German Particle Physics School Maria Laach - Herbstschule Maria ...

Beyond the 

Standard Model 

German Particle Physics School 

Maria Laach 

Ch!"ophe Grojean 

CERN-TH & CEA-Saclay/IPhT 

( christophe.grojean@cern.ch )

Two decades of experimental successes 

top discovery 

solar and atmospherical neutrino oscillations 

direct CP violation in the K system (ds) (K-long decaying into 2 pions) 

CP violation in the B system (db) 

evidence of an accelerated phase in the expansion of the Universe 

measure of the dark energy/dark matter composition of the Universe 

DRAFT 

These results have strengthened the SM as a successful 

description of Nature at the quantum level ... but 

Christophe Grojean Beyond the Standard Model 2 

Maria Laach, Sept. '10

DRAFT 

... these experimental results also concluded that there is a 

physics beyond the Standard Model. 



Experimental/Theoretical Needs for BSM 

Precisions measurements 

(gμ-2, LR asymmetries etc) 

Neutrinos masses 

Dark matter 

Dark energy 

Matter-antimatter asymmetry 

Inflation 

Stability of Higgs potential 

Fermion mass and mixing 

hierarchies 

Strong CP problem 

Charge quantization & GUT 

Quantization of gravity 

DRAFT 

the LHC won’t answer all these puzzles! 



The questions addressed in these lectures 

we expect new physics to play a crucial role in 

the mechanism of electroweak symmetry breaking (EWSB). 

What is the scale of new physics in the EWSB sector? 

What is the population of this new scale? Which particles? 

Which interactions? 

Identifying the new spectroscopy should allow to decipher the 

organization principle that governs the EWSB sector 

DRAFT 

vector bosons gauge principle 

Higgs/EWSB sector 

↕ 

↕ 


Maria Laach, Sept. '10 

? 

strong dynamics, susy, xdims

1 

2 

3 

4 

First Lecture 

Lecture Outline 

Standard Model and EW symmetry breaking ➲ 

Higgs mechanism ➲ 

EW precision tests ➲ 

Second Lecture 

Higgs as a UV moderator ➲ 

UV behaviour of the Higgs ➲ 

Connections between EWSB and the top sector ➲ 

Third Lecture 

Supersymmetric Higgs(es) ➲ 

DRAFT 

Little Higgs ➲, gauge-Higgs unification ➲, Higgsless ➲ 

New physics & flavour ➲ 

Fourth Lecture 

Composite Higgs models ➲ 



DRAFT 

Standard Model & EW Symm. Breaking 



➲

The Standard Model 

the strong, weak and electromagnetic interactions of the 

elementary particles are described by gauge interactions 

SU(3)CxSU(2)LxU(1)Y 

DRAFT 

elastic scattering event observed by the Gargamelle [Gargamelle Collaboration [10] collaboration, at CERN. Muon ’73] neutrinos enter the 

ble chamber from the right. A recoiling electron appears near the center of the image and travels toward the 



wer of curling branches. 

νμ e - → νμ e - 

e - e - 

νμ 

Z 

νμ



e + 

e - 

e + e - → W + W - 

e + 

e - 

ν 

Z, γ 

W + 

W - 

The Standard Model 


DRAFT 

W + 

W - 



The Standard Model and the Mass Problem 




the masses of the quarks, leptons and gauge bosons 

don’t obey the full gauge invariance 

νe 

e 

 

is a doublet of SU(2)L but 

a mass term for the gauge field isn’t 

invariant under gauge transformation 

mνe 

DRAFT 

spontaneous breaking of gauge symmetry 

≪ me 

δA a µ = ∂µɛ a + gf abc A b µɛ c 



The longitudinal polarization of massive W, Z 

c! c! c! 

a massless particle is never at rest: always possible to distinguish 

(and eliminate!) the longitudinal polarization 

v! 0! 

DRAFT 

the longitudinal polarization is physical for a massive spin-1 particle 

symmetry breaking: new phase with more degrees of freedom 

ɛ = 

 

|p| E 

, 

M M 

 

p 

|p| 

polarization vector grows with the energy 

(pictures: courtesy of G. Giudice) 



The source of the Goldstone's 

symmetry breaking: new phase with more degrees of freedom 

massive W ± , Z: 3 physical polarizations=eaten Goldstone bosons SU(2)LxSU(2)R 

➾ 

Where are these Goldstone's coming from?➾ 

SU(2)V 

what is the sector responsible for the breaking SU(2)LxSU(2)R to SU(2)V? 

with which dynamics? with which interactions to the SM particles? 

H = 

common lore: from a scalar Higgs doublet 

h + 

h 0 

 

Higgs doublet = 4 real scalar fields 

3 eaten 

Goldstone bosons 

One physical degree of freedom 

the Higgs boson 

DRAFT 



PT 

Bounds on (Dangerous) New Physics 

Heavy Particles ➾ new interactions for SM particles 

broken symmetry operators scale Λ 

B, L (QQQL)/Λ 2 10 13 TeV 

flavor (1,2 nd family), CP ( ¯ ds ¯ ds)/Λ 2 1000 TeV 

flavor (2,3 rd family) mb(¯sσµνF µν b)/Λ 2 50 TeV 

DRAFT 

At colliders, it will mγ be difficult < 6 × 10to find direct evidence 

of new physics in these sectors... 

−17 eV 

m W ± = 80.425 ± .038 GeV 

mZ 0 = 91.1876 ± .0021 GeV 



New Physics in the EW sector 

(H † σ a H)W a µνB µν /Λ 2 

H † DµH 2 /Λ 2 

Λ ~ few TeV only 

H † H 3 /Λ 2 

DRAFT 

high potential for direct detection at LHC, ILC !!! 



DRAFT 

Higgs Mechan%m. Standard Model Higgs 



➲

Higgs Mechanism 

Symmetry of the Lagrangian Symmetry of the Vacuum 

SU(2)L × U(1)Y 

Higgs Doublet Vacuum Expectation Value 

H = 

h + 

h 0 

 

DµH = ∂µH − i 

2 

|DµH| 2 = 1 

 

3 gWµ + g ′ Bµ √ 

− 2gWµ 4 g2v 2 W + µ W − µ + 1 

8 

Gauge boson spectrum 

electrically charged bosons 

electrically neutral bosons 

√ 2gW + µ 

−gW 3 µ + g ′ Bµ 

W 3 µ Bµ 

〈H〉 = 

0v√2 

DRAFT 

M 2 W = 1 

Weak mixing angle 

g 

c = √ 

g2 +g ′2 

U(1)e.m. 

γµ = sW 



3 µ + cBµ 

g 

s = 

′ 

√ Mγ =0 

g2 +g ′2 

 

 

H with W ± µ = 1 √ 

2 

g 2 v 2 −gg ′ v 2 

4 g2 v 2 

Zµ = cW 3 µ − sBµ 

−gg ′ v 2 g ′2 v 2 

with v ≈ 246 GeV 

W 3 µ 

W 1 µ ∓ W 2 µ 

B µ 

 

 

M 2 Z = 1 

4 (g2 + g ′2 )v 2

Interactions Fermions-Gauge Bosons 

Gauge invariance says: 

 

T3Li ¯ ψi¯σ µ 

ψi 

L = gW 3 µ 

Going to the mass eigenstate basis: 

Zµ = cW 3 µ − sBµ 

γµ = sW 3 µ + cBµ 

L = g 2 + g ′2 Zµ 

 

not protected by gauge invariance 

corrected by radiative corrections + new physics 

i 

i 

with 

(T3Li − s 2 Qi) ¯ ψi¯σ µ ψi 

+ g ′ Bµ 

DRAFT 

protected by U(1)em gauge invariance 

➾ no correction 

electric charge 



 

c = 

s = 

√ g 2 +g ′2 γµ 

+ gg′ 

e = 

 

i 

√ g 

g2 +g ′2 

g ′ 

√ 

g2 +g ′2 

gg ′ 

 

g2 + g ′2 

yi ¯ ψi¯σ µ ψi 

 

 

Qi ¯ ψi¯σ µ 

ψi 

i 

 

Q = T3L + Y 

= sg = cg′

Rho parameter 

ρ ≡ 

Custodial Symmetry 

M 2 W 

M 2 Z cos2 θw 

= 

1 

4g2 v2 1 

4 (g2 + g ′2 )v2 g 2 

g 2 +g ′2 

Consequence of an approximate global symmetry of the Higgs sector 

 

+ h 

H = 


h0 

 

V (H) =λ H † H − v2 

2 

2 

SU(2)L 

SU(2)R 

is invariant under the rotation of the four real components 

DRAFT 

iσ 2 H ⋆ H = Φ 

SO(4) ∼ SU(2)L × SU(2)R 

V (H) = λ 

2x2 matrix explicitly invariant under 



=1 

Φ † Φ = H † H 

4 

1 

trΦ † Φ − v 2 2 

1 

 

SU(2)L ! SU(2)R

(Zµ γµ) 

 

2 MZ 0 

0 0 

Custodial Symmetry 

〈H〉 = 

0v√2 

Higgs vev 

 

unbroken symmetry in the broken phase 

DRAFT 

ρ = 1 

〈Φ〉 = v √ 2 

The hypercharge gauge coupling and the Yukawa couplings break the custodial SU(2)V, 

which will generate a (small) deviation to ρ = 1 at the quantum level. 



1 

SU(2)L × SU(2)R → SU(2)V 

1 

Wµ,W 2 µ,W 3 

µ transforms as a triplet 

Z µ 

γ µ 

 

1 

 

= W 3 

µ Bµ 

c2M 2 Z −csM 2 Z 

−csM 2 Z 

s 2 M 2 Z 

W 3 µ 

The SU(2)V symmetry imposes the same mass term for all W i thus c 2 M 2 Z = M 2 W 

B µ

ion at(SM) the LHC Higgs Production @ the LHC 

eralities 

eff ∼√s/3 ∼ 5 TeV 

nd 100 fb−1 later 

. 

ls 

ts! 

! (fb) 

10 15 

10 14 

10 13 

10 12 

10 11 

10 10 

10 9 

10 8 

10 7 

10 6 

10 5 

10 4 

10 3 

10 2 

10 

1 

10 -1 

jet ¬ 

! jet 

(E > !s 

T 

! jet (E T 

pp/pp _ 

! tot 

_ ! bb 

/20) 

! W 

! Z 

jet 

> 100GeV) 

jet ¬ 

! jet 

(E > !s 

T 

_ ! tt 

/4) 

! Higgs (M H =150GeV) 

! Higgs (M H =500GeV) 

cross sections 

10 3 

Tevatron 

pp _ 

pp 

7 

LHC 

14 

LHC 

DRAFT 

10 4 

!s ¬ 

(GeV) 

Higgs Physics – A. Djouadi – p.20/47 



(SM) Higgs Production 

3. Higgs 3. production Higgs production at LHC: at LHC: main main processes processes 

Production Production mechanisms mechanisms Cross sections Cross sections at the at LHC the LHC 

Higgs-strahlung 

QQ associated 

production 

Vector boson fusion 

ggs production at LHC: main processes 

n mechanisms Cross sections at the LHC 

Production mechanisms Cross sections at the L 

Gluon fusion 

DRAFT 

There are also subleading processes, gg → HH, etc... 


3. Higgs production at LHC: main processe 

SM Higgs at the Tevatron 

Current experimental information (limits @ 95% CL): 

forward jet tagging 

! ∝1/s: SM LEP Tevatron, direct LHC search: mH>114.4 GeV 

central jet veto 

! SM indirect constraint: mH





QQ associated 

production 

Vector 3. Higgs boson production fusion at LHC: main processes 




∝1/s: Tevatron, LHC 



small hadronic activity 

Gluon fusion 

DRAFT 



(see for instance A. Djouadi, hep-ph/0503172) 


Production mechanisms Cross sections at the LHC 

Higgs production @ LHC 

ISSCSMB ’08, Mugla, 10–18/09/08 Higgs Physics – A. Djouadi – p.23/47 




single final state 

large NLO enhancement 

so subleading processes, ggThere → HH, are also etc... subleading processes, gg → HH, etc... 



(SM) Higgs Decays 

Higgs couples proportionally to masses: 

4. Higgs at the LHC: decay modes 

it decays into the heaviest particle available by phase space 

BRs 

Higgs decays in the SM: 

light Higgs 

H 

H 

H 

• 

• 

• 

f=t,b,c,τ 

¯f 

V=W,Z 

V 

V=W,Z 

V ¯f ∗ 

f 

DRAFT 



g/γ 

• H decays into the heaviest particle 

available by phase space: g ∝ m. 

• MH < ∼ 130 GeV, H → b¯ b 

– H → cc, τ + τ − • 

¯f 

heavy Higgs H f=t,b,c,τ 

• 

H 

, gg = O(few ¯f • %) V 

– H → γγ = O(0.1%) H 

decay into VV below threshold 

• MH > ∼ 

130 GeV, H → WW, ZZ f 

– below threshold decays • 

• t 

possible 

– decays into t¯t for heavy Higgs. 

