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1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007
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Page 1: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

1

Extra dimensioni e la fisica elettrodebole

G.F. Giudice

Napoli, 9-10 maggio 2007

Page 2: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

2

SPACE DIMENSIONS AND UNIFICATION

Minkowski recognized special relativistic invariance of Maxwell’s eqs connection between unification of forces and number of dimensions

Electric & magnetic forces unified in 4D space time

r∇ ⋅

rE = ρ

r ∇ ×

r E = −

∂r B

∂tr

∇ ⋅r B = 0

r ∇ ×

r B =

∂r E

∂t+

r J

⎨ ⎪ ⎪

⎩ ⎪ ⎪

space - time t,r x → x μ = (t,

r x )

EM potentials r E = −

r ∇φ −

∂r A

∂t,

r B =

r ∇ ×

r A → Aμ = (φ,

r A )

EM fields r E ,

r B → Fμν = ∂μ Aν −∂ν Aμ =

0 −Ex −Ey −E z

Ex 0 Bz −By

Ey −Bz 0 Bx

E z By −Bx 0

⎜ ⎜ ⎜ ⎜

⎟ ⎟ ⎟ ⎟

current ρ,r J → Jμ = ( ρ,

r J )

Maxwell's eqs → ∂μ F μν = Jν

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3

UNIFICATION OF EM & GRAVITYNext step:

New dimensions?

1912: Gunnar Nordström proposes gravity theory with scalar field coupled to T

1914: he introduces a 5-dim A to describe both EM & gravity

1919: mathematician Theodor Kaluza writes a 5-dim theory for EM & gravity. Sends it to Einstein who suggests publication 2 years later

1926: Oskar Klein rediscovers the theory, gives a geometrical interpretation and finds charge quantization

In the ‘80s the theory, known as Kaluza-Klein becomes popular with supergravity and strings

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4

GRAVITY

In General Relativity, metric (4X4 symmetric tensor) dynamical variable describing space geometry (graviton)

ds2 = gμν dx μ dxν

gμν

Dynamics described by Einstein action

SG =1

16π GN

d4∫ x −g R(g)

• GN Newton’s constant

• R curvature (function of the metric)

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Consider GR in 5-dim

ˆ S G =1

16π ˆ G Nd5∫ x −ˆ g R( ˆ g )

Choose

ˆ g MN ( ˆ x ) =gμν + κ 2φ Aμ Aν κ φ Aμ

κ φ Aν φ

⎝ ⎜

⎠ ⎟( ˆ x )

ˆ g MN ⇔ gμν , Aμ , φDynamical fields

Assume space is M4S1

• First considered as a mathematical trick

• It may have physical meaning

(t,x)

x5

R

Page 6: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

6

Extra dim is periodic or “compactified”

x5 + 2π R = x5

All fields can be expanded in Fourier modes

ϕ ( ˆ x ) =ϕ (n )(x)

2π Rn=−∞

+∞

∑ exp in x5

R

⎝ ⎜

⎠ ⎟

5-dim field set of 4-dim fields: Kaluza-Klein modes

ϕ (n )(x)

Each has a fixed momentum p5=n/R along 5th dim

ϕ (n )

4-d space

extra dimensions

mass

D-dim particle

E2 = p 2 + p2extra + m2

KK mass

From KK mass spectrum we can measure the geometry of extra dimensions

Page 7: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

7

R

r << R r >> R

2-d plane

1-d line

Suppose typical energy << 1/R only zero-modes can be excited

Expand SG keeping only zero-modes and setting ϕ=1

ˆ S G ( ˆ g MN ) = SG (g(0)μν ) + SEM (A(0)

μ )

SG (g) =1

16π GN

d4 x −g R(g)∫

SEM (A) = −1

4d4 x Fμν F μν∫

⎨ ⎪

⎩ ⎪

To obtain correct normalization:

SG →1

GN

=dx5∫ˆ G N

=2π R

ˆ G N

SEM → κ = 16π GN

Gravity & EM unified in higher-dim space: MIRACLE?

