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Way Beyond the SMWay Beyond the SM

G.F. GiudiceIoP meeting on the Physics of the ILC

Oxford, 23 May 2007

Original work with C. Grojean, A. Pomarol, R. Rattazzi

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Supersymmetry is still the most “credible” theory BSM

• gauge-coupling unification

• EW breaking triggered by dynamics

• dark-matter candidate

• pass EW tests

But, increasing difficulty with direct limits % tuning

Reason to look “way beyond”

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Extra dimensions have brought new theoretical tools

Exciting new phenomena: graviton emission, transplanckian scattering, black-hole production

They require the largest possible energy: is LHC enough?

Nevertheless, ILC can give complementary information, especially for indirect signals

Some of the most interesting twists of extra dimension are related to EW breaking

€

e+e− → γγ, ff s = 0.5 TeV 1 fb−1 ΛH ≈ 2 TeV

100 fb−1 ΛH ≈ 4 TeV

s =1 TeV 500 fb−1 ΛH ≈ 8 TeV

e+e− → γGn s = 0.8 TeV 1ab −1 MD ≈ 6 TeV (n = 2)

(P− = 0.8, P+ = 0.6) MD ≈10 TeV (n = 2)

Weiglein et al., 2004

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AdS/CFT correspondence relates 5-d gravity with negative cosmological constant to strongly-coupled 4-d

conformal field theory

Warped gravity with SM fermions and

gauge bosons in bulk and Higgs on brane

Technicolor-like theory with slowly-running couplings in 4 dim

TeV brane Planck brane

5th dim

IR UV

RG flow

5-D gravity 4-D gauge theory

Motion in 5th dim RG flow

UV brane Planck cutoff

IR brane breaking of conformal inv.

Bulk local symmetries global symmetries

Technicolor strikes back?

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DUALITY: familiar conceptual distinction between force and spatial dimension becomes blurry

Is it a particle or is it a wave?

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are needed to see this picture.

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QuickTime™ and aTIFF (Uncompressed) decompressor

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TC

Technicolor-like theories in new disguise

Old problems

The presence of a light Higgs helps

• Light Higgs screens IR contributions to S and T

• (f pseudo-Goldstone decay constant) Can be tuned small for strong dynamics 4f at few TeV

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S =N

6π

v 2

f 2

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New constructions with light Higgs & strong dynamics

Higgs as pseudogoldstone boson

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Φ=ρ + f

2e iθ / f Φ = f Φ → e iaΦ :

ρ → ρ

θ →θ + a

⎧ ⎨ ⎩

Non - linearly realized symmetry h → h + a forbids m2h2

Gauge, Yukawa and self-interaction are non-derivative couplings Violate global symmetry and introduce quadratic divergences

Top sector ●●

➤

➤

No fine-tuning

Strong dynamics at a low scale, in conflict with LEP data

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€

One loopδmH2 =

GF

π 2mSM

2 Λ2 ⇒ Λ <π

GF

≈ TeV

Two loops δmH2 =

GF2

π 4mSM

4 Λ2 ⇒ Λ ≈π 2

GF mSM

≈10TeV ≈ ΛLH

“Collective breaking”: many (approximate) global symmetries preserve massless Goldstone bosonℒ1ℒ

2

H2

222

44=

δ Hm

ℒ1 ℒ2

LITTLE HIGGS: delays strong dynamics by cancelling one-loop effects only

New states at TeV reduce UV sensitivity of mH

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HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD

AM = (A,A5), A5 A5 +∂5 forbids m2A52

gauge HiggsHiggs/gauge unification as

graviton/photon unification in KK

Correct Higgs quantum numbers by projecting out unwanted states with orbifold

The difficulty is to generate Yukawa and quartic couplings without reintroducing quadratic divergences

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mh = 0

h → h + a

A5 → A5 + ∂5Λ

Same thing? (duality)

Relation between models of strong dynamics and extra dimensions

Common low-energy theory of Higgs interactions (particularly useful for linear collider, as S,T useful

parametrization of new physics at LEP)

Higgs is the 4th Goldstone

Light Higgs

pseudoGoldstone of a strong force

Belong to higher-dim gauge multiplet

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Structure of the theory

mρ mass of resonances gρ coupling of resonances

Communicate via gauge (ga) and (proto)-Yukawa (i)

quarks, leptons &

gauge bosons

strong sector

Strong sector characterized by

In the limit I, ga =0, strong sector contains Higgs as Goldstone bosons

Ex. H = SU(3)/SU(2)U(1) or H = SO(5)/SO(4)

-model with f = mρ / gρ

Take I, ga << gρ < 4

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ga , i break global symmetry Higgs mass

New theory addresses hierarchy problem reduced sensitivity of mH to short distances (below mρ

-1)

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mH2 ≈

α

4πmρ

2

Ex.:

• Georgi-Kaplan: gρ=4, f = v, no separation of scales

• Holographic Higgs: gρ= gKK, mρ= mKK

• Little Higgs: gρ, mρ couplings and masses of new t’, W’, Z’

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Production of resonances at mρ allows to test models at the LHC

Study of Higgs properties allows a model independent test of the nature of the EW breaking sector

Is the Higgs

fundamental?

