1. 1 EXTRA DIMENSIONS AT FUTURE HADRON COLLIDERS G.F. Giudice CERN

2. 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. 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. 4 GRAVITY IN EXTRA DIMENSIONS  Fundamental scale at  SM Any short-distance scale <  SM -1 explained by geometry FLAT Arkani Hamed-Dimopoulos-Dvali WARPED Randall-Sundrum

5. 5 H QUANTUM GRAVITY AT LHC Graviton emission Missing energy (flat) Resonances (warped) Contact interactions (loop dominates over tree if gravity is strong) Higgs-radion mixing

6. 6 These processes are based on linearized gravity valid at √s <<M D ~TeV Suitable for LHC VLHC can extend limits, but the motivations are weak VLHC can probe the region √s >>M D ~TeV (only marginal at LHC)  independent test, crucial to verify gravitational nature of new physics

7. 7 TRANSPLANCKIAN REGIME Planck length quantum-gravity scale Schwarzschild radius classical gravity same regime

8. 8 b > R S Non-perturbative, but calculable for b>>R S (weak gravitational field) Gravitational scattering: two-jet signal at hadron colliders G.G.-Rattazzi-Wells

9. 9 b < R S Giddings-Thomas, Dimopoulos-Landsberg At b<R S, 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. 10 2-jets with large M inv and  Black holes Jets + missing E T 2-leptons QUANTUM GRAVITY Semi-classical approximation Linearized gravity Transplanckian Cisplanckian VLHC LHC

11. 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 LEP1 LEP2 MFV Bounds on  LH  LH > 5-10 TeV  +

12. 12  SM 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

13. 13 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

14. 14 y R y Z2Z2 Orbifold projection RR 0 n=1 n=2 0 n=0 n=1 n=2 RR Z 2 : y   y cos(ny/R) sin(ny/R)   Chiral theories

15. 15 5D SM compactified on S 1 /(Z 2 ×Z 2 ) Different susy breaking at each boundary  effective theory non-susy (susy recovered at d<R -1 ) Higgs boson mass (rather) insensitive to UV  m H = 127 ± 10 GeV SUPERSYMMETRY BREAKING: AN INTERESTING EXAMPLE Barbieri-Hall-Nomura

16. 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. 17 5-D SU(N) YANG-MILLS Elastic gauge-boson scattering in spin-0 gauge-singlet channel Chivukula-Dicus-He

18. 18 HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD A M = (A ,A 5 ), A 5  A 5 + ∂ 5  forbids m 2 A 5 2 gaugeHiggs 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. 19

20. 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. 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 sin 2  W R in bulk Different location of quarks and leptons in bulk Low-scale inflation, EW baryogenesis

22. 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