(3)R

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ

QCD（no scalar）

1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

9/35


10 TeV

1 TeV

0.1 TeVv ~ f/4π


K, η

H, H±, …Hʼ

Gʼ

SU(3)V

SU(3)L × SU(3)R

Energy

ψ ψ

h

W ,̓ Zʼ?

Energy

Λ=4πf

f

q q

π

ρ

QCD（no scalar）

1 GeV

0.1 GeV

Λ=4πf

f

QCD-like Th.

9/35


10 TeV

1 TeV

0.1 TeVv ~ f/4π


K, η, …

H, H±, …

・Higgs phenomenology

・Neutrino masses・Dark matter ・Baryon asymmetry (CPV)

S. De Curtis, R. Nagai and KY (in progress)

S. De Curtis, L. Delle Rose, S. Moretti and KY

1803.01865 (PLB) & 1810.06465 (JHEP)

Mrazek et al, NPB 853 (2011) 1-48

G [dim] H [dim] Higgs sector

SO(5) [10] SO(4) [6] Φ

SO(6) [15] SO(5) [10] Φ + S

SO(6) [15] SO(4)×SO(2) [7]SU(5) [24] SU(4)×U(1) [16] Φ + ΦʼSp(6) [21] Sp(4)×SU(2) [13]

SU(5) [24] SO(5) [10] Φ + Δ + Setc


16/35

G

H

G

f

vEM

The structure of the Higgs sector is determined by the coset G/H.

H should contain the custodial SO(4) ≃ SU(2)L×SU(2)R symmetry.

The number of NGBs (dimG-dimH) must be 4 or lager.

Explicit breaking of G must be introduced.

Basic Rules for the Construction

sm

Composite 2HDM（C2HDM）

SO(6) generators (15): (A=1-15, a=1-3, a=1-4)^

6 SO(4) 1 SO(2) 8 Broken

G→H: SO(6) × U(1)X → SO(4) × SO(2) × U(1)X

NGB Mat.:

2 Higgs Doublets

De Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph] (PLB)

15-plet︓

Setup for C2HDM

We introduce SO(6) 6-plet fermions for the explicit Lagrangian:

Z2-like symmetry in the strong sector can be introduced.

C2 symmetry(to avoid FCNCs) C2 = diag(1,1,1,1,1,-1)

Setup for C2HDM

Z2-like symmetry in the strong sector can be introduced.

C2 symmetry(to avoid FCNCs) C2 = diag(1,1,1,1,1,-1)

1. Unbroken case, 2. Spontaneously broken case and 3. Hardly broken case(there is no option for the softly-breaking)

We introduce SO(6) 6-plet fermions for the explicit Lagrangian:

CP-Violation

CP-violation in the strong sector

Yukawa interactions Higgs potentialCorrelations

EDMs Higgs couplings & decays

test test

S. De Curtis, R. Nagai and KY (work in progress)

T parameter SO(6)/SO(4)×SO(2) model

f > O(10 TeV) for O(1) tanβ, α and arg(v2).

O(10-3)

Aμ: SO(6) adjoint gauge boson, Σ: SO(6) adjoint pNGB

SO(9)/SO(8) model Aμ: SO(9) adjoint gauge boson, Σ: SO(9) 9-plet pNGB

S. De Curtis, R. Nagai and KY (work in progress)

With CP-conservation

The effective potential is formally written as

Effective Potential

Gauge loop contributions

No EWSB and no Z2 breaking.

+ O(Φ6)

The effective potential is formally written as

+ O(Φ6)

Effective Potential

Fermion loop contributions

m12 and m2

2 can be negative → EWSB.

Typical Prediction of Mass Spectrum

h ~ 125 GeV

H±, H, A

f ~ TeV

Ψ, ρμ

E

Y1: C2 breaking term

Typical Prediction of Mass Spectrum

h ~ 125 GeV

H±, H, A

f ~ TeV

Ψ, ρμ

E

Y1: C2 breaking term

★f ∞ : All extra Higgses are decoupled (elementary) SM limit

★To get M≠0, we need C2 breaking (Yukawa alignment is required).

Correlation b/w f and mADe Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph]

Correlation b/w mA and κV (= ghVV/ghVVSM)

MSSM: FeynHiggs v2.14.1

De Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph]

Summary

The CHMs are one of the attractive candidates for new physics to

naturally explain the light Higgs mass.

The Higgs potential is predicted by setting a strong sector Lagrangian.

Non-minimal CHMs can be applied to explain BSM phenomena.

Rich phenomenological consequences are obtained which can be quite

different from the other scenarios such as SUSY, E2HDMs, and so on.

