1. 1 THEORETICAL PREDICTIONS FOR COLLIDER SEARCHES “Big” and “little” hierarchy problems Supersymmetry Little Higgs Extra dimensions G.F. Giudice CERN

2. 2 HIERARCHY PROBLEM no  fine-tuning   SM < TeV “Big” hierarchy between  SM and M Pl Cosmological constant  Cut off of quartic divergences at  <10 -3 eV

3. 3 LITTLE HIERARCHY 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  +

4. 4  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 Successful new physics at  SM has to pass non-trivial tests

5. 5 SUPERSYMMETRY  m H 2 = H H + t ~ exp Ghilencea-Ross t  can be extended to M Pl -Link with quantum gravity -Successful scenario for GUT exp

6. 6 UNIFICATION WITHOUT DESERT Accelerated running from extra dimensions or from gauge group replication Different tree-level expression for sin 2  W GUT: trace over GUT irrep Little running needed Dienes-Dudas-Gherghetta Arkani Hamed-Cohen-Georgi Dimopoulos-Kaplan

7. 7 SUPERSYMMETRY Gauge-coupling unification Radiative EW breaking Light Higgs Satisfies “little” hierarchy  LH ~4  SM Dark matter Sparticles have not been observed Susy-breaking sector unspecified 

8. 8 Degrassi-Heinemeyer- Hollik-Slavich-Weiglein M  GeV

9. 9 Giusti-Romanino-Strumia

10. 10 Supersymmetry-breaking sector unspecified Susy flavour violations  gauge, gaugino mediation Connection with gravity  supergravity, anomaly mediation  problem  supergravity Predictivity  gauge, gaugino, anomaly med. Scenarios with different spectra and different experimental signals

11. 11 y R NEW INGREDIENTS FROM EXTRA DIMENSIONS Scherk-Schwarz breaking Supersymmetry is broken Non-local susy breaking  involves global structure At short distances (<R), susy-breaking effects are suppressed

12. 12 y R y Z2Z2 NEW INGREDIENTS FROM EXTRA DIMENSIONS 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

13. 13 5D SUSY SM compactified on S 1 /(Z 2 ×Z 2 ) Different susy breaking at each boundary  effective theory non-susy (susy recovered at d<R) Higgs boson mass (rather) insensitive to UV  m H = 127 ± 10 GeV  Large corrections to  ?  UV completion at  ~ 5 TeV ? AN INTERESTING EXAMPLE Barbieri-Hall-Nomura Barbieri-Hall-Marandella-Nomura-Okui- Oliver-Papucci

14. 14 Mass spectrum is non-supersymmetric one Higgs and two sparticles for each SM particle LSP stable stop with mass 210 GeV

15. 15 USING WARPED DIMENSIONS Susy-breaking in Higgs sector is non-local  finite effects AdS/CFT  SM non-susy Higgs sector: susy bound states of spontaneously broken CFT Light Higgs & higgsino New CFT states at L -1 ~ TeV Considerable fine tuning Susy breaking Higgs sector SM Gherghetta-Pomarol

16. 16 SUPERSYMMETRY: CONCLUSIONS Susy at EW scale can be realized in very different ways: E T miss E T miss +  E T miss + ℓ Stable charged particle Nearly-degenerate Stable stop Partial susy spectrum

17. 17 HIGGS AS PSEUDOGOLDSTONE BOSON Gauge, Yukawa and self-interaction are large non- derivative couplings  Violate global symmetry and introduce quadratic div.

18. 18 A less ambitious programme: Explain only little hierarchy At  SM new physics cancels one-loop power divergences LITTLE HIGGS “Collective breaking”: many (approximate) global symmetries preserve massless Goldstone boson ℒ1ℒ1 ℒ2ℒ2 H ℒ1ℒ1 ℒ2ℒ2 Arkani Hamed-Cohen-Georgi

19. 19 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. SU 2 gauge with   doublets such that V(           ) and   spontaneously break SU 2 Turning off gauge coupling to    Local SU 2 (  2 ) × global SU 2 (   ) both spont. broken Kaplan-Schmaltz

20. 20 Realistic models are rather elaborate Effectively, new particles at the scale f ~  SM canceling (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 ?) Arkani Hamed-Cohen-Georgi-Katz-Nelson-Gregoire-Wacker- Low-Skiba-Smith-Kaplan-Schmaltz-Terning…

21. 21 Bounds from: Tevatron limits on new gauge bosons EW data (  from new gauge and top) In minimal model: Variations significantly reduce the fine tuning Csaki-Hubisz-Kribs-Meade-Terning

22. 22 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 Do not reintroduce quadratic divergences Csaki-Grojean-Murayama Burdman-Nomura Scrucca-Serone-Silvestrini

23. 23 EXTRA DIMENSIONS Forget about symmetries, about little hierarchy  cut off at  SM Any short-distance scale <  SM -1 explained by geometry FLAT Arkani Hamed-Dimopoulos-Dvali WARPED Randall-Sundrum

24. 24 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

25. 25 Graviton emission Tree-level graviton exchange Graviton loops Gauge/graviton loop G.G.-Strumia

26. 26 √As s approaches M D, linearized gravity breaks down  underlying quantum gravity (strings?) TRANSPLANCKIAN REGIME S>>M D  R S >> Pl and (semi)classical effects dominate over quantum-gravity effects b > R S b < R S Gravitational scattering G.G.-Rattazzi-Wells Black-hole production Giddings-Thomas, Dimopoulos-Landsberg √

27. 27 SM PARTICLES IN EXTRA DIMENSIONS Gauge bosons in 5D: Direct + indirect limits M c > 6.8 TeV Cheung-Landsberg At LHC up to 13-15 TeV Weaker bounds in universal extra dimensions After compactification, momentum conservation in 5 th dim  KK number conserved KK particles pair produced; no tree-level exchange M c > 0.3 TeV Appelquist-Cheng-Dobrescu

28. 28 CONCLUSIONS Many open theoretical options for new physics at EW scale Direct searches + precision measurements  no existing theory is completely free of fine-tuning EW SUSY GUT E Connection with M Pl Gauge coupling unification Connection with M Pl Gauge coupling unification  LH or  SM  Need for UV completion at 