• t 

• Total Higgs decay width: 

– very small for a light Higgs 

f=t,b,c,τ 

- comparable to mass for heavy Higgs. 

H 

V=W,Z 

H 

• 

V=W,Z H 

V=W,Z 

V=W,Z 

V ¯f ∗ 

decay into massless particles (γ, gluons) at 1-loop 

H 

H 

• 

V 

V ∗ 

¯ f 

f 

g/γ 

g/γ 

g/γ 

g/γ 

Ors 

Orsay, 1

(SM) Higgs Decays 

Higgs couples proportionally to masses: 

4. Higgs at the LHC: decay modes 

it decays into the heaviest particle available by phase space 

BRs 

Higgs decays in the SM: 

light Higgs 

H 

H 

H 

• 

• 

• 

f=t,b,c,τ 

¯f 

V=W,Z 

V 

V=W,Z 

V ¯f ∗ 

f 

DRAFT 



g/γ 

H 

H 

H 

H 

• H decays into the heaviest particle 

available by phase space: g ∝ m. 

• MH < ∼ 130 GeV, H → b¯ b 

– H → cc, τ + τ − heavy Higgs Total width 

, gg = O(few %) 

• 

f=t,b,c,τ 

¯f 

– H → γγ = O(0.1%) 

• MH > V=W,Z 

V ∼ 

• 

130 GeV, H → WW, ZZ 

– below V=W,Z threshold decays possible 

• 

V ∗ 

¯ f 

– decays f into t¯t for heavy Higgs. 

g/γ 

t • Total Higgs decay width: 

• 

g/γ 

light Higgs: narrow – very small for a light Higgs 

heavy Higgs: 

- 

broadOrsay, 

19/12/08 

comparable to mass for heavy Higgs.

(SM) Higgs Searches @ Tevatron 

Low Mass Higgs 

1 high p T lepton 

MET 1 high pT lepton 

ET 

2 b-jets 

2 b-jets 

95%CL Limits at m H = 115 GeV 

Analysis Lum 

(fb-1 Limit ( /SM) 

Higg Mass Higgs 

) Exp. Obs. 

WH l bb (CDF) 2.7 4.8 5.6 

WH l bb (DØ) 2.7 6.4 6.7 

ZH bb (CDF) 2.1 5.6 6.9 

ZH bb (DØ) 2.1 8.4 7.5 

ZH l + l - bb (CDF) 2.7 9.9 7.1 

ZH l + l - bb (DØ) 2.3 12.3 11.0 

SM Low Mass Higgs 

2 high p T leptons 

High MET 

2 high 2 b-jets pT leptons/high 2 ET b-jets 

2 b-jets 

Issues: 

lepton identification 

b-tagging performance 

dijet mass resolution 

Key issues: 

! Lepton identification 

! B-tagging performance 

! Dijet mass resolution 

! Background modeling 

! W/Z+heavy-flavor jets 

! Multijets (ZH bb) 

! All analyses use multivariate 

techniques for signal-to-bckg 

discrimination. 

ZH bb (CDF) 

SM High Mass Higgs 

DRAFT 

ee, , e 

At early stage of selection: 

49 

Best individual channels have expected limits ~5-6xSM 



(SM) Higgs Searches @ the LHC 

What can we measure at 

due to the overwhelming QCD background, need to use clean but rare decay modes 

DRAFT 

With 10fb -1 , the LHC cannot miss a SM Higgs 

If there is a Higgs like particle 



DRAFT 

SM &EW prec%ion data 



➲

TH vs. EXP: SM @ the classical level 

How good is the agreement of the SM with exp. data? 

SM has 3 parameters: g, g' and v (forgetting the fermions) 

several observables 

α (Coulomb potential), GF (µ decay), mZ, mW, (LR asymmetry in Z decay), 

SM 

at the 

classical level 

SM 

at the 

classical level 

s 2 eff 

g, g' and v are extracted from α, GF and mZ 

Γ(Z → l + l − ) 

α =1/137.03599911(46) GF =1.16637(1) × 10 −5 GeV −2 mZ = 91.181876(21) GeV 

v = 

α = e2 

4π 

, e = 

gg ′ 

 

g2 + g ′2 , GF = 1 

√ 

2v2 , m2Z = 1 

4 (g2 + g ′2 )v 2 

DRAFT 

1 

√ 

2GF 

g = 

 

1 − 

 

√ 8πα 

1 − 4πα/( √ 2GF m 2 Z ) 



g ′ = 

 

1+ 

 

√ 8πα 

1 − 4πα/( √ 2GF m 2 Z )






s 2 eff 


and we can predict the values of other observables 

Γ(Z → l + l − ) 

α =1/137.03599911(46) GF =1.16637(1) × 10 −5 GeV −2 mZ = 91.181876(21) GeV 

mW = 1 

DRAFT 



2 gv 

gL = −1/2+s 2 , gR = s 2 ALR = (−1/2+s2 eff )2 − s4 eff 

(−1/2+s2 eff )2 − s4 eff 

Γ(Z → l + l − )= 

√ 

2GF 

6π m3Z(g 2 L + g 2 R) 

s 2 eff = s 2 W = g′2 

g2 + g ′2






s 2 eff 



Γ(Z → l + l − ) 

α =1/137.03599911(46) GF =1.16637(1) × 10 −5 GeV −2 mZ = 91.181876(21) GeV 

m 2 W = 

1 − 

√ −1 

2παGF 

1 − 4πα/( √ 2GF m2 Z ) 

DRAFT 

Γ(Z → l + l − )= 

s 2 eff =1/2 − 

√ 2GF m 3 Z 

12π 

 

1/4 − πα/( √ 2GF m2 Z ) 

 

1/2 − 

1 − 4πα( √ 2GF m2 Z ) 

2 Christophe Grojean Beyond the Standard Model Maria Laach, Sept. '10 

+1/4






s 2 eff 



SM at tree-level 

DRAFT 

experiment (LEPEWWG’05) 

15 σ 120 σ 9 σ 

Γ(Z → l + l − ) 

α =1/137.03599911(46) GF =1.16637(1) × 10 −5 GeV −2 mZ = 91.181876(21) GeV 

mW = 80.938 GeV s 2 eff =0.21215 Γ(Z → l + l − ) = 84.841 MeV 

mW = 80.425 ± 0.034 GeV s 2 eff =0.23153 ± 0.00016 Γ(Z → l + l − ) = 83.992 ± 0.010 MeV 

Christophe Grojean Beyond the Standard Model Maria Laach, Sept. '10

TH vs. EXP: importance of quantum corrections 

Quantum corrections have to be included in the previous analysis 

accuracy in EW data: 1‰ 

mW = mW | SM 

s 2 eff = s2 eff |SM 

Γ l + l − = Γ l + l − | SM 

SM loop corrections: 

Many physicists have devoted 

their lives to compute them. 

Require a deep knowledge of 

all areas of high energy physics 

typical size of EW loops: 

O(g few ‰ 

2 /16π 2 ) ∼ 

new physics corrections: 

O(v 2 /M 2 NP) 

 

 

tree + ∆mW SM 

loop + ∆mW |New Physics 

tree + ∆s2 

 

eff SM 

loop + ∆s2 eff |New Physics 

 

 

tree + ∆Γ l + l − 

DRAFT 

Test of SM: 

Are these NP comtributions 

needed to fit EW data? 



SM 

loop + ∆Γ l + l − |New Physics

∆Γll = − 

TH vs. EXP: EW fit - II 

Usually, EW fits don’t use 

∆mW |NP, ∆s 2 eff|NP , ∆Γ l + l − |NP 

instead introduce perverse linear combinations S, T, U 

∆mW = − αmW 

4(c2 0 − s20 ) S + αc20mW 2(c2 0 − s2 αmW 

T + 

0 ) 8s2 0 

∆s 2 α 

eff = 

4(c2 0 − s20 ) S − αc20s 2 0 

c2 0 − s2 T 

0 

2(1 − 4s2 0)αΓ0 

ll 

8(1 − 4s 

S + 1+ 

) 2 0)s2 0c2 0 

(1 + (1 − 4s 2 0 )2 )(c 2 0 − s2 0 

DRAFT 



U 

(1 + (1 − 4s 2 0 )2 )(c 2 0 − s2 0 ) 

 

αΓ 0 ll T

0.0005 

∆Γll 0.002= 

− 

Out[125]= 

0.001 

∆Γll 

0.000 

Γll 

0.001 

0.002 

0.0000 

TH vs. EXP: EW fit - II 

Usually, EW fits don’t use 


instead introduce perverse linear combinations S, T, U 

∆s2 eff 

s2 eff 

0.0000 

0.0005 

0.0010 

∆mW = − 

mtop=171.4 GeV 

αmW 

4(c2 0 − s20 ) S + αc20mW 2(c2 0 − s2 αmW 

T + 

0 ) 8s2 0 

∆s 2 α 

eff = 

4(c2 0 − s20 ) S − αc20s 2 0 

c2 0 − s2 T 

0 

2(1 − 4s2 0)αΓ0 

ll 

8(1 − 4s 

S + 1+ 

) 2 0)s2 0c2 0.5 

0.0015 

m =171.4 GeV 

top 

0.4 

0.3 

0 

0.2 

(1 + (1 − 4s 2 0 )2 )(c 2 0 − s2 0 

0.0005 

∆mW 

mW 

DRAFT 

0.0010 



T 

0.1 

−0.1 

−0.2 

U 

(1 + (1 − 4s 2 0 )2 )(c 2 0 − s2 0 ) 

0 

100 

from scalars 

68 % CL 

95 % CL 

95% CL 

68% CL 

m EWPT,eff 

500 

from cutoff 

from fermions? 

 

−0.3 

−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 

S 

αΓ 0 ll T

Oblique Parameters 

are useful to perform a EW fit 

but cumbersome to compute explicitly in a given model 


S,T (and U) are directly related to the Lagrangian 

(=friendly objects for theorists) 

oblique parameters=modified propagators of W ± and Z 

L = W µ 

+ Π+−(p 2 ) W− µ + 1 µ 

2W 3 Π33(p 2 ) W3 µ + W µ 

3 Π3B(p 2 ) Bµ + 1 

2Bµ ΠBB(p 2 S =4s 

) Bµ 

2 w S/αem ≈ 119 S, T = T/αem ≈ 129 T , U = −4s 2 w U/αem ≈−119 U 

S = g 

Coefficients Dim. 6 Operators SU(2)c SU(2)L 

g ′ Π ′ 3B (0) OWB = (H † τ a H)W a µν Bµν/gg ′ + − 

DRAFT 

T = 1 

M 2 (Π33(0) − Π+−(0)) OH = |H 

W 

† DµH| 2 − − 

U = Π ′ +− (0) − Π′ 33 (0) dim. 8 − − 

 

′′ Π 33(0) − Π ′′ +−(0) 

 

 

dim. 10 − − 

V = M 2 W 

X = M 2 W 

S =4s 2 

2 w S/αem ≈ 119 S, T = T/αem ≈ 129 T , U = −4s 2 w U/αem ≈−119 U 

2 Π′′ 3B 

(0) dim. 8 + − 

Y = M 2 W Π ′′ BB (0) OBB = (∂ρBµν) 2 /2g ′2 + + 



unitary 

gauge 

S & T from higher dimensional Operators 

exercise 

L = (g2 + g ′2 )v4 Z 2 µ 

16Λ 2 

L = 1 

Λ2 ➩ ➩ 

we need to write observables in terms of α, GF and mZ 

DRAFT 

➩ 

T measured the deviation to ρ=1: 

 

H † DµH 2 

2 mZ = 1 

4 (g2 + g ′2 )v2 + 1 

8Λ2 (g2 + g ′2 )v4 m 2 W 

∆mW = 

1 = 4g2 v2 s 2 eff = g′2 

c 2 0mW 

4 √ 2(c 2 0 − s2 0 )GF Λ 2 

g 2 + g ′2 

∆Π33 = − g2 v 4 

∆s 2 −s 

eff = − 

2 0c2 0 

2 √ 2(s2 0 − c20 )GF Λ2 ρ = 



m2W c2 W m2 Z 

≈ 1+αT 

8Λ 2 

1 

T = − 

2 √ 2αGF Λ2 } 

1 

T = − 

2 √ 2αGF Λ2

S & T from higher dimensional Operators 

exercise 

L = 1 

unitary 

gauge 

L = − kinetic mixing ➩ 

v2 

2Λ2 BµνW 3 µν ∆Π ′ 30 = − v2 

Z = 

γ = 

because of the kinetic mixing, the Z 

and the γ are not obtained from the 

usual weak rotation from W3 and B 

g 

g 2 + g ′2 

g ′ 

g 2 + g ′2 

 

1 − gg′ 

 

1+ 

g 2 + g ′2 

g 3 

v2 

Λ 2 

v2 

g ′ (g2 + g ′2 ) Λ2 W3 − 

W3 − 

m 2 Z = 1 

4 (g2 + g ′2 

) 1+ 

g ′ 

g 2 + g ′2 

 

g 

1 − 

g2 + g ′2 

 

1 − gg′ 

Λ 2 H† WµνHBµν 

g 2 + g ′2 

v2 

B 

the definition of the electric charge 

is also affected (check that the γ still 

couples to Q=T3L+Y) 

DRAFT 

expressing mW in terms of α, GF and mZ, we arrive at 

g ′3 

2gg ′ 

√ 

2(g2 + g ′2 )Λ2 Λ 2 

g(g2 + g ′2 ) Λ2 v2 

B 



e = 

∆mW = − s! c! mW 

√ 

2(c " 

! − s " 

! )Λ" 

➩ 

Λ 2 

➩ 

gg ′ 

 

g2 + g ′2 

S = 

S = 

 

1 − gg′ 

4s0c0 

√ 

2αGF Λ2 g 2 + g ′2 

4s0c0 

√ 

2αGF Λ2 v 2 

Λ 2

EW Precision Measurements & Higgs Mass 

The SM 1-loop corrections are computed for a reference Higgs mass. 

