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Discover the potential of extra dimensions with a focus on future hadron colliders. Contribute to new physics understanding beyond the Electroweak breaking scale and verify theories with energy scales around 10 TeV. Various scenarios discussed, including Quantum Gravity implications and SUSY breaking effects. Extra Dimensions and Symmetry Breaking concepts are explored with relevance to VLHC.
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EXTRA DIMENSIONS AT FUTURE HADRON COLLIDERS G.F. Giudice CERN
Desert, e.g. conventional susy need for precision m < TeV measurements after LHC Multi-TeV linear collider? NEW THEORY New thresholds around 10 TeV need for energy increase to make next step of discoveries VLHC ? 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
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
Any short-distance scale < LSM-1 explained by geometry GRAVITY IN EXTRA DIMENSIONS Fundamental scale at LSM FLAT Arkani Hamed-Dimopoulos-Dvali WARPED Randall-Sundrum
QUANTUM GRAVITY AT LHC Missing energy (flat) Resonances (warped) Graviton emission Contact interactions (loop dominates over tree if gravity is strong) Higgs-radion mixing H
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 classical gravity Schwarzschild radius same regime
b > RS Non-perturbative, but calculable for b>>RS (weak gravitational field) Gravitational scattering: two-jet signal at hadron colliders G.G.-Rattazzi-Wells
At b<RS, no longer calculable Strong indications for black-hole formation Giddings-Thomas, Dimopoulos-Landsberg b < RS See talk by T. Rizzo At the LHC, limited space for transplanckian region and quantum-gravity pollution At the VLHC, perfect conditions
2-jets with large Minv and Dh Black holes VLHC Semi-classical approximation Transplanckian QUANTUM GRAVITY Linearized gravity Cisplanckian LHC Jets + missing ET 2-leptons
- + LEP1 Bounds on LLH LLH> 5-10TeV LEP2 MFV EXTRA DIMENSIONS AND THE THEORY OF ELECTROWEAK BREAKING
LSM<1 TeV, LLH>5-10 TeV “Little” hierarchy between LSM and LLH a • New physics at LSM is weakly interacting • No (sizable) tree-level contributions from new physics at LSM • Strongly-interacting physics can only occur at scales larger than LLH
EXTRA DIMENSIONS AND SYMMETRY BREAKING y Scherk-Schwarz breaking R Supersymmetryisbroken Non-local susy breaking _ involves global structure At short distances (<R), susy-breaking effects are suppressed
y y R Z2 n=0 n=1 n=1 n=2 n=2 0 0 pR pR Orbifold projection Z2 : y g-y cos(ny/R) sin(ny/R) +- Chiral theories
SUPERSYMMETRY BREAKING: AN INTERESTING EXAMPLE Barbieri-Hall-Nomura • 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
Interesting phenomenology at LHC • Mass spectrum is non-supersymmetric • one Higgs and two sparticles for each SM particle • LSP stable stop with mass 210 GeV • 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 Elastic gauge-boson scattering in spin-0 gauge-singlet channel Chivukula-Dicus-He
Higgs/gauge unification as graviton/photon unification in Kaluza-Klein gauge Higgs HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELD AM = (Am,A5), A5g A5 +∂5L forbids m2A52 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.
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 LSM New strong-dynamics thresholds at LLH within the reach of VLHC
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 sin2qW • nR in bulk • Different location of quarks and leptons in bulk • Low-scale inflation, EW baryogenesis
CONCLUSIONS • 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