The Composite Nambu-Goldstone Higgs Andrea Wulzer Natural or - - PowerPoint PPT Presentation

Andrea Wulzer

The Composite Nambu-Goldstone Higgs

“Is EWSB scale Natural of Fine-tuned?” One sure goal of the LHC is to answer the question:

Natural or Unnatural ?

= New Physics (Top Partners) scale MP

∆ δm2

H

m2

H

' ✓126 GeV mh ◆2 ✓ MP 500 GeV ◆2

“Is EWSB scale Natural of Fine-tuned?” One sure goal of the LHC is to answer the question:

Natural or Unnatural ?

= New Physics (Top Partners) scale MP

∆ δm2

H

m2

H

' ✓126 GeV mh ◆2 ✓ MP 500 GeV ◆2

Optimistic view:

∆

MP [TeV]

0.5

1

1 4

“Is EWSB scale Natural of Fine-tuned?” One sure goal of the LHC is to answer the question:

Natural or Unnatural ?

= New Physics (Top Partners) scale MP

∆ δm2

H

m2

H

' ✓126 GeV mh ◆2 ✓ MP 500 GeV ◆2

Optimistic view:

∆

MP [TeV]

0.5

1

1 4

Pessimistic view:

∆

MP [TeV]

0.5

1

1 4

“Is EWSB scale Natural of Fine-tuned?” One sure goal of the LHC is to answer the question:

Natural or Unnatural ?

= New Physics (Top Partners) scale MP

∆ δm2

H

m2

H

' ✓126 GeV mh ◆2 ✓ MP 500 GeV ◆2

Optimistic view:

∆

MP [TeV]

0.5

1

1 4

Pessimistic view:

∆

MP [TeV]

0.5

1

1 4

In both cases we will learn something!

Composite Higgs

Composite Higgs scenario:

• 1. Higgs is hadron of new strong force

Corrections to screened above

The Hierarchy Problem is solved

• 2. Higgs is a Goldstone Boson, this is why it is light
• 3. Partial Fermion Compositeness: linear coupling to strong sector

1/lH

mH

Composite Higgs

Composite Higgs scenario:

• 1. Higgs is hadron of new strong force

Corrections to screened above

The Hierarchy Problem is solved

• 2. Higgs is a Goldstone Boson, this is why it is light
• 3. Partial Fermion Compositeness: linear coupling to strong sector

1/lH

mH

Composite Higgs

Composite Higgs scenario:

• 1. Higgs is hadron of new strong force

Corrections to screened above

The Hierarchy Problem is solved

• 2. Higgs is a Goldstone Boson, this is why it is light
• 3. Partial Fermion Compositeness: linear coupling to strong sector

1/lH

mH

Higgs Br. Ratios Higgs Production c

• O(v2

/ f 2)20% ⇥

A) Corrections to SM: B) New Non-ren. Couplings: e.g. Double His

gg → hh

Indirect effects from sigma-model couplings Indirect, but “direct” (robust) signature of compositeness

Composite Higgs

Composite Higgs scenario:

• 1. Higgs is hadron of new strong force

Corrections to screened above

The Hierarchy Problem is solved

• 2. Higgs is a Goldstone Boson, this is why it is light
• 3. Partial Fermion Compositeness: linear coupling to strong sector

1/lH

mH

Composite Sector Elementary Sector

fL, fR

W 1,2,3

µ

, Bµ

Lint

gauge: fermions:

Lint =gJµW µ Lint =yLqLOL+yRqROR

Composite Higgs

Low energy Higgs physics from symmetries

Lπ = f2 4 di

µdµ iπ = 1

2(@h)2 + g2 4 f2 sin2 h f ✓ |W|2 + 1 2c2

w

Z2 ◆

=i g2 4 v p 1 − ξ gHV V

ξ ⌘ v2 f 2 =sin2 hhi f

Composite Higgs

Low energy Higgs physics from symmetries

Lπ = f2 4 di

µdµ iπ = 1

2(@h)2 + g2 4 f2 sin2 h f ✓ |W|2 + 1 2c2

w

Z2 ◆

=i g2 4 v p 1 − ξ gHV V

ξ ⌘ v2 f 2 =sin2 hhi f c = p 1 − ξ

c = 1 − 2ξ √1 − ξ

MCHM4

MCHM5

MCHM10

. . .

=i mf v c Fermion couplings are less sharply predicted. Do depend on fermionic operator representations

Composite Higgs

A rough comparison with data:

courtesy of R.Torre

Higher order effects, from resonances exchange, should be also taken into account

OL,R ↔ QL,R h0|O|Qi 6= 0

Top Partners

In the IR, fermionic operators correspond to particles:

and carry color !

O Q Q = “vector-like colored fermions”

(partners)

OL,R ↔ QL,R h0|O|Qi 6= 0

Top Partners

In the IR, fermionic operators correspond to particles:

and carry color !