A variation of the Higgs mass can be seen as a contribution to S and T. 

Higgs contribution 

δS = 1 

δT = − 3 

➾ constraints on the Higgs mass 

12π log m2 h 

m 2 h0 

16π c 2 log m2 h 

m 2 h0 

DRAFT 

The SM Higgs cannot get too heavy 

unless there exist other 

(tuned) contributions to S and T 

−0.3 

−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 

S 



T 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

−0.1 

−0.2 

mtop=171.4 m =171.4 GeV 

top GeV 

mH 

100 

100 

from scalars 

68 % CL 

95 % CL 

95% CL 

68% CL 

m EWPT,eff 

500 

500 

from cutoff 

from fermions?

T 




0.5 

0.4 

0.3 

0.2 

0.1 

0 

−0.1 

−0.2 

mtop=171.4 m =171.4 GeV 

top GeV 

mH 

100 

100 

from scalars 

68 % CL 


95 % CL 

95% CL 

68% CL 

m EWPT,eff 

DRAFT 

500 

500 

from cutoff 

from fermions? 

−0.3 

−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 

S 

Is the Higgs R 

• Standard Model with a li 

fit to all data, indirect de 






2 

" ! 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

LEP 95% CL 

Tevatron 95% CL 


Theory uncertainty 

G fitter SM 

DRAFT 

Fit including theory errors 

Fit excluding theory errors 

50 100 150 200 250 300 

M 

H 

Mar 09 

[GeV] 

3# 

2# 

1# 

100 150 200 250 300 



2 

" ! 

12 

10 

8 

6 

4 

2 

0 

LEP exclusion at 95% CL 

Tevatron exclusion at 95% CL 

Theory uncertainty 

G fitter SM 

Fit including theory errors 

Fit excluding theory errors 

Figure 1: Dependence on MH of the ∆χ2 function obtained from the global fit of the SM 

parameters to precision electroweak data [ 3], excluding (left) or including (right) the results 

from direct searches at LEP and the Tevatron. 

M 

H 

Mar 09 

[GeV] 

3# 

2# 

1#

only SM particles 

+ 

SM Higgs 

➾ 

all Higgs couplings 

fixed 

➾ 

SM Higgs & EW fits 

Quite a good fit to EW precision data... but 

best fit obtained for a Higgs mass already 

excluded by direct search 

tension between leptonic and hadronic 

asymmetries 

Is the Higgs R 

• Standard Model with a l 

fit to all data, indirect de 

MH < 186 GeV 

DRAFT 

Chanowitz ’08 



& 

leptonic asym. 

hadronic asym.

σ (e + e − → hZ) 

A SM-like Higgs with modified BRs 

SM-like=unitarity properties unchanged 

σSM 

Direct exclusion bound 

is very sensitive to Higgs BR’s 

Suppressing SM BR’s to 20% 

allows for a Higgs around 90 GeV 

For a light Higgs, it is very easy to 

modify Higgs BR’s without modifying 

its couplings to SM particles 

a light Higgs can decay only to light SM 

particles, light particles to which it couples 

weakly (eg. coupling to b quark is only ~1/60) 

DRAFT 

new particles with mild couplings to the Higgs 

will significantly affect Higgs BR’s 

ΓZ ∼ 1000 × ΓH(mH = 115 GeV) 

easy to modify Higgs BR’s 

without destroying EW data 



A SM-like Higgs with modified BRs 

Many physics-motivated models: 

MSSM: 

NMSSM: 

h → χχ → 6q/2l4q/4l2ν 

h → aa → 2b2 ¯ b/4τ/4g 

Little Higgs/Composite Higgs (SO(6)/SO(5)): 

Many signatures-motivated models: Higgs=portal to New Sector 

New sector with string-like confinement: “Quirks” 

New sector with QCD-like confinement: “Hidden valleys” 

DRAFT 

New sector = CFT, ie no confinement: “Unparticles” 

h → ! ! 

Harnik, Luty 

Strassler, Zurek 

Georgi 

(courtesy: J. Terning, talk @ Aspen’09) 



Higgs Mechanism: a model without dynamics 

Why is EW symmetry broken ? 

Because µ 2 is negative 

Why is µ 2 negative ? 

Because otherwise, EW symmetry won’t be broken 

V (h) = 1 

2 µ2h 2 + 1 

4λh4 DRAFT 

The Higgs mechanism is a description of EWSB. It is not an 

explanation. No dynamics to explain the instability at the origin. 



H = 

h + 

h 0 

 


3 eaten 

Goldstone bosons 

One physical degree of freedom 

the Higgs boson 

DRAFT 

Higgs as a UV moderator 



➲

Indeed a massive 

spin 1 particle has 

3 physical polarizations: 

Why do we need a Higgs ? 

The W and Z masses are inconsistent with the known particle 

content! Need more particles to soften the UV behavior of 

massive gauge bosons. 

µ 

ikµx 

Aµ = ɛµ e 

ɛ µ ɛµ = −1 k µ ɛµ =0 

DRAFT 



with 

2 transverse: 

1 longitudinal: 

( in the R-ξ gauge, the time-like polarization ( ) is arbitrarily massive and decouple ) 

Bad UV behavior for 

the scattering of the longitudinal 

polarizations 

ɛ µ ɛµ =1 k µ ɛµ = M 

k µ =(E,0, 0,k) 

kµk µ = E 2 − k 2 = M 2 

ɛ µ 

WL 

WL 

=(k M 

ɛ µ 

1 

ɛ µ 

2 

, 0, 0, E 

= (0, 1, 0, 0) 

= (0, 0, 1, 0) 

M 

WL 

WL 

) ≈ kµ 

M 

+ O( E 

M )


Bad UV behavior for 

the scattering of the longitudinal 

polarizations 

A = ɛ µ 

(k)ɛν (l) ig2 (2ηµρηνσ − ηµνηρσ − ηµσηνρ) ɛ ρ 

DRAFT 

A = g 

2 E4 

4M 4 W 

violations of perturbative unitarity around E ~ M 

(p)ɛσ (q) 



WL 

WL 

k µ 

l ν 

p ρ 

q σ 

WL 

WL

+ 

W + W + 

W - 

W + W + 

W - 

γ, Z 0 

h 0 


W - 

W - 

W + W + 

W - 

W + W + 

DRAFT 

W - 

The Higgs boson unitarize the W scattering 

(if its mass is below ~ 700 GeV) 

h 0 

W - 

WL scattering = pion scattering 

Goldstone equivalence theorem 

Aµ → Aµ + ∂µɛ 



A = g 2 

A = g 2 

A = g 2 

A = −g 2 

A = −g 2 

A = −g 2 

A = g 2 

A = g 2 

A = g 2 

E 

E 

E 

MW 

MW 

E 

E 

MW 

MW 

MW 

 

MH 

MH 

 

2MW MH 

2MW 

2MW 

Christophe Grojean Beyond the Standard Model 53 X 


W - 

W + W + 

W - 

γ, Z 0 

W - 

MW 

E 

2 

2 

2 

+ 

2 

2 

2 

2 

2 

2 

Lewellyn Smith ‘73 

Dicus, Mathur ‘73 

Cornwall, Levin, Tiktopoulos ‘73

massive W, Z 

Higgs as UV moderator 

massless W, Z gauge invariance 

low energy 

large distance 

Puzzle: 

compatiblity between 

high and low energy 

high energy 

small distance 

A ∝ g 2 E 2 /M 2 

non sense 

DRAFT 



massive W, Z 

Higgs as UV moderator 

massless W, Z gauge invariance 

low energy 

large distance 

Higgs 

mechanism 

high energy 

small distance 

A ∝ g 2 E 2 /M 2 

non sense 

DRAFT 



Physics Beyond the Higgs? 

Is the Standard Model with a Higgs a UV finite theory? 

i.e. valid to arbitrarily high energies 

Of course, the SM will fail around the Planck scale 

but the real question is 

Is there any reason to think there is new physics 

between the weak scale and the Planck scale? 

DRAFT 



DRAFT 

UV behavi&r of ' Higgs boson 



➲

Quantum Behavior of the Higgs 4 Coupling (I) 

= 

V (h) =− 1 

2 dλ 

16π 

d ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 

8g′4 + 3 

4g′2 g 2 + 9 

8g4 − 6y 4 t + 

Large mass (λ dominated RGE) 

Higher loops 

Small Yukawa 

DRAFT 

16π 

2 dλ 

d ln Q 

= 24λ2 

λ increases with Q: IR-free coupling 

λ(Q) = 

2 µ2h 2 + 1! 

4 

h4 

vev: v 2 = µ 2 /λ mass: m 2 H =2λv 2 



m 2 H 

2v2 − 3 

2π2 m2 H ln(Q/v)

Quantum Behavior of the Higgs 4 Coupling (II) 

2 dλ 

16π 

d ln Q = 24λ2 − (3g ′2 +9g 2 − 12y 2 t )λ + 3 

8g′4 + 3 

4g′2 g 2 + 9 

8g4 − 6y 4 t + 

( 

16π 

2 dyt 

d ln Q 

= 9 

Small mass (yt dominated RGE) 

16π 

2 dλ 

d ln Q 

λ decreases with Q. 

Higher loops 

Small Yukawa 

= −6y4 

2 y3 t + y 2 (Q) = 

Higher loops 

Small Yukawa 

DRAFT 

λ(Q) =λ0 − 

3 

8π2 y4 0 ln Q 

1 − 9 

16π2 y2 0 



! 

y 2 (Q0) 

1 − 9 

16π2 y2 (Q0) ln ! 

Q0 

ln Q 

Q0 

) ! 0

Figure 6: Summary of the uncertainties connected to the bounds on MH. The up- 

per solid area indicates the sum of theoretical uncertainties in the MH upper bound 

when keeping mt = 175 GeV fixed. The cross-hatched area shows the additional 

DRAFT 

uncertainty when varying mt from 150 to 200 GeV. The upper edge corresponds to 

Higgs masses for which the SM Higgs sector ceases to be meaningful at scale Λ (see 

text), and the lower edge indicates a value of MH for which perturbation theory is 

certainly expected to be reliable at scale Λ. The lower solid area represents the the- 

oretical uncertaintites in the MH lower bounds derived from stability requirements 

[30, 31, 32] using mt = 175 GeV and αs =0.118. 

Only a light Higgs (160 GeV

survival 

collapse 

[GeV] 

H 

M 

350 

300 

250 

200 

150 

$ = # 

LEP exclusion 

at >95% CL 

$ = 2# 

blow-up 

Perturbativity bound 

Stability bound 

Finite-T metastability bound 

Zero-T metastability bound 

Shown are 1" 

error bands, w/o theoretical errors 

Tevatron exclusion at >95% CL 

100 

4 6 8 10 12 14 16 18 

log ( ! / GeV) 

DRAFT 

Figure 2: The scale Λ at which the two-loop RGEs drive the quartic SM Higgs coupling 

non-perturbative, and the scale Λ at which the RGEsEllis, createEspinosa, an instability Giudice, in the Hoecker electroweak & Riotto ’09 

vacuum (λ < 0). The width of the bands indicates the errors induced by the uncertainties 

in mt and αS (added quadratically). The perturbativity upper bound (sometimes referred to 

as ‘triviality’ bound) is given for λ = π (lower bold line [blue]) and λ =2π (upper bold line 

Only a light Higgs (130 GeV

Solution to the Higgs 4 Coupling Instabilities 

find a symmetry such that 

the Higgs quartic will inherit the good UV asymptotically free 

behavior of the gauge coupling 

supersymmetry 

λ ≡ g 2 

Examples of such symmetry: 

DRAFT 

gauge-Higgs unification: the Higgs is identified as a component of 

the gauge field along some extra-dimensions. 



