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THEORETICAL PREDICTIONSFOR COLLIDER SEARCHES Big and little hierarchy problems Supersymmetry Little Higgs Extra dimensionsG.F. Giudice CERN

HIERARCHY PROBLEMno fine-tuning a LSM < TeVBig hierarchy between LSM and MPl

Cosmological constant aCut off of quartic divergences at L

LITTLE HIERARCHY

LSM5-10 TeVLittle hierarchy between LSM and LLH aNew physics at LSM is weakly interactingNo (sizable) tree-level contributions from new physics at LSMStrongly-interacting physics can only occur at scales larger than LLHSuccessful new physics at LSM has to pass non-trivial tests

SUPERSYMMETRYexpGhilencea-Ross can be extended to MPlLink with quantum gravitySuccessful scenario for GUTexp

UNIFICATION WITHOUT DESERTAccelerated running from extra dimensions or from gauge group replicationDifferent tree-level expression for sin2qWGUT: trace over GUT irrep

Little running needed Dienes-Dudas-GherghettaArkani Hamed-Cohen-GeorgiDimopoulos-Kaplan

SUPERSYMMETRYGauge-coupling unificationRadiative EW breakingLight HiggsSatisfies little hierarchy LLH~4pLSMDark matter

Sparticles have not been observedSusy-breaking sector unspecified

Degrassi-Heinemeyer-Hollik-Slavich-WeigleinMc+ > 103.5 GeV

Giusti-Romanino-Strumia

Supersymmetry-breaking sector unspecifiedSusy flavour violations gauge, gaugino mediation Connection with gravity _ supergravity, anomaly mediation problem _ supergravityPredictivity _ gauge, gaugino, anomaly med.Scenarios with different spectra and different experimental signals

- yRNEW INGREDIENTS FROM EXTRA DIMENSIONSScherk-Schwarz breakingSupersymmetry is brokenNon-local susy breaking _ involves global structureAt short distances (
NEW INGREDIENTS FROM EXTRA DIMENSIONSOrbifold projectionpR0n=1n=20n=0n=1n=2pRZ2 : y g-y cos(ny/R) sin(ny/R) + -Chiral theories

- 5D SUSY SM compactified on S1/(Z2Z2)Different susy breaking at each boundaryeffective theory non-susy (susy recovered at d
Mass spectrum is non-supersymmetric one Higgs and two sparticles for each SM particle LSP stable stop with mass 210 GeV

USING WARPED DIMENSIONSSusy-breaking in Higgs sector is non-local _ finite effectsAdS/CFT _ SM non-susyHiggs sector: susy bound states of spontaneously broken CFT

Light Higgs & higgsinoNew CFT states at L-1 ~ TeVConsiderable fine tuningSusy breakingHiggs sectorSMGherghetta-Pomarol

SUPERSYMMETRY: CONCLUSIONSSusy at EW scale can be realized in very different ways:ETmiss ETmiss + gETmiss + Stable charged particleNearly-degenerate Stable stopPartial susy spectrum

HIGGS AS PSEUDOGOLDSTONE BOSONGauge, Yukawa and self-interaction are large non-derivative couplings _Violate global symmetry and introduce quadratic div.

LITTLE HIGGSA less ambitious programme:Explain only little hierarchy

At LSM new physics cancels one-loop power divergences

Collective breaking: many (approximate) global symmetries preserve massless Goldstone bosonArkani Hamed-Cohen-Georgi

It can be achieved with gauge-group replicationGoldstone bosons in gauged subgroups, each preserving a non-linear global symmetry which breaks all symmetriesField replication Ex. SU2 gauge with F1,2 doublets such that V(F1+F1,F2+F2) and F1,2 spontaneously break SU2Turning off gauge coupling to F1 _ Local SU2(F2) global SU2(F1) both spont. brokenKaplan-Schmaltz

Realistic models are rather elaborate

Effectively, new particles at the scale f ~ LSM canceling (same-spin) SM one-loop divergences with couplings related by symmetryTypical spectrum:Vectorlike charge 2/3 quarkGauge bosons EW triplet + singlet

Scalars (triplets ?)Arkani Hamed-Cohen-Georgi-Katz-Nelson-Gregoire-Wacker-Low-Skiba-Smith-Kaplan-Schmaltz-Terning

Bounds from: Tevatron limits on new gauge bosons EW data (Dr from new gauge and top) In minimal model:Variations significantly reduce the fine tuningCsaki-Hubisz-Kribs-Meade-Terning

HIGGS AS EXTRA-DIM COMPONENT OF GAUGE FIELDAM = (Am,A5), A5 g A5 +5 L forbids m2A52Correct Higgs quantum numbers by projecting out unwanted states with orbifold Yukawa couplingsQuartic couplingsDo not reintroduce quadratic divergencesCsaki-Grojean-MurayamaBurdman-NomuraScrucca-Serone-Silvestrini

FLAT Arkani Hamed-Dimopoulos-DvaliWARPED Randall-Sundrum

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

Graviton emission

Tree-level graviton exchange

Graviton loops

Gauge/graviton loop

G.G.-Strumia

Gravitational scatteringG.G.-Rattazzi-WellsBlack-hole productionGiddings-Thomas, Dimopoulos-Landsberg

SM PARTICLES IN EXTRA DIMENSIONSGauge bosons in 5D: Direct + indirect limits Mc > 6.8 TeV Cheung-Landsberg At LHC up to 13-15 TeV

Weaker bounds in universal extra dimensions After compactification, momentum conservation in 5th dim _ KK number conserved KK particles pair produced; no tree-level exchange Mc > 0.3 TeV Appelquist-Cheng-Dobrescu

CONCLUSIONSMany open theoretical options for new physics at EW scaleDirect searches + precision measurements _ no existing theory is completely free of fine-tuning Connection with MPl Gauge coupling unification ~ LLH or LSM _ Need for UV completion at L

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

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