1

EXTRA DIMENSIONS AT FUTURE HADRON COLLIDERS

G.F. Giudice

CERN

2

LHC is the machine to study the scale of EW breaking

NEW THEORY

Desert, e.g. conventional susy need for precision

New thresholds around 10 TeV need for energy increase to make next step of discoveries

Multi-TeV linear collider?

VLHC ?

m < TeV measurements after LHC

VLHC not meant to push new-physics limits by an order of magnitude, but to explore a well-motivated

(after some LHC discoveries) energy region

3

EXTRA DIMENSIONS offer good motivations for explorations with a √s ~ 100 TeV hadron collider

• Need to test the theory well above the EW breaking scale

• Existence of new thresholds (new physics, not just some more KK) in the 10 TeV region

Motivations and implementions of extra dimensions are quite different

Not a systematic review, but some examples relevant to VLHC

4

GRAVITY IN EXTRA DIMENSIONS

GRAVITY IN EXTRA DIMENSIONSFundamental scale at SM

Any short-distance scale < SM

-1 explained by geometry

42/12/ DMRM DPl

KRPl eMM 5

FLAT Arkani Hamed-Dimopoulos-Dvali

WARPED Randall-Sundrum

5H

QUANTUM GRAVITY AT LHCQUANTUM GRAVITY AT LHC

Graviton emissionMissing energy (flat)

Resonances (warped)

TT

4

1

252

1ff

Contact interactions (loop dominates over tree if gravity is strong)

Higgs-radion mixing

6

These processes are based on linearized gravity valid at √s <<MD ~TeV

• Suitable for LHC

• VLHC can extend limits, but the motivations are weak

VLHC can probe the region √s >>MD~TeV

(only marginal at LHC)

independent test, crucial to verify gravitational nature of new physics

7

TRANSPLANCKIAN REGIME

2

1

3

c

GDP

1

1

3

1

1

2

3

2

81

c

sGR D

S

Planck length quantum-gravity scale

PSD

PS

RM

R

:slimit kian transplanc

:0 limit classical

Schwarzschild radius

classical gravity

same regime

8

b > RS

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

Gravitational scattering: two-jet signal at hadron colliders

G.G.-Rattazzi-Wells

9

b < RSGiddings-Thomas, Dimopoulos-Landsberg

At b<RS, no longer calculable

Strong indications for black-hole formation

At the LHC, limited space for transplanckian region and quantum-gravity pollution

At the VLHC, perfect conditions

See talk by T. Rizzo

10

2-jets with large Minv and Black holes

Jets + missing ET 2-leptons

QUANTUM GRAVITY

Semi-classical approximation

Linearized gravity

Transplanckian

Cisplanckian

VLHC

LHC

11

EXTRA DIMENSIONS AND THE THEORY OF ELECTROWEAK BREAKING

10

5.6

9.2

9.7

4.6

7.3

6.1

4.3

4.5

3.2

6.4

9.3

5.0

12.4

FqdH

qq

bbee

ee

LLHDiH

HDH

BWHH

LuudR

uuL

aa

2

55

2

2

1

LEP1

LEP2

MFV

Bounds on LH

LH > 5-10 TeV

+

O2LH

1L

12

SM<1 TeV, LH>5-10 TeV

“Little” hierarchy between SM and LH

•New physics at SM is weakly interacting

•No (sizable) tree-level contributions from new physics at SM

•Strongly-interacting physics can only occur at scales larger than LH

2

22222

2

2 GeV200TeV

4228

3

SM

tHZWSMF

H mmmmG

m

13

y

R

EXTRA DIMENSIONS AND SYMMETRY BREAKING

Scherk-Schwarz breaking

symmetry -R is Q If

)(),(

conditionsboundary with expansion KK

),()2,(

2

22//

2

R

Qnmxeeyx

yxeRyx

nnn

RinyRyiQ

iQ

Supersymmetry is broken

Non-local susy breaking involves global structure

At short distances (<R), susy-breaking effects are suppressed

14

y

R yZ2

Orbifold projection

R 0

n=1

n=2

0

n=0n=1

n=2

R

Z2 : y y cos(ny/R) sin(ny/R)

Chiral theories

15

5D SM compactified on S1/(Z2×Z2)

•Different susy breaking at each boundary

effective theory non-susy

(susy recovered at d<R-1)

• Higgs boson mass (rather) insensitive to UV

mH = 127 ± 10 GeV

SUPERSYMMETRY BREAKING: AN INTERESTING EXAMPLE Barbieri-Hall-Nomura

16

Mass spectrum is non-supersymmetric

• one Higgs and two sparticles for each SM particle

• LSP stable stop with mass 210 GeV

Interesting phenomenology at LHC

• Strong dynamics at 5/R ~ 1.7 TeV (5-10 TeV in other models)

• UV completion new unknown dynamics within VLHC range

17

5-D SU(N) YANG-MILLS

Elastic gauge-boson scattering in spin-0 gauge-singlet channel

Chivukula-Dicus-He

KKMgN

s

Rgg

sgN

T

2

5

2500

23

96

2

1

192

23 Unitarity

18

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 Kaluza-Klein

Higgs/gauge unification as graviton/photon unification in Kaluza-Klein

Correct Higgs quantum numbers by projecting out unwanted states with orbifold

Yukawa couplings, quartic couplings without reintroducing quadratic divergences

Csaki-Grojean-Murayama

Burdman-Nomura

Scrucca-Serone-Silvestrini

EW BROKEN BY BOUNDARY CONDITIONS? Csaki et al.

19

20

Calculable description of EW breaking with strong dynamics at 5-10 TeV

New realizations of technicolour theories with new elements (extra dimensions, AdS/CFT correspondence) allowing some calculability

“Little hierarchy” is satisfied

LHC will discover weak physics at SM

New strong-dynamics thresholds at LH within the reach of VLHC

21

DESERT

• Connection with GUT, strings, quantum gravity

• Gauge-coupling unification

• Neutrino masses

• Suppression of proton decay and flavour violations

• Setup for cosmology (inflation, baryogenesis)

NON DESERT

• Low-scale string theory,…

• Accelerated running, different sin2W

• R in bulk

• Different location of quarks and leptons in bulk

• Low-scale inflation, EW baryogenesis

22

• Extra dimensions ubiquitous ingredient in non-desert scenarios

• Physics goals of VLHC quite distinct from those of LHC

Examples:

• “Need to test the theory well above the EW breaking scale”

Transplanckian physics: new energy regime to test extra-dim gravity

• “Existence of new thresholds (new physics, not just some more KK) in the 10 TeV region”

Extra-dim theories of EW breaking require UV completion at a scale not far from EW

CONCLUSIONS