Quantum Instability of the Higgs Mass 

so far we looked only at the RG evolution of the Higgs quartic coupling (dimensionless 

parameter). The Higgs mass has a totally different behavior: it is higly dependent on the 

UV physics, which leads to the so called hierarchy problem 

= 

h W ± Z 

h h 

 

d 4 k 

(2π) 4 

h h 

 

1 

k2 − m 

2 ∝ Λ2 

m 2 H ∼ m 2 0 − (115 GeV) 2 

Higher loops 

Smaller Yukawa 

DRAFT 



top 

h h 

d 4 k 

(2π) 4 

Λ 2 

400 GeV 

k2 (k2 − m2 ) 

2 

+ 

2 ∝ Λ2


Λ = 1 TeV 

= 

h W ± Z 

h h 

 

d 4 k 

(2π) 4 

h h 

 

1 

k2 − m 

2 ∝ Λ2 

20000 

Higher loops 


DRAFT 

-20000 

-40000 

GeV 

Christophe Grojean Beyond the Standard Model Maria Laach, Sept. '10 

2 

physical 

bare 

top 

W 

Z 

-60000 

-80000 

Higgs 

66 

0 

40000 

top 

h h 

d 4 k 

(2π) 4 

k2 (k2 − m2 ) 

m 2 H ∼ m 2 0 − (115 GeV) 2 

+ 

2 ∝ Λ2 

Λ 2 

400 GeV 

2


= 

Λ = 10 TeV 

h W ± Z 

h h 

 

d 4 k 

(2π) 4 

h h 

 

1 

k2 − m 

2 ∝ Λ2 

2000000 

DRAFT 

-2000000 

-4000000 

physical 

bare 

top 

W 

Z 

-6000000 

-8000000 

GeV 

Christophe Grojean 

Higgs 

Beyond the Standard Model Maria Laach, Sept. '10 

2 

67 

0 

6000000 

4000000 

top 

h h 

d 4 k 

(2π) 4 

k2 (k2 − m2 ) 

m 2 H ∼ m 2 0 − (115 GeV) 2 

+ 

2 ∝ Λ2 

Higher loops 


Λ 2 

400 GeV 

2

1 

2 

3 

Beyond the Higgs: The hierarchy problem 

need new degrees of freedom to cancel Λ 2 divergences 

and ensure the stability of the weak scale 

h W ± Z 

h h 

add a sym. such that a Higgs mass is forbidden until this sym. is broken 

supersymmetry 

[Witten, ’81] 

gauge-Higgs unification 

[Manton, ’79, Hosotani ’83] 

Higgs as a pseudo Nambu-Goldstone boson 

lower the UV scale 

[Georgi-Kaplan, ’84] 

DRAFT 

large extra-dimension 

1032 species 

remove the Higgs 

technicolor 

h h 

[Dvali ’07] 

top 

h h 

[Arkani-Hamed-Dimopoulos-Dvali, ’98] 

[Weinberg ’79, Susskind ’79] 

m 2 H ∼ m 2 0 − (115 GeV) 2 

Λ 2 

400 GeV 



2

DRAFT 

Symmet!es for a natural EWSB 



How to Stabilize the Higgs Potential 

Goldstone’s Theorem 

spontaneously broken global symmetry massless scalar 

The spin trick 

a particle of spin s: 

... but the Higgs has sizable non-derivative 

couplings 

2s+1 polarization states 

...with the only exception of a particle moving at the 

speed of light 

... fewer polarization states 

Spin 1 Gauge invariance no longitudinal polarization 

Spin 1/2 

DRAFT 

Chiral symmetry only one helicity 

... but the Higgs is a spin 0 particle 

m=0 



Symmetries to Stabilize a Scalar Potential 

Supersymmetry 

Higher Dimensional 

Lorentz invariance 

fermion ~ boson 

Aµ ∼ A5 

4D spin 1 4D spin 0 

gauge-Higgs 

unification models 

DRAFT 

These symmetries cannot be exact symmetry of the Nature. 

They have to be broken. We want to look for a soft breaking in 

order to preserve the stabilization of the weak scale. 



➾ 

[Manton ’79, Fairlie 79, Hosotani ’83 +...]

Ghost symmetry 

Other symmetries? 

SM particle ~ ghost 

[Grinstein, O’Connell, Wise ‘07] 

It was known since Pauli-Villars that ghosts can soften the UV 

behavior of the propagators. But they are unstable per se. 

Lee-Wick in the 60’s proposed a trick to stabilize the ghosts (at 

the price of of a violation of causality at the microscopic scale). 

DRAFT 



DRAFT 

Connections between EWSB and Top physics 



➲

1 

Why should (P.) Higgs care about the top? 

It might help him getting a Nobel prize! 

Direct probe of the Higgs/EWSB sector 

stants can be determined in a model–independent way. This is crucial in e 

mass generation mechanism for elementary particles and very useful to expl 

yond the SM. For instance, radion-Higgs mixing in warped extra dimensiona 

reduce the magnitude of the Higgs couplings to fermions and gauge bosons in a 

[56, 57] and such effects can be probed only if absolute coupling measuremen 

Another example is related to the electroweak baryogenesis scenario to expl 

number of the universe: to be successful, the SM Higgs sector has to be exte 

a strong first-order phase transition and the change of the Higgs potential c 

servable effects in the triple Higgs coupling [111, 112]. Finally, the loop induc 

photonic decay channels are sensitive to scales far beyond the Higgs mass and 

particles that are too heavy to be produced directly [113]. 

top=heaviest fermion, i.e., largest coupling to the Higgs boson 

controls the Higgs production 

Coupling Mass Relation 

DRAFT 

1 10 

Mass (GeV) 

100 



Coupling constant to Higgs boson 

1 

0.1 

0.01 

c 

! 

b 

W Z 

FIGURE 2.16. The relation between the Higgs couplings and the particle masses as dete 

high–precision ILC measurements [4]; on the y axis, the coupling κi of the particle i 

defined in a such a way that the relation mi = vκi with v 246 GeV holds in the SM. 

2.3 THE HIGGS BOSONS IN SUSY THEORIES 

H t





QQ associated 

production 

Vector boson fusion 




Gluon fusion 

DRAFT 




SM Higgs at the Tevatron 

Current experimental information (limits @ 95% CL): 


! ∝1/s: SM LEP Tevatron, direct LHC search: mH>114.4 GeV 


! SM indirect constraint: mH





QQ associated 

production 

Vector 3. Higgs boson production fusion at LHC: main processes 




∝1/s: Tevatron, LHC 



small hadronic activity 

Gluon fusion 

DRAFT 



(see for instance A. Djouadi, hep-ph/0503172) 


Production mechanisms Cross sections at the LHC 

Higgs production @ LHC 





single final state 

large NLO enhancement 

so subleading processes, ggThere → HH, are also etc... subleading processes, gg → HH, etc... 



1 






Hierarchy problem 

m 2 H = m 2 Hbare − 3GF Λ 2 

4 √ 2π 2 

2 

2mW + m 2 Z + m 2 H − 4m 2 t 

DRAFT 



1 







Indirect probe of the Higgs/EWSB sector 

EW precision data 

δS = 1 

δT = − 3 

12π log m2 h 

16π c 2 W 

m 2 h0 

DRAFT 

log m2 h 

m 2 h0 

+ 1 

+ 

6π log m2t m2 Z 

3 

16πs 2 W c2 W 

m 2 t 

m 2 Z 

160 

10 10 2 

Excluded 



m t [GeV] 

200 

180 

July 2010 

High Q 2 except mt 68% CL 

m H [GeV] 

m t (Tevatron) 

10 3

1 









top rare decays and anomalous couplings 

flavour physics, CP violation 

LHC≈1 tt pair/s 

DRAFT 

sensitive to rare decays with BR~10 -(6÷7) 

t Zc, Hc, γc, gc 10 -13 ÷10 -10 for SM 

channel 95%CL sensitivity on BR @ LHC14TeV 

10 fb -1 

t Zq t γq t gq 

3.1x10 -4 4.1x10 -5 1.3x10 -3 

[ATLAS coll. ’07] 



1 





iggs production at LHC: main processes 


on mechanisms Hierarchy problem Cross sections at the LHC 

3 



top rare decays and anomalous couplings 

flavour physics, CP violation 

Behind the scene 

g 

g 

DRAFT 

tt+jets (large) background to many searches 

t 

t 

b 

b 

ttH NLO cross section @ LHC14TeV 

mH [GeV] 

σ [fb] 

120 150 180 

634-719 334-381 194-222 

Top @ LHC v 

[Moch et al., ’08+’09] 

[Dawson et al., ’03] 



4 



Mass [GeV] 

600 

500 

400 

300 

200 

100 

0 

2 4 6 8 10 12 14 16 18 

Log (Q/1 GeV) 

10 

DRAFT 

Sharing the front stage with the Higgs boson 

[Martin hep-ph/9709356] 

sleptons 

squarks 

radiative EWSB triggered but top loop, e.g., susy, little Higgs, composite Higgs 

a reasonable approximation, the entire mass spectrum in minimal supergravity models is determined 

by only five unknown parameters: m 

Christophe Grojean Beyond the Standard Model Maria Laach, Sept. '10 

2 0 , m1/2, A0, tan β, and Arg(µ), while in the simplest gaugemediated 

supersymmetry breaking models one can pick parameters Λ, Mmess, N5, 〈F 〉, tan β, and 

81 

H d 

H u 

M 2 

M 1 

M 3 

(µ 2 +m 0 

Figure 7.4: RG evolution of scalar and gaugino mass parameters in the MSSM with typical minimal 

supergravity-inspired boundary conditions imposed at Q0 =2.5 × 1016 GeV. The parameter µ 2 + m2 Hu 

runs negative, provoking electroweak symmetry breaking. 

m 1/2 

m 0 

2 ) 1/2

4 



mHiggs [GeV] 

 

 

 

 

 

DRAFT 

Sharing the front stage with the Higgs boson 

 

 

 

 

LEP 

stable 

[Espinosa, Giudice & Riotto ’07] 

metastable 

 

mtop [GeV] 

unstable 

Figure 2: Lower bounds on Mh from absolute stability (upper curves) and T = 0 metastability 

(lower curves). The width corresponds to αs(MZ) = 0.1176 ± 0.0020 (with the higher 

curve corresponding to lower αs) and we do not show the uncertainty from higher-order 

effects, which we estimate to be below 2–3 GeV. The horizontal line is the LEP mass bound. 

radiative EWSB triggered but top loop, e.g., susy, little Higgs, composite Higgs 

dictating the destiny of the Universe: (meta)stability of EW vaccum 



(Composite) Top Sector 

could the right-handed top belong to the strong sector too? 

ctyt 

f 2 |H|2 ¯qL ¯ HtR + icR 

f 2 H† DµH¯tRγ µ tR + c4t 

(composite left-handed top/bottom gives rise to 

a too large mass difference of neutral B mesons) 

f 2 ( tRγ ¯ µ tR)(¯tRγµtR) 

Modified top-quark couplings to h and Z 

ght¯t = gmt 

 

1 − 

2mW 

v2 

f 2 

 

ct + cy + cH 

 

2 

 

gZtR¯tR = −2g sin2 

θW 

1 − 

3 cos θW 

3 v 

cR 

2 

f 2 

 

8 sin 2 θW 

DRAFT 

gg → ¯tth h → ! ! 

htt can be measured through and 

ILC accuracy with √s=800 GeV and L=1000fb -1 : 5% 



ing to learn from 

Composite top: pair production 

ment at the LHC? 

he 12% gg channel uncertainty is only very roughly @ Tevatron constrained!!! 

e might have missed some big and important NP 

ffect connected with an gg initial state (such a scalar...). 

DRAFT 

ow can we study such effects in a model independent 

ay? 

[Degrande, Gerard, Grojean, Maltoni & Servant, to appear] 

Fabio Maltoni 

30 15 0 

4 

4 2 0 2 4 



c V 1TeV 2 

4 

2 

0 

2 

0 

g h1TeV 2 

15 

30 

large deviations allowed @ LHC 

green: Tevatron constraints, blue: mtt distribution 

Tevatron is dominated (85%) by qq production 

LHC is dominated (90%) by gg production 

➾ 

room for large departure from SM result 

➾ 

➾

Conclusions 

Why do we expect to find a Higgs? 

1. discovery already announced to journalists and politics 

2. simplest parametrization of EWSB 

3. unitarity of WW scattering amplitude 

4. EW precision tests 

Why do we expect more than the Higgs? 

1. dark matter and matter-antimatter asymmetry 

new physics not necessarily coupled to SM 

2. triviality 

3. stability 

4. naturality ➲ 

} 

new physics might be heavy if the Higgs is light 

new physics has to be light if the Higgs is light 

DRAFT 

new particles/symmetries are expected to populate the TeV scale 

to trigger the breaking of the EW symmetry 

what is the organization principle that governs this new sector? 