Page 8: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

8

Gauge transformation has a geometrical meaning

dˆ s 2 = ˆ g MN ( ˆ x ) dˆ x M dˆ x N

ˆ g MN ( ˆ x ) =gμν + κ 2φ Aμ Aν κ φ Aμ

κ φ Aν φ

⎝ ⎜

⎠ ⎟( ˆ x )

Keep only zero-modes:

dˆ s 2 = g(0)μν dx μ dxν + φ(0) dx 5 + κ A(0)

μ dx μ( )

2

Invariant under local

x 5 → x 5 −κ Λ

A(0)μ → A(0)

μ + ∂μ Λ(where g and ϕ

do not transform)

• Gauge transformation is balanced by a shift in 5th dimension

• EM Lagrangian uniquely determined by gauge invariance

Page 9: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

9

CHARGE QUANTIZATION

Matter EM couplings fixed by 5-dim GR

Consider scalar field

S = d5 ˆ x −ˆ g ˆ g MN∂Mϕ∫ ∂Nϕ

Expand in 4-D KK modes:

S = dx5 d4 x −g(0) ∂ μ − inκ

RA(0)μ ⎛

⎝ ⎜

⎠ ⎟ϕ (n )

2

−n2

R2

ϕ (n )2

φ

⎣ ⎢ ⎢

⎦ ⎥ ⎥

∫n

∑∫

2π R

Each KK mode n has: mass n/R charge n/R

• charge quantization

• determination of fine-structure constant

• new dynamics open up at Planckian distances

α = 2

4π R2=

4GN

R2⇒ R =

4GN

α≈ 4 ×10−31 m = 5 ×1017 GeV( )

−1

Page 10: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

10

Not a theory of the real world

ϕ=1 not consistent (ϕ dynamical field leads to inconsistencies: e.g. F(0)

F(0)=0 from eqs of motion)

• Charged states have masses of order MPl

• Gauge group must be non-abelian (more dimensions?)

Nevertheless

• Interesting attempt to unify gravity and gauge interactions

• Geometrical meaning of gauge interactions

• Useful in the context of modern superstring theory

• Relevant for the hierarchy problem?

Page 11: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

11

Usual approach: fundamental theory at MPl, while W is a derived quantity

Alternative: W is fundamental scale, while MPl is a derived effect

New approach requires• extra spatial dimensions

• confinement of matter on subspaces

Natural setting in string theory Localization of gauge theories on defects (D-branes: end points

of open strings)

We are confined in a 4-dim world, which is embedded in a higher-dim space where gravity can propagate

Page 12: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

12

COMPUTE NEWTON CONSTANT

Einstein action in D dimensions

SED =

1

16π ˆ G NdD x −ˆ g R( ˆ g )∫

Assume space R4SD-4: g doesn’t depend on extra coordinates

Effective action for g

SE =VD−4

16π ˆ G Nd4 x −g R(g)∫

⇒1

GN

=VD−4

ˆ G N

MPl = MD RMD( )D−4

2

ˆ G N =1

MDD−2

VD−4 = RD−4

Page 13: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

13

Suppose fundamental mass scale MD ~ TeV

MPl = MD RMD( )D−4

2 very large if R is large (in units of MD-1)

Arkani-Hamed, Dimopoulos, Dvali

5 ×10−4 eV( )−1

≈ 0.4 mm D − 4 = 2

R = 20 keV( )−1

≈10−5 μ m D − 4 = 4

7 MeV( )−1

≈ 30 fm D − 4 = 6

Radius of compactified space

• Smallness of GN/GF related to largeness of RMD

• Gravity is weak because it is diluted in a large space (small overlap with branes)

• Need dynamical explanation for RMD>>1

Page 14: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

14

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V (r) = −GN

m1m2

r1+ α exp −r λ( )[ ]

α

Gravitational interactions modified at small distances

FN (r) = GN

m1m2

r2 at r > R

At r < R, space is (3+)-dimensional (=D-4)

FN (r) = ˆ G N(4 +δ ) m1m2

r2+δ=

= GN Rδ m1m2

r2+δ

From SN emission and neutron-star heating:

MD>750 (35) TeV for =2(3)

Page 15: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

15

Probability of producing a KK graviton

≈E 2

MPl2

σ pp → G(n ) jet( ) =α s

πGN =10−28 fb 1 event ⇒ run LHC for 1016 tU

Number of KK modes with mass less than E (use m=n/R)

∝ nD−4 ≈ ER( )D−4

≈E D−4 MPl

2

MDD−2

Inclusive cross section

σ pp → G(n ) jet( ) ≈α sE

D−4

π MDD−2

n

graviton

gluon

It does not depend on VD (i.e. on the Planck mass)