SM (with mH < 180 GeV)

supersymmetry

composite?

Holographic Higgs

Gauge-Higgs unification

Little Higgs

ILC can give a fundamental contribution to answer this question

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Construct the Lagrangian of the effective theory below mρ

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U = e iπ aT a

Goldstones; Φ heavy fields

LSILH =mρ

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gρ2

L(0) U,Φ,∂

mρ

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟+

gρ2

16π 2L(1) U,Φ,

∂

mρ

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟+

gρ4

16π 2( )

2 L(2) U,Φ,∂

mρ

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟+ ...

⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

From the kinetic term, we obtain the definition of f = mρ / gρ

Each extra H insertion gives operators suppressed by 1 / f

• Each extra derivative “ “ 1 / mρ

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g2

mW2 − q2

=4

v 21+

q2

mW2

+ ... ⎛

⎝ ⎜

⎞

⎠ ⎟

f: symmetry-breaking scale mρ: new-physics mass threshold

• Operators that violate Goldstone symmetry are suppressed by corresponding (weak) coupling

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Operators testing the strong self coupling of the Higgs (determined by the structure of the model)

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cH

2 f 2∂ μ H +H( )∂μ H +H( ) −

c6λ

f 2H +H( )

3+

cy y f

f 2H +Hf LHfR + h.c.

⎛

⎝ ⎜

⎞

⎠ ⎟

and yf are SM couplings; ci model-dependent coefficients

Form factors sensitive to the scale mρ

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icW g

2mρ2

H +σ it D μ H( )D

ν Wμνi +

icB ′ g

2mρ2

H +t D μ H( )∂

ν Bμν

cγ ′ g 2g2

16π 2mρ2

H +HBμν Bμν +cggS

2y t2

16π 2mρ2

H +HGμνa Gaμν

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ic HW g

16π 2 f 2Dμ H( )

+σ i Dν H( )Wμν

i +ic HB ′ g

16π 2 f 2Dμ H( )

+Dν H( )Bμν

Loop-suppressed strong dynamics

€

1

f 2

€

1

mρ2

€

gρ2

16π 2

1

mρ2

17€

cH → L =1

21+ cH

v 2

f 2 1+h

v

⎛

⎝ ⎜

⎞

⎠ ⎟2 ⎡

⎣ ⎢

⎤

⎦ ⎥∂ μ h∂μ h All Higgs couplings

rescaled by

€

1

1+ cH

v 2

f 2

≈1−cH

2

v 2

f 2

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cy → L = −mψ

v1− cy

v 2

f 2

⎛

⎝ ⎜

⎞

⎠ ⎟ψ ψ h Modified Higgs couplings to matter

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v 2

f 2=

1

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Effects in Higgs production and decay

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Dührssen 2003

SLHC Report 2002

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LHC can measure cHv2/f2 and cyv2/f2 up to 20-40%

SLHC can improve it to about 10%

A sizeable deviation from SM in the absence of new light states would be indirect evidence for the composite nature of the Higgs

ILC can test v2/f2 up to the % level

ECFA/DESY LC Report 2001

ILC can explore the Higgs compositeness

scale 4f up to 30 TeV !!

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• Effective-theory approach is half-way between model-dependent and operator analyses

• Dominant effects come from strong self-Higgs interactions characterized by

• From operator analyses, Higgs processes loop-suppressed in SM are often considered most important for searches

• However, operators h and hgg are suppressed 1/(162mρ

2)

• Since h is charge and color neutral, gauging SU(3)cU(1)Q does not break the generator under which h shifts (Covariant derivative acting on h does not contain or g)

• Not the case for hZ (loop, but not 1/gρ suppressed)

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gρ

mρ

=1

f

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Higgs decay rates

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Genuine signal of Higgs compositeness at high energies

In spite of light Higgs, longitudinal gauge-boson scattering amplitude violate unitarity at high energies

hWL

WL

WL

WLModified coupling

LHC with 200 fb-1 sensitive up to cH 0.3

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Higgs is viewed as pseudoGoldstone boson: its properties are related to those of the exact

(eaten) Goldstones: O(4) symmetry

Can bbbb at high invariant mass be separated from background? h WW leptons is more promising

Sum rule (with cuts δ and s<M2)

Strong gauge-boson scattering strong Higgs production

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In many realizations, the top quark belongs to the strongly-coupled sector

At leading order in 1/f2

Modified top-quark couplings to h and Z

At ILC ghtt up to 5% with s=800 GeV and L=1000 fb-1

From gZtt, cR ~ 0.04 with s=500 GeV and L=300 fb-1 (no accuracy at LHC)

FCNC effects

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CONCLUSIONS

• Several new classes of theories with light Higgs and strong interactions

• Experimental question: is Higgs fundamental or composite?

• Model-independent approach to characterize its phenomenological consequences

• Modifications of Higgs production and decay rates, strong WW scattering, strong Higgs production

• ILC can help significantly in settling the issue