DRAFT 

Supersymmet!c Higgs(es) 



➲

SUSY has good assets: 

gauge coupling unification, 

The Goodies of SUSY 

radiative EWSB, 

As Top and W Mass Measurements 

DM candidate(s), 

become more precise, 

no oblique corrections: R-parity the MSSM ➲ one-loop sector effects getting only... 

more and more favorable 

Within the SM 

- M H = 76+33-24 

- M H < 144 GeV @ 9 

• SM is “ruled out” 

standard deviation 

DRAFT 

Tension between indirect bounds on MH in the SM and direct search limit 



The not so Goodies of SUSY 

SUSY need new (super)particles that haven’t been seen yet 

SUSY (at least MSSM) predicts a very light Higgs 

V =(|µ| 2 + m 2 Hu ) 

0 

H 

u 

2 +(|µ| 2 + m 2 Hd ) 

0 

Hd tree-level 

2 − B(H 0 uH 0 d + c.c.)+ g2 + g ′2 

m 2 h = m 2 Z cos 2 2β 

m 2 Z/2 =−µ 2 + m2Hd − m2Hu tan2 β 

tan2 β − 1 

excluded 

DRAFT 



8 

H 

0 u 

2 − 

0 

H 

d 

22

The not so Goodies of SUSY 

SUSY need new (super)particles that haven’t been seen yet 

SUSY (at least MSSM) predicts a very light Higgs 

V =(|µ| 2 + m 2 Hu ) 

0 

H 

u 

2 +(|µ| 2 + m 2 Hd ) 

0 

Hd one-loop level 

2 − B(H 0 uH 0 d + c.c.)+ g2 + g ′2 

m 2 h ≈ m 2 Z cos 2 2β + 3GF m4 t √ 

2π2 log m2˜t m 2 Z/2 =−µ 2 + m2Hd − m2Hu tan2 β 

tan2 β − 1 

mH > 115 GeV mt > 1 TeV 

fine-tuned 

DRAFT 

δm 2 Hu = −3√ 2GF m 2 t m 2 ˜t 

4π 2 

requires some fine-tuning O(1%) in mZ 



~ 

log Λ 

m˜t 

m 2 t 

8 

H 

0 u 

2 − 

0 

H 

d 

22 susy 

little hierarchy 

problem

Solving the susy little hierarchy pb 

Various proposals on the market: 

singlet extensions of the Higgs sector: NMSSM and friends 

gauge extensions with new non-decoupled D-terms: 

low scale susy breaking mediation (Λ~100 TeV) 

double protection: (super-little) Higgs as a Goldstone boson 

add higher dimensional terms: BMSSM 

WBMSSM = λ1 

... your own model? 

Birkedal, Chacko, Gaillard ’04 + O(20) papers 

Dine, Seiberg, Thomas ’07 

M (HuHd) 2 + λ2 

M Zsoft(HuHd) 2 ) 

Fayet ’76 + O(500) papers 

Batra, Delgado, Kaplan, Tait ’03 + O(10) papers 

DRAFT 

allow for much lighter susy particles 

window for MSSM baryogenesis extended and more natural 

LSP can account for DM relic density in larger region of parameter space 



DRAFT 

Li)le Higgs 



➲

Little Higgs Models 

Higgs as a pseudo-Nambu-Goldstone boson 

QCD: π + , π 0 are Goldstone associated to 

αem → 0,mq → 0 

LxR exact 

EW pions 

mπ =0 

αtop → 0, g, g ′ → 0 

exact global sym. 

mH =0 

αem = 0 

m 2 π ± ≈ αem 

αtop = 0 

m 2 H ≈ αtop 

...too low ! 

DRAFT 

Little Higgs = PNGB + Collective Breaking 

m 2 H ≈ αiαj 

4π Λ2 QCD 

4π Λ2 strong 

(4π) 2 Λ2 strong 

[Arkani-Hamed et al. ‘02] 

SU(2)L × SU(2)R 

SU(2)isospin 

would require 

Λstrong ∼ 1 TeV 



2x2 symmetric 

Littlest Higgs: SU(5)/SO(5) 

Σ → UΣU t 〈Σ〉 = 

Goldstone parameterization: 

〈Σ〉 = 

⎛ 

⎝ 

gauge symm. 

SU(2)L 

SU(2)R 

12 

1 

⎛ 

⎝ 

12 

⎞ 

⎠ 

⎛ 

⎝ 

12 

SO(5) unbroken symmetry 

SU(3) unbroken global sym. 

DRAFT 

⎛ 

⎝ 

2 × 2 

2 × 2 

1 × 1 

1 × 1 

2 × 2 

2 × 2 

⎞ 

⎠ 

⎞ 

⎠ 

SU(3) unbroken global sym. 



1 

12 

⎞ 

⎠ UU t =1 

Σ = e 

⎛ 

⎜ 

i⎜ 

⎝ 

H → H + ɛ 

H → H − ɛ 

H φ 

−H † Ht −φ ⋆ −H ⋆ 

⎞ 

⎟ 

⎠ /f 

〈Σ〉 

φ → φ − (Hɛ t + ɛH t )/f 

φ → φ +(Hɛ t + ɛH t )/f

LH = Λ 2 cancelled by same spin partner 

W ± Z 

h h 

g 2 

W ± Z 

H H 

h h 

gauge boson loops cancelled by heavy gauge boson loops 

t, T 

y y 

h h 

t 

DRAFT 



-g 2 

T x T 

h h 

top loop cancelled by heavy toop loop 

Relation among different couplings follows from global sym. 

cancellation of div. occurs only at one-loop 

yf 

− y 

2f

v ∼ f/4π 

Anatomy of Little Higgs models 

f 

4πf 

10 TeV 

1 TeV 

100 GeV 

UV completion 

New particles (W’, Z’,top’...) 

SM particles (Higgs,W,Z...) 

cancellation of Higgs mass Λ 2 divergences 

W,Z loop cancelled by heavy W’, Z’ loops 

DRAFT 

top loop cancelled by heavy top' loop 

Higgs loop cancelled by heavy scalar loops 



DRAFT 

Gau*-Higgs Unification 



➲

How to Get a Doublet from an Adjoint 

Consider a 5D 

gauge symmetry G 

1 

2 

will belong tho the adjoint rep. of G 

The SM Higgs is not an adjoint of SU(2)xU(1), it is a doublet ! 

⎛ 

⎜ 

⎝ 

SU(3) 

H ∼ A a 5 

Consider a bigger gauge group 

G → SU(2)L × U(1)Y 

Adj doublet + other rep. 

SU(2)xU(1) 

DRAFT 

W3 + W8/ √ 3 W1 − iW2 W4 − iW5 

W1 + iW2 −W3 + W8/ √ 3 W6 − iW7 

W4 + iW5 W6 + iW7 −2W8/ √ 3 

Adj 

2 √ 3/2 



⎞ 

⎟ 

⎠

πR 

πR 

y 

Towards a Complete Construction 

so far we haven’t broken any symmetry... we even enlarged the gauge group 

We need to break G down to SU(2)xU(1) 

we can achieve this breaking while compactifying the extra-dimension 

0 

Compactification on a Circle 

φ(x, y) = 

y ∼ y +2πR 

circle: 

φ(y +2πR) =φ(y) 

DRAFT 

5D 

field 

n 

1 

 

ny 

 

√ cos 

2δn0πR R 

wavefunction = 

localization of KK mode 

along the xdim 

φ + n (x) + sin 

 

ny 

 

R 

4D 

Kaluza-Klein modes 

mn = p n y = n 

R 

φ − 

n (x) 



πR 

πR 

y 

−y 

Towards a Complete Construction 

so far we haven’t broken any symmetry... we even enlarged the gauge group 

We need to break G down to SU(2)xU(1) 

we can achieve this breaking while compactifying the extra-dimension 

0 

Compactification on an Orbifold 

Z2 

⤶ 

y ∼ y +2πR 

circle: 

φ(y +2πR) =φ(y) 

orbifold: 

DRAFT 

 

ny 

 

cos 

R 

ny 

 

sin 

R 

y ∼−y 

U=+1: wavefunctions 

U=-1: wavefunctions 

φ(−y) =Uφ(y) U 2 =1 



E 

E 

massless mode 

massless mode

R 

πR 

y 

−y 

0 

⤶ 

Orbifold breaking 

orbifold 

Breaking of gauge group at the end-points of the orbifold 

KK effective theory 

Z2 

U 2 =1 

y ∼−y 

Aµ(−y) =UAµ(y)U † 

A5(−y) =−UA5(y)U † 

at the end-points, the surviving gauge group commute 

with the orbifold projection matrix U 

zero mode: is independent of 

0 π R 

DRAFT 

Aµ = UAµU † 

Aµ 

gauge symmetry breaking 

(+ chiral fermions) 



G 

H0 H0 

Aµ(0) = UAµ(0)U † 

y 

A5 = −UA5U †

SU(3) → SU(2)xU(1) 5D Orbifold Breaking 

massless vectors Aµ Aµ 

[Aµ,U]=0 Aµ = SU(2) × U(1) 

1 

⎛ 

A 

⎜ 

2 ⎜ 

⎝ 

3 µ + A8 / √ 3 A1 µ − iA2 µ 

A1 µ + iA2 µ −A3 µ + A8 µ/ √ ⎞ 

⎟ 

[Aµ,U]=0 

3 

⎟ 

⎠ 

massless scalars A5 A5 

{A5,U} =0 

U = 

⎛ 

⎝ 

−1 

−2A 8 µ/ √ 3 

DRAFT 

A5 = 1 

2 

⎛ 

⎜ 

⎝ 

−1 

1 

A 4 5 + iA 5 5 

A 6 5 + iA 7 5 

A 4 5 − iA 5 5 

A 6 5 − iA 7 5 



⎞ 

⎠ U ∈ SU(3) U 2 =1 

⎞ 

⎟ 

⎠ 

SU(2) × U(1) 

SU(3) 

SU(2) ! × U(1)

Orbifold Projection as Boundary Conditions 

H subgroup 

AH µ (−y) =AH A µ (y) 

H µ (−y) =AH µ (y) 

AH 5 (−y) =−AH A 5 (y) 

H 5 (−y) =−AH 5 (y) 

G/H coset 

A G/H 

(−y) =−A G/H 

A (y) 

G/H 

(−y) =−A G/H 

(y) 

µ µ 

y 

µ 

A G/H 

(−y) =A G/H 

A (y) 

G/H 

(−y) =A G/H 

(y) 

5 5 

πR 

−πR 

y 

5 

by orbifold projection 

DRAFT 

⤶Z2 

which is equivalent to the BCs 

at the fixed points 

which is equivalent to the BCs 

at the fixed points 

∂5A H µ =0 

A H 5 =0 

A G/H 

A G/H 

πR 0 

−y U 2 0 ≈ 

U =1 BC BC 

2 =1 

−y 

G → H 

Z2 

∂5A H µ =0 

A H 5 =0 



µ 

∂5A G/H 

∂5A5 G/H 

5 

πR 0 

=0 

=0

Two examples 

SU(3) 

SU(2)xU(1) SU(2)xU(1) 

0 π R 

(+,+) µ 

(-,-) µ 

: SU(2)xU(1) : SU(3)/SU(2)xU(1) 

(-,-)5 

(+,+)5 

S0(5)xU(1)X 

SU(2)LxU(1)Y SO(4)xU(1)X 

0 π R 

massless Higgs doublet 

DRAFT 

(+,+) µ (-,-) 

: µ 

(-,+) SO(4)xU(1)X 

SU(2)LxU(1)Y : SO(5)/SO(4) µ 

: 

(-,-)5 

(+,+)5 

(+,-)5 SU(2)LxU(1)Y 

massless Higgs doublet 



Susy, Little Higgs, gauge-Higgs unification: 

three concrete classes of models with 

new particles/symmetries that populate the TeV scale 

to stabilize the EW scale and suppress dangerous Λ2 quantum corrections 

to the Higgs mass 

Models designed to address the question: 

what is canceling the infamous divergent diagrams? 

h 

h h 

W ± Z 

DRAFT 

h h 



top 

h h

But this is assuming that we already know the answer to the central 

question of EW symmetry breaking 

what is unitarizing the WW scattering amplitude? 

A = g 2 

WL 

WL 

E 

finite 

DRAFT 

MW 

2 

other way to unitarize the WW amplitude: 

Higgsless models & composite Higgs 



WL 

WL 

!A

What is the mechanism of EWSB? 

what is unitarizing the WW scattering amplitude? 

Weakly coupled models Strongly coupled models 

W + W + 

W - 

h 0 

W - 

prototype: Susy 

prototype: Technicolor 

DRAFT 

susy partners ~ 100 GeV 

other ways? 

