1 THEORETICAL PREDICTIONS FOR COLLIDER SEARCHES “Big” and “little” hierarchy problems Supersymmetry Little Higgs Extra dimensions G.F. Giudice CERN
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 LITTLE HIERARCHY LEP1 LEP2 MFV Bounds on LH LH > 5-10 TeV +
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 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 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 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 Degrassi-Heinemeyer- Hollik-Slavich-Weiglein M GeV
9 Giusti-Romanino-Strumia
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 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 y R y Z2Z2 NEW INGREDIENTS FROM EXTRA DIMENSIONS Orbifold projection RR 0 n=1 n=2 0 n=0 n=1 n=2 RR Z 2 : y y cos(ny/R) sin(ny/R) Chiral theories
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 Mass spectrum is non-supersymmetric one Higgs and two sparticles for each SM particle LSP stable stop with mass 210 GeV
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 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 HIGGS AS PSEUDOGOLDSTONE BOSON Gauge, Yukawa and self-interaction are large non- derivative couplings Violate global symmetry and introduce quadratic div.
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 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 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 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 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 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 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 Graviton emission Tree-level graviton exchange Graviton loops Gauge/graviton loop G.G.-Strumia
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 SM PARTICLES IN EXTRA DIMENSIONS Gauge bosons in 5D: Direct + indirect limits M c > 6.8 TeV Cheung-Landsberg At LHC up to 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 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