49

Slide from M. Peskin @HPNP2015

50

Slide from Csaba Csaki

51

Slide from Csaba Csaki

Correlation b/w mA and mass differencesDe Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph]


SO(5)×U(1)X Model︓Gauge sectorDe Curtis, Redi, Tesi, JHEP04 (2012) 042


Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X

U1

SO(5)L ×SO(5)R → SO(5)V (10 NGBs)~1

SO(5) → SO(4) (4 NGBs)~Σ0

SO(5)×U(1)X

SO(4)×U(1)X

Σ2

14 NGBs = 10 massive ρ and 4 pNGB Higgs

SO(5)×U(1)X Model︓Gauge sectorDe Curtis, Redi, Tesi, JHEP04 (2012) 042


Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X

U1

SO(5)×U(1)X

SO(4)×U(1)X

Σ2

＋ A-ρ mixing

Effective Lagrangian︓Gauge sector

2-site model

Expand at p2 ~ 0

S, T parameterPanico, Wulzer, arXiv:1506.01961

Contribution from modified Higgs couplings (1-loop)

Here, Λ = mρ = 3 TeV

ξ = v2/f2 <

ξ = v2/f2

ξ < 0.05 @2σ (0.08 @3σ) f < 1.1TeV @2σ (870 GeV @3σ)

S, T parameterPanico, Wulzer, arXiv:1506.01961

Contribution from heavy resonances

yL = ΔL/f , m : lightest fermion partner mass

G1 × G2 × G3

U1(15=7+8) Σ2(8)GVʼ(gauged)

GVH [SO(4)×SO(2)]

Gi : Global SO(6)

8 + 8(Φ1, Φ2)

mixed

Gauge Sector Lagrangian

7 + 8 NGBs are absorbed into the longitudinal components of gauge bosons of adj[SO(6)].

De Curtis, Redi, Tesi, JHEP04 (2012) 042

59

Naïve Dimensional Analysis

General 2 Higgs Doublet Model

SM + one additional iso-doublet scalar︓Φ1 + Φ2

Physical Higgs bosons︓８－３=5 : H± , A , H, h (125 GeV)

Most general Higgs potential under SU(2)L×U(1)Y

Charged CP-odd CP-even

2 VEVs:

General 2 Higgs Doublet Model

SM + one additional iso-doublet scalar︓Φ1 + Φ2

Physical Higgs bosons︓８－３=5 : H± , A , H, h (125 GeV)

Most general Higgs potential under SU(2)L×U(1)Y with softly-broken Z2 +CPC

Charged CP-odd CP-even

2 VEVs:

m2 and λ can be determined by new physics dynamics, e.g., λ ~ g2 in SUSY.

Effective Lagrangian

Integrating out the heavy degrees of freedom (ρA and ψ6), we obtain the effective low energy Lagrangian

≔ G ≔ K

Effective Lagrangian

Integrating out the heavy degrees of freedom (ρA and ψ6), we obtain the effective low energy Lagrangian

≔ G ≔ K

These coefficients can be expanded as

c1, c2, … are determined by strong parameters.

Matching Conditions

We need to reproduce the top mass and the weak boson mass.

g2 Vsm2 ~ (246 GeV)2

Yt



Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X

U1

SO(5)×U(1)X

SO(4)×U(1)X

Σ2


X=2/3X=2/3

4=2×2

1

4=2×2

1


Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X

U1

SO(5)×U(1)X

SO(4)×U(1)X

Σ2X=2/3X=2/3

2 flavour case (I, J=1,2) → Minimal choice for

UV div. free potential.

21/35




Gsm = SU(2)L×U(1)Y

SO(5)×U(1)X

U1

SO(5)×U(1)X

SO(4)×U(1)X

Σ2X=2/3X=2/3

21/35



68

なぜデカップリングがSUSYより遅いか。 Βが正でなければならない理由は何か。なぜMT1が軽いところにでるのか。

Q. When the 2HDM is realized as EFT…

Properties of the 2HDM tell us the direction!

SUSY︖ex. MSSM

Composite (pNGB)︖ex. SO(6) → SO(4) × SO(2)

or

f VS tanβ De Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph]

Masses of heavy top partners

C2HDM MSSM

De Curtis, Delle Rose, Moretti, KY, arXiv: 1803.01865 [hep-ph]


Numerical Analysis

Input parameters (to be scanned):

Tadpole conditions: T1 = T2 = 0

165 GeV < mt < 175 GeV

120 GeV < mh < 130 GeV

Documents

Kei Yagyu - Osaka University · 2019. 6. 19. · Kei Yagyu 2019, 18thJune, Osaka U Collaboration with S. De Curtis, L. DelleRose (U. of Florence), S. Moretti (U. of Southampton),