W + W + 

TeV 

QCD 

rho meson ~ 1 TeV 



W - 

W -

Strongly coupled models 

a phenomenological challenge: how to evade EW precision data 

The resonance that unitarizes the WW scattering amplitudes 

W + W + 

W - 

TC 

W - 

= 

generates a tree-level effect on the SM gauge bosons self-energy 

DRAFT 

W3 B 

ρ 

W + W + 

W - 



+ ... 

parameter of order 

In conflict with EW precision data from LEP 

( exp: | @ 95% CL) 

ˆ S| < 10 −3 

a theoretical challenge: need to develop tools to do computation 

ˆS 

ρ 

W - 

m 2 W /m 2 ρ

DRAFT 

Higgsless Models 



➲

πR 

−πR 

y 

−y 

Higgsless Approach 

0 

Z2 

⤶ 

U 2 =1 

Csaki, Grojean, Murayama, Pilo, Terning ‘03 

Csaki, Grojean, Pilo, Terning ‘03 

Gauge symmetry breaking 

In the gauge-Higgs unification models, we have been breaking 

bigger gauge groups down to SU(2)xU(1) by orbifold. 

Why can’t we break directly SU(2)xU(1) to U(1)em by orbifold? 

DRAFT 



Higgsless Models 

mass without a Higgs 

m 2 = E 2 − p3 2 − p⊥ 2 

momentum along extra dimensions ~ 4D mass 

quantum mechanics in a box 

boundary conditions generate a transverse momentum 

Is it better to generate a transverse momentum than introducing 

by hand a symmetry breaking mass for the gauge fields? 

DRAFT 

ie how is unitarity restored without a Higgs field? 



(4) 2 

∝ gnnnn − 

g 2 nnk 

A (4) ∝ g 2 nnnn − 

g 2 mnpq = g2 A 5D dyfm(y)fn(y)fp(y)fq(y) 

0 

(2) ∝ 4g 2 

nnnn − 3 g 2 Mk nnk 

Unitarization M of (Elastic) Scattering Amplitude 

k 

k 

2 n k 

k 

Same KK mode 

4g 

‘in’ and ‘out’ 

2 

nnnn − 3 g 2 M 

nnk 

2 k 

M 2 g 

k 

n 

2 nnk 

M 2 A 

k 

(4) ∝ g 2 nnnn − 

g 

k 

2 nn g p 

nnk |p| E 

k ɛ = , 

M M 

2 M 

nnk 

2 k 

M 2 n p 

A k 

(2) ∝ 4g 2 nnnn 

k 

− 3 θ 

p 

q 

 

f abe cde 

f (3 + 6cθ − c 2 θ ) + 2(3 − c2θ )f ace f bde 

M 2 

f k ace bde 2 

f − sθ/2f abe f cde 

p 

q 

g 

k 

2 

f abe cde 

nnk f (3 + 6cθ − c 2 θ ) + 2(3 − c2θ )f ace f bde 

A (2) ∝ 4g 2 nnnn g 

k 

2 nnk 

M 2 n 

p 

q 

 

nn − g 2 

f abe cde 


g 2 

f abe cde 


 

nn − 3 g 

k 

2 M 

nnk 

2 k 

M 2 

f 

ace bde 2 

f − sθ/2f n 

abe f cde 

q 

g 2 q 

g 

nnnn 

2 q 

nnnn g 

gnnk 

2 nnnn 

n n n n 

k 

gnnk 

g 2 nnk 

M 

k 

= 0 KK sum rules (enforced by 5D Ward identities) 

2 n 

gnnk 

g 2 nnnn 

4 E 

+ A (2) 

 

nnn − 3 g 

k 

2 E 

+ . . . 

2 M 

nnk 

2 k 

M 2 

f 

ace bde 2 


abe f cde 

gnnk 

g 2 k 

 

i 4g 

nnnn 

2 

nnnn − 3 g 

k 

2 M 

nnk 

2 k 

M 2 

f 

ace bde 2 


abe f cde 

gnnk 

g 2 gnnk 

g 

nnnn 

2 nnnn 

A (4) 

4 E 

+ A 

M 

(2) 

A 2 E 

+ . . . 

M 

(4) 

= i g 2 nnnn − 

g 

k 

2 

f abe cde 

nnk f (3 + 6cθ − c 2 θ) + 2(3 − c 2 θ)f ace f bde 

gnnk 

be cde 

f (3 + 6cθ − c 

 

 

 

2 θ ) + 2(3 − c2θ )f ace f bde 

 

nn − g 

k 

2 

f 

abe cde 


 

4g 2 nnnn − 3 

g 2 M 

nnk 

2 

f k ace bde 2 


 

(4) 

= i g 2 

nnnn − g 

k 

2 

f 

abe cde 


A (2) 

= i 4g 2 nnnn − 3 

g 2 M 

nnk 

2 

f k ace bde 2 


A (4) 

= i g 2 

nnnn − g 

k 

2 

f 

abe cde 

nnk f (3 + 6cθ − c 2 θ ) + 2(3 − c2 θ ) 

A (2) 

= i 4g 2 nnnn − 3 

g 2 M 

nnk 

2 k 

M 2 

f 

ace bde 2 


abe f c 

A (4) 

= i g 2 

nnnn − g 

k 

2 

f 

abe cde 

nnk f (3 + 6cθ − c 2 θ ) + 2(3 − c2θ ) 

 

 

f 

ace bde 2 

f − sθ/2f abe f c 

A (4) 

= i g 2 

nnnn − g 

k 

2 

f 

abe cde 

nnk f (3 + 6cθ − c 2 A 

θ ) + 2 

 

 

f 

ace bde 

f − s 

(4) 

= i g 2 

nnnn − g 

k 

2 

f 

abe cde 

nnk f (3 + 6cθ − c 2 θ ) + 

A (2) 

= i 4g 2 nnnn − 3 

g 2 M 

nnk 

2 k 

M 2 n n n 

n 

n n n n 

 

f 

ace bde 

f − s 

n 

DRAFT 

} 

} 

gnnk M 2 k 

n 

n− 

3 g 

Csaki, Grojean, p k 

Murayama, Pilo, Terning ’03 

2 M 

nnk 

2 k 

M 2 A 

n 

(2) ∝ 4g 2 

nnnn − 3 g 

k 

2 M 

nnk 

2 k 

M 2 k 

n 

p 

n 

M 

M 

Christophe ⊥ Grojean Beyond the Standard Model 123 


= 

 

|p|, E p 

4 E 

+ A 

M 

(2) 

2 E 

A = A + . . . 

M 

(4) 

4 E 

+ A 

M 

(2) 

ɛ 2 E 

+ . . . 

M 

µ 

⊥ = 

 

|p| E p 

 

, A 

M M |p| 

(2) = i 4g 2 nnnn − 3 

g 

k 

2 M 

nnk 

2 k 

M 2 f 

n 

ace f bde − s 2 

! /2f abe f cde 

M 

k 

 

2 n M 

k 

2 k 

A n 

(2) = i 4g 2 nnnn − 3 

g 

k 

2 M 

nnk 

2 k 

M 2 A 

n 

(2) = i 4g 2 nnnn − 3 

g 

k 

2 M 

nnk 

2 k 

M 2 k 

n 

= A (4) 

ɛ µ 

− 3 

p 

A ∝ 4gnnnnA− 3 ∝ 4gg nnnn nnk − 3 

M 2 

A n (2) ∝ 4g 2 nnnn 

 

−q 3 

g 2 nnk 

M 2 n 

M 2 k 

 

p 

|p| 

p 

A = A (4) 

E 

M 

4 

p 

q 

+ A (2) 

q 

g 2 nnnn 

n n 

g 

gnnk 

2 nnnn 

k 

gnnk 

p 

 

q E 

q 

M 

g 2 nnnn 

g 2 nnnn 

gnnk 

gnnk 

2 

n n 

k 

+ . . .

exercise 

A (4) ∝ g 2 nnnn − 

E 4 Sum Rule 

k 

KK Sum Rules 

Csaki, Grojean, Murayama, Pilo, Terning ’03 

g 

k 

2 M 

nnk 

2 k 

M 2 n 

g 2 nnk A (2) ∝ 4g 2 nnnn − 3 

In a KK theory, the effective couplings are given by overlap integrals of the wavefunctions 

g 2 mnpq = g 2 5D 

k 

πR 

dyfm(y)fn(y)fp(y)fq(y) 

0 

g 2 nnnn − 

g 2 nnk = g 2 πR 

5D dyf 4 n(y) − g 2 πR πR 

5D dy dzf 2 n(y)f 2 n(z) 

fk(y)fk(z) =0 

DRAFT 

0 

A (4) =0 

Completness of KK modes 



0 

gmnp = g5D 

0 

 

k 

πR 

0 

dyfm(y)fn(y)fp(y) 

k 

fk(y)fk(z) =δ(y − z)

exercise 

A (4) ∝ g 2 nnnn − 

E 2 Sum Rule 

4g 2 nnnnM 2 n − 3 

 

fk(y)fk(z) =δ(y − z) 

k 

k 

k 

g 2 nnkM 2 k =4g 2 5DM 2 n 

KK Sum Rules 

g 2 nnk A (2) ∝ 4g 2 nnnn − 3 

 

=4g 2 5DM 2 n 

πR 

0 

dyf 4 n(y) − 3g 2 5D 

DRAFT 

A (2) =0 

up to boundary terms... 



πR 

0 

k 

dy dz f 2 n(y)f 2 n(z) 

int. by part 

dz f 

int. by part 

2 n(z)f ′′ 

 

k (z) = −2 dz fn(z)f ′ n(z)f ′ k(z) 

 

= 2 dz fn(z)f ′′ 

 

n(z)fk(z)+2 

= −2M 2 

n dz f 2 

n(z)fk(z)+2 

 

0 

0 

g 2 nnk 

k 

dz f ′2 

dz f ′2 

M 2 k 

M 2 n 

fk(y) fk(z)M 2 k 

n (z)fk(z) 

n (z)fk(z) 

 

πR 

dy f 4 n(y) − 6g 2 5DM 2 πR 

n dy f 4 n(y)+6g 2 πR 

5D dy f 2 n(y)f ′2 

n (y) 

int. by part 

dy f 2 n(y)f ′2 

 

n (y) = −2 

= 1 

3M 2 n 

dy f 2 n(y)f ′2 

 

n (y) − 

 

dy f 4 n(y) 

0 

dy f 3 n(y)f ′′ 

n(y) 

−f ′′ 

k (z)

UV brane IR brane 

z = RUV ~ 1/MPl z = RIR ~ 1/TeV 

SU(2)LxSU(2)R 

x 

U(1)B-L 

SU(2)LxU(1)y U(1)B-LxSU(2)D 

∂5A La 

A 

log suppression 

⤶ “lig 

µ =0 

R ± 

µ 

=0 

g ′ R 3 

5Bµ − g5Aµ =0 

∂5(g5Bµ + g ′ R 3 

5Aµ ) = 0 

ht” mode: 

KK tower: 

U(1)em 

{ Warped Higgsless Model 

Csaki, Grojean, Pilo, Terning ‘03 

ds 2 = 

2 R ηµνdx µ dx ν − dz 2 

BCs kill all A5 massless modes: no 4D scalar mode in the spectrum 

DRAFT 

M 2 W = 

1 

R2 IR log(RIR/RUV ) 

M 2 KK ! 

ALa µ − ARa µ =0 

! 5(ALa µ + ARa ! 5Bµ =0 

µ )=0 

M 2 Z ∼ g2 5 +2g ′2 

5 

g2 5 + g′2 

"ſɏ&ÿ (ÿʯ*+ɏ˿ 



R 2 IR 

z 

Ω = RIR 

RUV 

≈ 10 16 GeV 

1 

R2 IR log(RIR/RUV )

SM Fermions in Higgsless Models 

SU(2)Lx U(1)y 

Chiral brane 

no possible mass term 

SU(2)LxSU(2)R 

x 

U(1)B-L 

SU(2)DxU(1)B-L 

vector-like brane 

isospin invariant mass only 

DRAFT 

(same mass for the top and bottom or electron and neutrino) 

The fermions have to live in the bulk 



Collider Signatures 

unitarity restored by vector resonances whose masses and 

couplings are constrained by the unitarity sum rules 

σ (W + Z → W + Z) (pb) 

q 

q 

WZ elastic cross section 

10 4 

10 3 

Higgsle 

Pade 

VBF (LO) dominates over DY since 

couplings of q to W’ are reduced 

K-matrix 

10 2 

200 300 500 700 1000 2000 3000 5000 

Z 0 

W ± 

W’ 

SM 

s1/2 (GeV) 

Z 0 

W ± 

q 

Birkedal, Matchev, Perelstein ’05 

He et al. ‘07 

√ 

3MW 

a narrow and light resonance 

no resonance in WZ for SM/MSSM 

′MW 

Γ(W ′ → WZ) ∼ αM 3 W ! 