Missing energy and jet with characteristic spectrum

Testing extra dimensions at high-energy colliders

Page 16: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

16

Page 17: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

17

Contact interactions from graviton exchange

L = ±4π

ΛT4

T

T =1

2Tμν T μν −

1

D − 2Tμ

μTνν ⎛

⎝ ⎜

⎠ ⎟

• Sensitive to UV physics

• d-wave contribution to scattering processes

• predictions for related processes

• Limits from Bhabha/di- at LEP and Drell-Yan/ di- at Tevatron: T > 1.2 - 1.4 TeV

• Loop effect, but dim-6 vs. dim-8

• only dim-6 generated by pure gravity

• > 15 - 17 TeV from LEP

L = ±4π

ΛΥ2

Υ

Υ =1

2f γ μγ 5 f

f = q,l

∑ ⎛

⎝ ⎜ ⎜

⎠ ⎟ ⎟

2

Page 18: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

18

TRANSPLANCKIAN REGIME2

1

3

+⎟⎠

⎞⎜⎝

⎛=

c

GDP

h

1

1

3

1

1

2

3

2

81 ++

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ +Γ

+=

π c

sGR D

S

Planck length quantum-gravity scale

classical limit h → 0( ) : RS >> λ P

transplanckian limit s >> MD( ) : RS >> λ P

Schwarzschild radius

classical gravity

same regime

G-emission is based on linearized gravity, valid at s << MD2

The transplanckian regime is described by classical physics (general relativity) independent test, crucial to verify

gravitational nature of new physics

Page 19: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

19

b > RS

Non-perturbative, but calculable for b>>RS (weak gravitational field)

θ ≈∂b

∂L≈

bcδ

mvbδ +1 rel . ⏐ → ⏐ GD s

bδ +1θE =

4GD s

b

D-dim gravitational potential:

V (r) =GDmM

rδ +1D = 4 + δ

Quantum-mechanical scattering phase of wave with angular momentum mvb

b = −bc

b

⎝ ⎜

⎠ ⎟

δ

bc ≈GDmM

vh

⎝ ⎜

⎠ ⎟

1

δ

Gravitational scattering

θbvm

Page 20: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

20

Diffractive pattern characterized by

bc ≈GDs

h

⎝ ⎜

⎠ ⎟

1

δ

Gravitational scattering in extra dimensions: two-jet signal at the LHC

Page 21: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

21

b < RS At b<RS, no longer calculable

Strong indications for black-hole formation

Characteristic events with large multiplicity (<N> ~ MBH / <E> ~ (MBH / MD2)/(+1)) and typical energy <E> ~ TH

BH with angular momentum, gauge quantum numbers, hairs (multiple moments of the asymmetric distribution of gauge charges and energy-momentum)

σ ~ πRS2 10 pb (for MBH=6 TeV and MD=1.5 TeV)

Gravitational and gauge radiation during collapse spinning Kerr BH

Hawking radiation until Planck phase is reached TH ~ RS

-1 ~ MD (MD / MBH)1/1)

Evaporation with ~ MBH(+3)/(+1) / MD

2(+2)/(+1) (10-26 s for MD=1 TeV)

Transplanckian condition MBH >> MD ?

Page 22: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

22

WARPED GRAVITY

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are needed to see this picture.

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A classical mechanism to make quanta softer

For time-indep. metrics with g0=0 E |g00|1/2 conserved . (proper time d2 = g00 dt2)

Schwarzschild metric g00 =1−2GN M

r⇒

Eobs − Eem

Eem

= g00 −1= −GN M

rem

On non-trivial metrics, we see far-away objects as red-shifted

Page 23: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

23

Randall Sundrum

Consider observer & emitter as 3-d spaces (branes) embedded in non-trivial 5-D space-time geometries

5th dim S1 / Z2: identify y y+2πR, y -y

y

0 πR

y

0 πR

-y

0 πR

Two 3-branes on boundaries & appropriate vacuum-energy terms

ds2 = e−2K |y|η μν dx μ dxν + dy 2

Page 24: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

24

GRAVITATIONAL RED-SHIFT

ds2 = e−2K |y|η μν dx μ dxν + dy 2

Masses on two branes related by

mπR

m0

= e−πRK

Same result can be obtained by integrating SE over y

R ≈10 K−1 ⇒mπR

m0

≈MZ

MGUT

y=0 g00=1

y=πR g00=e-2πRK

Page 25: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

25

PHYSICAL INTERPRETATION• Gravitational field configuration is non-trivial

• Gravity concentrated at y=0, while our world confined at y=πR

• Small overlap weakness of gravity

WARPED GRAVITY AT COLLIDERS• KK masses mn = Kxne-πRK [xn roots of J1(x)] not equally spaced

