# Presentation: 505523

## EXTRA DIMENSIONS AT FUTURE HADRON COLLIDERS

- G.F. Giudice
- CERN

## LHC is the machine to study the scale of EW breaking

- 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

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

-  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

## GRAVITY IN EXTRA DIMENSIONS

- Fundamental scale at SM

- FLAT                        Arkani Hamed-Dimopoulos-Dvali

- WARPED                  Randall-Sundrum

## QUANTUM GRAVITY AT LHC

**H**

- Graviton emission

- Missing energy (flat)
- Resonances (warped)

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

- Higgs-radion mixing

## 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

## TRANSPLANCKIAN REGIME

- Planck length                                    quantum-gravity scale

- Schwarzschild radius

- classical gravity

- same regime

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

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

- Gravitational scattering: two-jet signal at hadron colliders

- G.G.-Rattazzi-Wells

## b < RS

**b < R****S**

- Giddings-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

## VLHC

- 2-jets with large Minv and Black holes

- Jets + missing ET 2-leptons

- QUANTUM GRAVITY

- Semi-classical approximation

- Linearized gravity

- Transplanckian

- Cisplanckian

- LHC

## 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 |

## SM<1 TeV,  LH>5-10 TeV

- 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

## EXTRA DIMENSIONS AND SYMMETRY BREAKING

- y

- R

**EXTRA DIMENSIONS AND SYMMETRY BREAKING**

- Scherk-Schwarz breaking

- Supersymmetry is broken

- Non-local susy breaking involves global structure
- At short distances (<R), susy-breaking effects are suppressed

## Orbifold projection

- Z2 :   y y                  cos(ny/R)              sin(ny/R)
-                                                                          

- Chiral theories

##     mH  = 127 ± 10 GeV

- 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

## 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

## 5-D SU(N) YANG-MILLS

**5-D SU(N) YANG-MILLS**

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

- Chivukula-Dicus-He

## HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD

- AM  = (A,A5),       A5  A5 +∂5     forbids  *m*2A52

- 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.

## Slide 19

## LHC will discover weak physics at SM 

- 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

## Slide 21

##  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