144s2 wM 2 W 

W’ production 

DRAFT 

2j+3l+ET 

q 

gWW ′ Z ≤ gWWZM 2 Z 

Number of events at the LHC, 300 fb -1 

discovery reach 

@ LHC 

(10 events) 

550 GeV → 10 fb −1 

1 TeV → 60 fb −1 

should be seen 

within one/two year 



DRAFT 

New physics & flav&r 



➲

1 

2 

Partial compositeness: fermion masses 

amount of 

compositeness 

fqL,R 

partial compositeness 

mixing elem. and composite fermions 

dim qR,L=3/2, dim =dR,L 

qLOR 

Λ dR−5/2 

R 

+ qROL 

Λ dL−5/2 

L 

} 

OR,L 

+ OLOR 

Λ dL+dR−4 

R 

integrating out heavy fields 

ΛRΛL 

fermion mass hierarchy easily generated by small diff. in anomalous dims 

DRAFT 

alignment mixing angles/masses is also explained 

⎛ 

1 λ λ 

⎝ 

3 

λ 1 λ2 ⎞ 

⎠ 

VCKM ∼ 

λ 3 λ 2 1 

Λ 

Λ 

ΛR 

dR Λ 



ΛL 

dL 

qLqR 

mui ∝ fqi fui mdi 

V ij 

CKM 

∝ fqi /fqj 

∝ fqi fdi

Partial Compositeness: fermion masses 

Higgs part of the strong sector: it couples only to composite fermions 

f 

cL 

|light〉L 

Y* 

H Yukawa coupling 

in the strong sector 

when the Higgs gets a vev, the light dof will acquire a mass prop. to 

DRAFT 

Y eff = Y⋆ fcL fcR 

Yukawa hierarchy comes from the hierarchy of compositeness 

the lighter the fermion, the less coupled to the strong sector 



f 

|light〉R 

cR

UV 

u,d,s 

c,bR 

Partial compositeness: xdim realization 

t,bL 

IR 

Higgs 

vev 

fermion zero-mode has 

an exponential profile 

in the bulk 

fc = 

 

fc is the "value" of wavefct. on the IR: 

1 − 2c 

1 − (R/R ′ ) 1−2c 

light fermion exponentially localized on the UV brane 

➲ overlap with Higgs vev on the IR tiny 

➲ exponentially small 4D mass 

c < 1/2: heavy fermion 

c > 1/2: light fermion 

DRAFT 

UV localized fermion=elementary 

IR localized fermion=composite 

5D models=weakly coupled dual of 4D strongly models 

[Grossman and Neubert, ’00] 

[Gherghetta and Pomarol, ‘00] 

[Huber, ‘03] 

−c χ(z) = fc 

√R 

′ 

 

z 

2 

z 

R R ′ 

fc ∼ O(1) 

fc ∼ (R/R ′ ) c−1/2 ≪ 1 



SU(2)LxU(1)Y 

UV 

Holographic Models of EWSB 

Gauge fields + fermions 

in the bulk 

G 

IR 

G=SU(2)LxSU(2)RxU(1)B-L 

G=SO(5)xU(1)X 

G=SO(6)xU(1)X 

Bulk gauge fields: [Pomarol, ’00] 

Holographic technicolor=Higgsless: [Csaki et al., ‘03 

Holographic composite Higgs: [Agashe et al., ’04] 

Higgs on the IR brane 

or 

Gauge breaking by 

boundary conditions 

DRAFT 

UV completion: log running of gauge couplings 

Custodial symmetry from bulk SU(2)R 



DRAFT 

Composite Higgs Models 



➲

What is the SM Higgs? 

A single scalar degree of freedom neutral under SU(2)LxSU(2)R/SU(2)L 

LEWSB = v2 

4 Tr DµΣ † 

 

DµΣ 1 + 2a h 

+ bh2 

v v2 

− λ ¯ 

ψLΣψR 1+c h 

 

v 

W - 

W + 

h 

W - 

W + 

‘a’, ‘b’ and ‘c’ are arbitrary free couplings 

A = 1 

v2 

s − a2 s 2 

s − m 2 h 

growth cancelled for 

a = 1 

restoration of 

perturbative unitarity 

DRAFT 



What is the SM Higgs? 

A single scalar degree of freedom with no charge under SU(2)LxU(1)Y 

LEWSB = v2 


 

DµΣ 1 + 2a h 

+ bh2 

v v2 

− λ ¯ 

ψLΣψR 1+c h 

 

v 

1 

10 -1 

10 -2 

10 -3 

‘a=1’, ‘b=1’ & ‘c=1’ define the SM Higgs 

Higgs properties depend on a single unknown parameter (mH) 

bb - 

BR(H) 

SM 

! + ! - 

gg 

cc - 

WW 

DRAFT 

Z" 

"" 

80 100 150 200 

Mh !GeV" 

ZZ 

qqH, H!WW!l"jj H!ZZ!4l 

H!WW!2l2" 

qqH, H!$$!l+j 

H!## total significance 



S 

50 

10 

5 

1 

SM 

CMS 

30fb -1 

120 140 160 180 200 

MH [GeV]

1-a 2 

Deformation of the SM Higgs 

LEWSB = v2 


 

DµΣ 1 + 2a h 

v 

+ bh2 

v2 generic ‘a’, ‘b’ & ‘c’ 

Examples of constraints on the “Higgs” couplings 

DRAFT 



1-a 2 

 

− λ ¯ ψLΣψR 

 

1+c h 

 

v

How many parameters for the Higgs? 

LEWSB = v2 


 

DµΣ 1 + 2a h 

v 

h 

+cg 

v GµνG µν h 

+ cγ 

v 

γµνγ µν 

+ bh2 

v2 Minimal Flavour Violation setup? cij=c 

DRAFT 

Loop suppressed decays to massless spin-1? 



 

− λij ¯ ψLi ΣψRj 

 

1+cij 

cg ∼ cγ ∼ O 

 

h 

v 

 

α 

 

4π

How to obtain a light composite Higgs? 

Higgs=Pseudo-Goldstone boson of the strong sector 

gSM 

proto-Yukawa 

gauge gρ 

SM 

3 scales: 

gρ 

2 

mρ =gρ f 

gSM/gρ 

4π f 

v 246 GeV 

Strong 

BSM 

global 

symmetry 

UV completion 

10 TeV 

mHiggs=0 when gSM=0 

G /H 

usual resonances of the strong sector 

Higgs = light resonance of the strong sector 

residual 

global symmetry 

DRAFT 

strong sector broadly characterized by 2 parameters 

mρ 

= mass of the resonances 

= coupling of the strong sector or decay cst of strong sector 

Giudice, Grojean, Pomarol, Rattazzi ‘07 

not directly 

accessible to LC 



} 

indirect 

probes 

f =mρ /gρ

Continuous interpolation between SM and TC 

SM limit Technicolor limit 

all resonances of strong sector, 

except the Higgs, decouple 

Composite Higgs 

vs. 

SM Higgs 

ξ = v2 

= 

f 2 

b 

Higgs decouple from SM; 

vector resonances like in TC 

DRAFT 

1 

Dilaton 

b=a 2 

(weak scale) 2 

(strong coupling scale) 2 

ξ =0 ξ =1 

SM 

a 

L EWSB = 

Composite Higgs 

universal behavior for large f 

a=1-v/2f b=1-2v/f 

1 



 

a v 

2 

1 

h + b 

4 h2 

 

Tr DµΣ † DµΣ

What distinguishes a composite Higgs? 

L ⊃ cH 

2f 2 ∂µ |H| 2 ∂µ 

U = e 

f 2 tr ∂µU † ∂ µ U = |∂µH| 2 + ♯ 

f 2 

⎛ 

i⎝ 

H † /f 

|H| 2 


2 

∂|H| 2 ♯ 

+ 

f 2 |H|2 |∂H| 2 + ♯ 

f 2 

 

† 2 

H ∂H DRAFT 



H/f 

⎞ 

⎠ 

U0 

cH ∼ O(1)

Modified 

Higgs propagator 

Anomalous Higgs Couplings 

L ⊃ cH 

2f 2 ∂µ |H| 2 ∂µ 

H = 

0 

v+h √2 

 

~ 

L = 1 

Higgs couplings 

rescaled by 

|H| 2 


cH ∼ O(1) 

DRAFT 



2 

 

1+cH 

 

1 

1+cH v2 

f 2 

v 2 

f 2 

 

∼ 1 − cH 

(∂ µ h) 2 + . . . 

v2 ≡ 1 − ξ/2 

2f 2

SILH Effective Lagrangian 

(strongly-interacting light Higgs) 

extra Higgs leg: 


extra derivative: 

Genuine strong operators (sensitive to the scale f) 

cH 

2f 2 

 

∂ µ |H| 2 2 cT 

2f 2 

Form factor operators (sensitive to the scale mρ) 

icHW 

m 2 ρ 

g 2 ρ 

icW 

2m 2 ρ 

 

H † σ i←→ D µ 

H 

DRAFT 

minimal coupling: 

H/f ∂/mρ 

 

H 

custodial breaking 

†←→ D µ 2 cyyf 

c6λ 

H 

|H|6 

f 2 f 2 |H|2fLHfR ¯ +h.c. 

(D ν Wµν) i 

16π 2 (Dµ H) † σ i (D ν H)W i µν 

cγ 

m 2 ρ 

g2 ρ 

16π2 g 2 

g 2 ρ 

h → γZ 

H † HBµνB µν 

Goldstone sym. 

loop-suppressed strong dynamics 



icB 

2m 2 ρ 

icHB 

m2 ρ 

cg 

m 2 ρ 

g2 ρ 

16π2 

H †←→ D µ 

H 

g 2 ρ 

(∂ ν Bµν) 

16π 2 (Dµ H) † (D ν H)Bµν 

y2 t 

g2 H 

ρ 

† HG a µνG aµν

ˆT = cT 

v 2 

f 2 

ˆS =(cW + cB) m2 W 

effective 

Higgs mass 

EWPT constraints 

m 2 ρ 

|cT 

There are also some 1-loop IR effects 

removed 

by custodial symmetry 

DRAFT 

LEPII, for mh~115 GeV: 

v2 | < 2 × 10−3 

f 2 

ˆS, ˆ T = a log mh + b 

ˆS, ˆ T = a ((1 − cHξ) log mh + cHξ log Λ)+b 

m eff 

h 

= mh 

Λ 

mh 

mρ ≥ (cW + cB) 1/2 2.5 TeV 

Barbieri, Bellazzini, Rychkov, Varagnolo ‘07 

modified Higgs couplings to matter 

cHv 2 /f 2 

>mh 

cHv 2 /f 2 < 1/3 ÷ 1/2 

IR effects can be cancelled by heavy fermions (model dependent) 



1+ 

cij|H| 2 

f 2 

 

mass terms 

Flavor Constraints 

Higgs fermion interactions 

mass and interaction matrices are not diagonalizable simultaneously 

if cij are arbitrary 

➾ FCNC 

DRAFT 

➾ 

yij ¯ fLiHfRj = 

 

1+ 

cijv 2 

SILH: cy is flavor universal 

Minimal flavor violation built in 



2f 2 

 

yijv 

√2 

 

1+ 

¯fLifRj 

3cijv 2 

2f 2 

 

yijv 

√2 h ¯ fLifRj

Higgs anomalous couplings for large v/f 

The SILH Lagrangian is an expansion for small v/f 

The 5D MCHM gives a completion for large v/f 

➾ 

4 g2f 2 sin 2 v/f ghW W = 1 − ξ g SM 

Fermions embedded in spinorial of SO(5) Fermions embedded in 5+10 of SO(5) 

MCHM4 

m 2 W = 1 

➾ 

➾ 

DRAFT 

universal shift of the couplings 

no modifications of BRs 

hW W 

mf = M sin v/f mf = M sin 2v/f 

ghff = 1 − ξ g SM 

hff 

ξ = v 2 /f 2 

ghff = 

1 − 2ξ 

√ g 

1 − ξ SM 

BRs now depends on v/f 

MCHM5 



hff

" ( ! * BR 

! * BR 

2 

1.8 

1.6 

& 

1.4 

1.2 

Γ 1 

h → f ¯ f 

0.8 

0.4 

0.2 

) 

Higgs anomalous couplings @ LHC 

Γ (h 0.6 → gg) SILH = Γ (h → gg) SM 

observable 0 @ LHC? 

" ( ! * BR) 

! * BR 

2 

1.8 

1.6 

1.4 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

110 115 120 125 130 135 140 145 150 

m [GeV] 

 

ATLAS 

L dt=30 fb 

ATLAS 

Ldt = 300 fb −1 

& 

-1 

SILH = Γ h → f ¯ f 

ATLAS 

L dt=300 fb 

-1 

SM 

! (VBF) * BR(H $ # # 

! (ttH) * BR(H $ b b) 

! (H) * BR(H $ % % ) 

! (VBF) * BR(H $ % % ) 

! (ttH) * BR(H $ % % ) 

! (WH) * BR(H $ % % ) 

! (ZH) * BR(H $ % % ) 

 

1 − v2 

f 2 (2cy 

 

+ cH) 

 

1 − v2 

f 2 (2cy 

 

+ cH) 

H 

! (VBF) * BR(H $ # # ) 

! (ttH) * BR(H $ b b) 

! (H) * BR(H $ % % ) 

! (VBF) * BR(H $ % % ) 

! (ttH) * BR(H $ % % ) 

! (WH) * BR(H $ % % ) 

! (ZH) * BR(H $ % % ) 

cHv 2 /f 2 =1/4 

cyv 2 /f 2 =1/4 

LHC can measure 

v 

cH 

up to 0.2-0.4 

2 v 

,cy 

f 2 2 

f 2 

Figure 1: The deviations from the SM predictions of Higgs production cross sect 

decay branching ratios (BR) defined as ∆(σ BR)/(σ BR) = (σ BR)SILH/(σ 

The predictions are shown for some of the main Higgs discovery channels at th 

production via vector-boson fusion (VBF), gluon fusion (h), and topstrahlung 

SILH Lagrangian parameters are set by cHξ =1/4, cy/cH = 1 and we have inclu 

terms quadratic in ξ, not explicitly shown in eqs. (78)–(83). 