• Characteristic mass Ke-πRK ~ TeV

• KK couplings

• KK gravitons have large mass gap and are “strongly” coupled

• Clean signal at the LHC from G l+l- €

L = −T μν Gμν(0)

MPl

+Gμν

(n )

Λπn=1

∑ ⎛

⎝ ⎜

⎠ ⎟ Λπ ≡ e−πRK MPl ≈ TeV

Page 26: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

26

Spin 2

Spin 1

Page 27: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

27

A SURPRISING TWISTAdS/CFT correspondence relates 5-d gravity with

negative cosmological constant to strongly-coupled 4-d conformal field theory

Theoretical developments in extra dimensions have much contributed to model building of 4-dim theories

of electroweak breaking: susy anomaly mediation, susy gaugino mediation, Little Higgs, Higgs-gauge

unification, composite Higgs, Higgsless, …

Warped gravity with SM fermions and

gauge bosons in bulk and Higgs on brane

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

Page 28: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

28

What screens the Higgs mass?

What screens the Higgs mass?

→ + a

no m2φ2

boson

Spont. broken global symm.

ψ → e iaγ 5ψ

no mψ ψ

fermion

Chiral symmetry

Aμ → Aμ + ∂μ a

no m2Aμ Aμ

vector

Gauge symmetry

mH

Dynamical EW breaking

Delayed unitarity violat.

Fundamental scale at TeV

• Very fertile field of research• Different proposals not mutually excluded

LITTLE HIGGS SUPERSYMMETRY HIGGS-GAUGE UNIF.

TECHNICOLOR HIGGSLESS EXTRA DIMENSIONS

Symmetry

Dynamics

Page 29: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

29

Cancellation of Existence of

positron

charmtop

10-3 eV??CAVEAT EMPTOR

electron self-energyπ+-π0 mass differenceKL-KS

mass differencegauge anomaly

cosmological constant

Necessary tuning MZ

2

Λ2→

MZ2

MGUT2

≈10−28

Qu

ickTim

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and

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d to

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ture

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n

It is a problem of naturalness, not of consistency!

Page 30: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

30

HIGGS AS PSEUDOGOLDSTONE BOSON

Φ= + 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

If the scale of New Physics is so low, why do LEP data work so well?

Page 31: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

31A less ambitious programme: solving the little hierarchy

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strong dynamics

new physics

energy 1 TeV 10 TeV

Little Higgs Composite Higgs

Higgsless

LEP

H +τ aHWμνa Bμν 10 9.7

H +Dμ H2

5.6 4.6

iH +Dμ H L γ μ L 9.2 7.3

e γ μe l γ μl 6.1 4.5

e γ μγ 5eb γ μγ 5b 4.3 3.2

1

2q Lλ uλ u

+γ μq( )2 6.4 5.0

H +d R λ d λ uλ u+σ μν qLF μν 9.3 12.4

LEP1

LEP2

MFV

-- +

L = ±1

Λ2O

Bounds on [TeV]

Page 32: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

32

Explain only little hierarchy

At SM new physics cancels one-loop power divergences

LITTLE HIGGS

LH

224

4

22

222

2

TeV10 loops Two

TeV loop One

≈≈≈⇒=

≈<⇒=

SMFSM

FH

FSMSMSM

FH

mGm

Gm

Gm

Gm

ππ

ππ

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

2

H2

222

44=

ππ Hm

ℒ1 ℒ2

Page 33: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

33

It can be achieved with gauge-group replication

•Goldstone bosons in

• gauged subgroups, each preserving a non-linear global symmetry

• which breaks all symmetries

Field replication Ex. SU2 gauge with Φ doublets such that V(Φ

ΦΦΦ) and

Φ spontaneously break SU2

Turning off gauge coupling to Φ

Local SU2(Φ2) × global SU2(Φ) both spont. broken

HG /

21 GGG ×⊃

21SM GG ×⊂

( )loops two

42

4

42 Λ≈

πδ

gmH

Page 34: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

34

Realistic models are rather elaborate

Effectively, new particles at the scale f cancel (same-spin) SM one-loop divergences with couplings related by symmetry

Typical spectrum:

Vectorlike charge 2/3 quark

Gauge bosons EW triplet + singlet

Scalars (triplets ?)