O Q Q = “vector-like colored fermions”

(partners)

Lmass =m∗

QQQ + y fqQ

|SMni=cos φn|elementaryni + sin φn|compositeni |BSMni=cos φn|compositeni sin φn|elementaryni

tan φn = yf m∗

Q

physical particles are partially composite

gives a mass-mixing in the IR:

Lint =yLqLOL+yRqROR

Top Partners

|SMni=cos φn|elementaryni + sin φn|compositeni

yf =

P.C. generates Yukawas ... ... and the Higgs Potential Top loop dominate because the top is largely composite.

Top Partners

Top partners cancel divergence, thus are directly bounded by Naturalness

∆ δm2

H

m2

H

' ✓125 GeV mH ◆2 ✓ MP 400 GeV ◆2

mH SUSY: light stops Composite Higgs: light fermionic partners

Top Partners

Top partners cancel divergence, thus are directly bounded by Naturalness

∆ δm2

H

m2

H

' ✓125 GeV mH ◆2 ✓ MP 400 GeV ◆2

mH

Q=2/3

Q=5/3

MCHM4,5,10

ξ = 0.2

Ξ0.2 1 2 3 4 5 6 1 2 3 4

: (low tuning) In a class of explicit CH models

mH ∈ [115, 130]

Light Higgs plus Low Tuning need Light Partners

(Matsedonsky,i Panico, AW 2012)

Top Partners

Top partners cancel divergence, thus are directly bounded by Naturalness

∆ δm2

H

m2

H

' ✓125 GeV mH ◆2 ✓ MP 400 GeV ◆2

mH Light Higgs plus Low Tuning need Light Partners

(Matsedonsky,i Panico, AW 2012)

Ξ0.1 1 2 3 4 5 6 1 2 3 4

Q=2/3

Q=5/3

MCHM4,5,10

In a class of explicit CH models : (larger tuning)

ξ = 0.1

mH ∈ [115, 130]

Top Partners

Fourplet of custodial SO(4) ✓ T X5/3 B X2/3 ◆

B T X2/3 X5/3

Spectrum: Couplings:

V t X ∼ MX/f

because Goldstones are derivatively coupled

Singlet of custodial

Unlike e e T

W

Unlike e e T

sizeable coupling to bottom quark

SO(4) b

Top Partners

single prod. with t model dep. coupling pdf-favoured at high mass comparing production rates:

(14 TeV LHC)

600 800 1000 1200 1400 1600 1800 2000 1 10 100 1000

M @GeVD Σ @fbD

Three possible production mechanisms

QCD pair prod. model indep., relevant at low mass

X X X t X

single prod. with b favoured by small b mass dominant when allowed

b

e T

Top Partners

Ξ0.2 1 2 3 4 5 6 1 2 3 4

Current limits (rough):

Q=2/3

Q=5/3

ξ = 0.2

Top Partners

Current limits (rough):

Ξ0.1 1 2 3 4 5 6 1 2 3 4

Q=2/3

Q=5/3

ξ = 0.1

Top Partners

Current limits, simplified model approach:

X5ê3êB excl . charge 2ê3 excl . Theoretically excl . x = 0.2 c = 0 c = 1ê 2 s=8 TeV L d20 fb-1 0.5 1.0 1.5 2.0 0.2 0.4 0.6 0.8 1.0 m 5ê3 HTeVL sin fL

Top Partners

Current limits, simplified model approach:

X5ê3êB excl . charge 2ê3 excl . Theoretically excl . x = 0.1 c = 0 c = 1ê 2 s=8 TeV L d20 fb-1 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0 m 5ê3 HTeVL sin fL

Top Partners

Projections, simplified model approach:

H X5ê3êB excl . charge 2ê3 excl . Theoretically excl . x = 0.1 c = 0 c = 1ê 2 s=13 TeV L =20 fb-1 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0 m 5ê3 HTeVL sin fL

Top Partners

Projections, simplified model approach:

H

X5ê3êB excl . charge 2ê3 excl . Theoretically excl . x = 0.05 c = 0 c = 1ê 2 s=13 TeV L =100 fb-1 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0 m 5ê3 HTeVL sin fL

Conclusions and Outlook

• Composite Higgs is the perfect benchmark for present

and future studies of Higgs couplings modifications

• Direct searches win over coupling determinations
• Important playground for (Un-)Naturalness tests from

fermionic Top Partner searches

• Much to be learned (on both) from the 13 TeV run!

Backup

Reach on CH vectors

500 1000 1500 2000 2500 3000 3500 1 2 3 4 5

eVD gV

Model B

theoretically excluded

V>lvu V>WZ>jj V>WZ>2lv EWPT H.L.S. model

(arXiv:1109.1570)