DRAFT 

110 115 120 125 130 135 140 145 150 

(ILC could go to few % ie 

test composite Higgs up to 4πf ∼ 30 TeV) 

Duhrssen rate ‘03 times branching ratio in the various channels with 20–40 % precision [27 

Figure 1: Relative error for the measurement of rates σ · BR for those channels 

Christophe Grojean Beyond the Standard determination Model of the 152b 

coupling is quite challenging [28]. This Maria willLaach, translate Sept. into '10 

i.e. 

a pseudo-Goldstone boson, and therefore relatively light. However, for a light 

experiments can measure the product σh × BRh in many different channels: 

through gluon, gauge-boson fusion, and top-strahlung; decay into b, τ, γ and (v 

gauge bosons. At the LHC with about 300 fb−1 m [GeV] 

, it is possible to measure Higg 

H 

4πf ∼ 5 – 7 TeV

Δa 1 

∆aH 

e + 

e - 

Higgs anomalous couplings @ LC 

Z 

h 

Z 

single Higgs production 

e + 

e - 

W + 

W - 

Barger et al. hep-ph/0301097 

DRAFT 



ν 

ν 

e + 

h h 

higgs-strahlung WW-fusion 

ZZ-fusion 

mH=120 GeV 

L = 1 ab −1 

a 1 Error 

-0.4 -0.2 0 0.2 0.4 

aH = cHv 2 /f 2 

a =f v 

1 1 2 /Λ 2 

500 GeV 

800 GeV 

0.012 

0.01 

0.008 

0.006 

0.004 

0.002 

0 

e - 

∆aH ∼ 0.005 

∆aH ∼ 0.02 

e + 

e - 

mH=120 GeV 

➾ 

mH=240 GeV 

➾ 

4πf ! 44 TeV 

4πf ∼ 22 TeV

∆a6 

Δa 2 

Higgs anomalous (self-)couplings @ LC 

double Higgs production 


W 

the accuracy on aH is not competitive compared to single Higgs production 

a Error 

2 + 

W - 

e ν 

ν 

+ 

e- h h 

h 

e + 

e- W 

ν 

h 

h 

ν 

+ 

W - 

e + 

e- Z h 

h 

h 

Z 

L = 1 ab −1 

mH=120 GeV 

it allows to constrain a6 

DRAFT 

-0.4 -0.2 0 0.2 0.4 

a =f v 

2 2 2 /Λ 2 

a6 = c6v 2 /f 2 

500 GeV 

800 GeV 

0.25 

0.2 

0.15 

0.1 

0.05 

0 

mH=120 GeV 



➾ 

∆a6 ∼ 0.1 4πf ∼ 10 TeV

Δa 1 

∆aH 

Higgs anomalous couplings @ CLIC 

mH=120 GeV 

L = 1 ab −1 

a 1 Error 

0.0012 

-0.1 -0.05 0 0.05 0.1 

a =f v 

1 1 2 /Λ 2 

aH = cHv 2 /f 2 

3 TeV 

5 TeV 

0.0026 

0.0024 

0.0022 

0.002 

0.0018 

0.0016 

0.0014 

L = 1 ab −1 

mH=120 GeV 

0.02 

-0.1 -0.05 0 0.05 0.1 

a6 = c6v 2 /f 2 

a =f v 

2 2 2 /Λ 2 

DRAFT 



∆a6 

Δa 2 

a 2 Error 

➾ 4πf ∼ 70 TeV 

➾ 


∆aH ∼ 0.002 ∆a6 ∼ 0.04 4πf ∼ 15 TeV 

a factor 2 better than ILC 

3 TeV 

5 TeV 

0.06 

0.05 

0.04 

0.03

Composite Higgs search @ LHC 

Espinosa, Grojean, Muehlleitner ’10 

the modification of Higgs couplings and BRs affects the Higgs search 

S 

50 

10 

5 

1 

SM 


H!WW!2l2" 

qqH, H!$$!l+j 


SM 

CMS 

30fb -1 

120 140 160 180 200 

MH !GeV" 

large 

compositeness scale 

signal significance 

for L=30/fb 

DRAFT 

small 

compositeness scale 

qqH, H!WW!l"jj 

H!WW!2l2" 

H!## 

H!ZZ!4l 

total significance 



S 

50 

10 

5 

1 

S 

50 

10 

5 

1 


H!WW!2l2" 

qqH, H!$$!l+j 


MCHM4 

CMS 

30fb -1 

%=0.2 

120 140 160 180 200 

MH !GeV" 

MCHM4 

MCHM4 

CMS 

30fb -1 

$=0.8 

120 140 160 180 200 

MH !GeV"



ξ 

MH 

MCHM5 

contour lines of 

signal significance 

for L=30/fb 

in the (ξ,MH) plane 

DRAFT 

(neglect effects from heavy resonances) 






ξ 

MH 

contour lines of 

signal significance for 

for L=30/fb 

in the (ξ,MH) plane 

DRAFT 

L=30/fb 

MCHM5 

(neglect effects from heavy resonances) 




How to probe the composite nature of Higgs? 

Look at pair production of strong states 

strong WW scattering 

W W 

h 

W W 

= −(1 − ξ)g 

no exact cancellation 

of the growing amplitudes 

Even with a light Higgs, growing amplitudes (at least up to mρ) 

DRAFT 

LET=SM-Higgs 

strong double Higgs production 


2 E2 

M 2 W 

A W a LW b L → W c LW d ab cd ac bd ad bc 

L = A(s, t, u)δ δ + A(t, s, u)δ δ + A(u, t, s)δ δ 

ALET(s, t, u) = s 

v 2 

Aξ = ξ ALET 

Contino, Grojean, Moretti, Piccinini, Rattazzi ’10 

A Z 0 LZ 0 L → hh = A W + − 

L WL → hh = cHs 

f 2 



Scale of Strong WW scattering? 

ATT→TT ∼ g 2 f(t/s) 

f is a rational fct 

expected O(1) for t~-s/2 

onset of strong scattering at the weak scale 

hard cross-section ‘inclusive’ cross-section 

dσLL→LL/dt 

 

dσTT→TT/dt t∼−s/2 

 

= Nh 

s 2 

DRAFT 

M 4 W 

NDA estimates 

σLL→LL(Qmin) 

σTT→TT(Qmin) 

ALL→LL ∼ s 

v2 (−s + Q ! "#< t < −Q ! "#) 

Nh ∼ 1 Ns ∼ 1 

= Ns 

sQ2 min 

M 4 W 



Total cross sections 

disentangling L from T polarization is hard 

σtot (W + W + !W + W + + + + + 

W W → W W ) [fb] 

[fb] 

σtot 

1x10 7 

1x10 6 

1x10 5 

LL ! LL 

TT !TT 

LT ! LT 

500 1000 1500 2000 2500 3000 

DRAFT 

√s [GeV] 

The onset of strong scattering is delayed to larger energies due to 

the dominance of TT → TT background 

!=0.5 

The dominance of T background will be further enhanced by the pdfs 

since the luminosity of WT inside the proton is log(E/MW) enhanced 



!=1 

!=0

A = at γ s 

t + at Z s 

t − M 2 Z 

W + 

W - 

Coulomb enhancement (SM) 

the total cross section is dominated by the poles 

in the exchange of γ and Z in the t- and u-channels 

= regulateur of Coulomb singularity=off-shellness of W ~ 

universal for T and L 

SM 

γ 

+ auγ s 

u + auZ s 

u − M 2 Z 

π + 

π + 

+ . . . σ ∼ 1 

16π 

eïkonal limit 

γ 

different for T and L 

DRAFT 



W + 

W - 

 

t 2 u2 aγ + aγ Mγ MW 

aγ =2· (electric charge of W + ) 2 

σTT→TT 

σLL→LL 

∼ 20 

(for Mγ ∼ MZ) 

➾➾ 

Z 

π + 

π + 

T-dominance is the result of multiplicity and larger SU(2) charges 

M 2 γ 

+ at 2 u 2 

Z + aZ M 2 γ + M 2 Z 

aZ =2· (“SU(2) charge” of W + ) 2 

Ns ∼ 1/500 

W + W + ! W + W + 

e e gcW g c2 W − s2 W 

2cW 

Z

σhard σhard Hard scattering (central region) 

we need to look at the central region, i.e. large scattering angle, 

to be sensitive to strong EWSB 

LL→LL 

TT→TT 

 

σtot (W + W + !W + W + t-cut 

) [fb] 

√ s 

1x10 7 

1x10 6 

1x10 5 

1x10 4 

1x10 3 

-3/4 < t/s < -1/4 

LL ! LL 

TT !TT 

LT ! LT 

500 1000 1500 2000 2500 3000 

DRAFT 

7.4MW 

Nh =1/2304 

4 

ξ 2 

√s [GeV] 



!=1 

!=0.5 

!=0 

hard cross-section = faster growth with energy 

onset of strong scattering still at high scale

10 

10 

10 

10 

10 

10 

3 

2 

1 

-1 

-2 

-3 

dσ 

dˆs 

-3 

10 10 10 

-4 -2 

Threshold production 

! 

1 

= 

ˆs ˆσ(qAqB → hh)ρAB(ˆs/s, Q 2 ) 

Q = 80 GeV 

ud 

gg 

ug 

uu 

0.1 1 

σ =ˆσ(s0) × 

integral is saturated at threshold 

inclusive cross-section is not 

probing the asymptotic regime of 

hard scattering 

DRAFT 

sensitivity on Higgs self-coupling and not only on strong scattering (b-a 2 ) 



➾ 

 

s! 

dˆs 

ˆs 

➾ 

ˆσ(ˆs) 

ˆσ(s0) ρ(ˆs/s) 

➾

Isolating Hard Scattering 

isolate events with large mhh 

luminosity factor drops out in ratios: extract the growth with mhh 

200 

150 

100 

50 

0 

dσ/dmhh|MCHM4 

dσ/dmhh|SM 

DRAFT 

500 1000 1500 2000 2500 

m hh [GeV] 

ξ =1 

ξ =0!8 

ξ =0.5 

500 1000 1500 2000 2500 



1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

measure 

H 3 

threshold 

asymptotic regime 

m hh [GeV] 

measure 

b-a 2 

dσ/dmhh|MCHM4 

dσ/dmhh|MCHM5

increase in # signal events 

40 

30 

20 

10 

Dependence on Collider Energy 

ρ LL 

ρ LL 

W (m2 hh /s, Q2 ) 

σ =ˆσ(s0) × 

W ((mhh/14 TeV) 2 ,Q 2 ) 

DRAFT 

0 

0 500 1000 1500 2000 2500 

m hh [GeV] 

 

s! 

40 TeV 

28 TeV 

sLHC vs. VLHC 

10 x lum ≈ 10 x events 

2 x √s = 10 x events 

iif mhh>1.6TeV 



dˆs 

ˆs 

ˆσ(ˆs) 


increase collider energy √s = sensitive to PDFs at smaller x 

bigger cross-sections

Number of Events/40 GeV 

0.4 

0.3 

0.2 

0.1 

Dependence on Collider Energy 

ξ = 1 

L = 300 fb -1 

10 x lum ≈ 10 x events 

2 x √s = 10 x events 

iif mhh>1.6TeV 

DRAFT 

ξ = 0 

σ =ˆσ(s0) × 

ξ = 0.5 

0 

0 200 400 600 800 1000 

vis 

mhh [GeV] 

 

s! 

sLHC vs. VLHC 

... very few events 

sLHC might be better 



dˆs 

ˆs 

ˆσ(ˆs) 


increase collider energy √s = sensitive to PDFs at smaller x 

bigger cross-sections

scaling dimension 

of the Higgs 

Multi-fields 

2 HDMs 

∞ 

2 

1 

RandallSundrum 

SM 

Conclusions 

5D 

Higgsless 

DRAFT 

0 

gaugephobic Higgs 

unHiggs 

Higgs-radion mixing 

pseudo-scalar mixing 

composite Higgs 



T 

e 

c 

h 

n 

i 

c 

o 

l 

o 

r 

1 

(v/f) 2 

deviations of Higgs 

couplings from SM

German Particle Physics School Maria Laach - Herbstschule Maria ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?