Page 35: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

35

New states have naturally mass

New states cut-off quadratically divergent contributions to mH

Ex.: littlest Higgs model

Log term: analogous to effect of stop loops in supersymmetry

Severe bounds from LEP data

Page 36: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

36

TESTING LITTLE HIGGS AT THE LHC

• Discover new states (T, W’, Z’, …)

• Verify cancellation of quadratic divergences

mT

f=

λ t2 + λT

2

2λT

f from heavy gauge-boson masses

mT from T pair-production

T : we cannot measure TThh vertex (only model-dependent tests possible)

Page 37: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

37

MT from T production can be measured up to 2.5 TeV

f and gH from DY of new gauge

bosons

Production rate and BR into leptons in region favoured by LEP (gH>>gW)

Can be seen up to ZH mass of 3 TeV

Page 38: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

38

Possible to test cancellation with 10% accuracy for mT < 2.5 TeV and mZ < 3 TeV

Cleanest peak from

In order to precisely extract T from measured cross section, we must control b-quark partonic density

Γ T → bW( ) = 2Γ T → tZ( ) = 2Γ T → th( )∝ λT2

Measure T width?

Page 39: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

39

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

NEW INGREDIENTS FROM EXTRA DIMENSIONS

Page 40: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

40

HIGGSLESS MODELS

Breakdown of unitarity:

4 d ⇒ Λ ≈4π mW

g≈ TeV

5d ⇒ Λ ≈24π 3

g52

≈12π 2 mW

g2≈10 TeV

no zero modes in restricted extra-D spaces (Scherk-Schwarz mechanism)

New ways of breaking gauge symmetries:

The gauge KK modes delay unitarity violation

Page 41: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

41

y

RScherk-Schwarz breaking

A field under a 2πR translation has to remain the same, unless there is a symmetry (the field has to be equal up

to a symmetry transformation)

Φ x, y + 2πR( ) = e iQ Φ x, y( )

KK expansion with orbifold boundary condition

Φ x, y( ) = eiQy

2πR einy

R

n=−∞

+∞

∑ Φ(n )(x) ⇒ mn2 = n +

Q

⎝ ⎜

⎠ ⎟2

1

R2

No more zero-modes!

Page 42: 1 Extra dimensioni e la fisica elettrodebole G.F. Giudice Napoli, 9-10 maggio 2007.

42

At the LHC discover KK resonances of gauge bosons and test sum rules on couplings and masses required

to improve unitarity

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43

DUALITY

AdS/CFT Composite Higgs

5-D warped gravity

large-N technicolor

SM in warped extra dims strongly-int’ing 4-d theory

KK excitations “hadrons” of new strong force

Technicolor strikes back?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

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44

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 4πf at few TeV

S =N

v 2

f 2

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45

Structure of the theory

m mass of resonances g 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)

σ-model with f = m / g

Take I, ga << g < 4π

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46

ga , i break global symmetry Higgs mass

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

-1)

mH2 ≈

α

4πmρ

2

Ex.:

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

• Holographic Higgs: g= gKK, m= mKK

• Little Higgs: g, m couplings and masses of new t’, W’, Z’

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47

Production of resonances at m 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

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48

Construct the Lagrangian of the effective theory below m

U = e iπ aT a

Goldstones; Φ heavy fields

LSILH =mρ

4

gρ2

L(0) U,Φ,∂

⎝ ⎜ ⎜

⎠ ⎟ ⎟+

gρ2

16π 2L(1) U,Φ,

⎝ ⎜ ⎜

⎠ ⎟ ⎟+

gρ4

16π 2( )

2 L(2) U,Φ,∂

⎝ ⎜ ⎜

⎠ ⎟ ⎟+ ...

⎢ ⎢

⎥ ⎥

From the kinetic term, we obtain the definition of f = m / g

Each extra H insertion gives operators suppressed by 1 / f

• Each extra derivative “ “ 1 / m

g2

mW2 − q2

=4

v 21+

q2

mW2

+ ... ⎛

⎝ ⎜

⎠ ⎟

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

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

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49

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

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 m

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

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

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50€

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

cy → L = −mψ

v1− cy

v 2

f 2

⎝ ⎜

⎠ ⎟ψ ψ h Modified Higgs couplings to matter

v 2

f 2=

1

4

Effects in Higgs production and decay

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51

Dührssen 2003

SLHC Report 2002

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52

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 4πf 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/(16π2m

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/g suppressed)

=1

f

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54

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 and s<M2)

Strong gauge-boson scattering strong Higgs production

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57

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

FCNC effects


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