"It is wrong to think that the task of Physics is to find out how Nature is. LHC Physics Physics concerns what we can say about Nature." [Niels Bohr, Nobel laureate 1922]

Antonella De Santo

Royal Holloway, University of London

Intercollegiate PG Lecture Series

UCL, December 11-12, 2007 December 11-12, 2007 Antonella De Santo, RHUL 1

LHC Main Goals What’s on the Physics Menu

Elucidate mechanism for EW symmetry breaking Higgs Boson Search or Higgs boson in O(100 GeV)-O(1 TeV) range Multipurpose If no light Higgs is found, study WW scattering at high mass (SUSY) detectors (ATLAS and CMS) Look for evidence of new physics at TeV-scale Non-SUSY BSM physics

Deviations from SM predictions No CP-violation (LHCb)

SM only low-energy “effective theory” of more fundamental theory valid at higher energies No Heavy Ions (ALICE)

December 11-12, 2007 Antonella De Santo, RHUL 2 December 11-12, 2007 Antonella De Santo, RHUL 3 Outline

Introduction The LHC ATLAS and CMS EW Symmetry Breaking THE LHC Higgs boson Not an exhaustive list! Supersymmetry mSUGRA Beyond SUSY

Extra Dimensions

December 11-12, 2007 Antonella De Santo, RHUL 4

The LHC – some basic facts

LHC housed in former LEP tunnel 27 km circumference

Proton-proton machine s =14 TeV

Superconducting magnets B = 8.4 T p[GeV/c] = 0.3 B[T] R[m] Limiting factor for total energy (Only 60% of circumference is magnetised)

December 11-12, 2007 Antonella De Santo, RHUL 6 December 11-12, 2007 Antonella De Santo, RHUL 7 Luminosity Luminosity – cont’d f n n Rate (= no. of interactions per unit time): 1 2 25 ns L = R = σ L A

f = revolution frequency Integrated number of interactions: n1 , n2 = # of particles per beam N = ∫σ L(t) dt A= effective beam x-sectional area

Design luminosity: 25 ns bunch crossing (Æ 40 MHz crossing frequency) σ = cross section 2835 / 3564 “full” bunches “Low” = 1033 cm-2 s-1 (O(10 fb-1) / yr ) L = luminosity n1 = n2 = 1011 34 -2 -1 -1 “High” = 10 cm s (O(100 fb ) / yr) 2 σbeam = 16 μm (gaussian transverse beam profile, A=4πσbeam )

December 11-12, 2007 Antonella De Santo, RHUL 8 December 11-12, 2007 Antonella De Santo, RHUL 9

Minimum Bias σinel(pp)~70 mb Minimum Bias and Pile-up

Non-single diffractive interactions At nominal high luminosity (L=1034cm-2s-1=107mb-1 Hz), on (soft partons) average 23 minimum bias events superimposed on any rare discovery signal “Operational” definition of “minimum bias” depends on experimental trigger And ~1000 low-pt tracks per event !

Moreover, due to finite detector response time, out-of-time pile-up from different bunch crossings

LHC predictions Measured at lower energies (SppS and Tevatron) Event must be “time stamped” CDF Large uncertainties on extrapolation Important impact on detector design to LHC energies Fast electronics, high granularity, radiation hardness UA5

December 11-12, 2007 Antonella De Santo, RHUL 10 December 11-12, 2007 Antonella De Santo, RHUL 11 The Challenge The Challenge

Rec. trks w/ pt>25 GeV Rec. trks w/ pt>25 GeV

HÆ 4μ HÆ 4μ +30 Minimum Bias

December 11-12, 2007 Antonella De Santo, RHUL 12 December 11-12, 2007 Antonella De Santo, RHUL 13

Collisions at a hadron collider Event kinematics – pT and η

x1p d d r pT = p cosθ r p u p pu p p pT Instead of polar angle θ : u u η x p θ 2 beam axis Etot=? ⎛ θ ⎞ Ptot=? = −log⎜ tan ⎟ ⎝ 2 ⎠ sˆ = x x s Pseudo-rapidity 1 2 η = 0 Equivalent to rapidity for No constraint on total initial energy η = −1.0 η = +1.0 massless particles Broad range of √s Æ good for discovery η = −2.5 η = +2.5 Invariant under boost (All possible processes are “on” simultaneously)

Typically x1≠x2 Æ hard scatter boosted along beam axis beam direction PDFs December 11-12, 2007 Antonella De Santo, RHUL 14 December 11-12, 2007 Antonella De Santo, RHUL 15 σ Event kinematics – Etmiss Cross Sections tot inel pp ~ 110 mb (σ pp ~ 70 mb) Total energy and momentum are always conserved Minimum Bias rate: For a hadron collider, this does not result in a constraint on the total O(109 Hz) !! transverse momentum pT (initial partons have unknown initial momenta) #evts Rates(Hz) Assuming that the partons in the initial state move parallel Process σ (nb) [10 fb−1] [ “high” L ] to the proton beams, and that the total p of the unseen T bb 500 μb 5x1012 5x106 proton remnants (lost along the beam pipe) is ~0 : W → eν 15 nb ~108 150 r miss r vis r (i) Can be used to infer the Z → ee 1.5 nb ~107 15 pT = − pT = − pT presence of “neutrino- ∑ like” particles that leave tt 800 pb ~107 10 i ∈ vis ~~ the detector unseen gg (1 TeV) ~1 pb ~104 10-2 Total missing p approximated by vector sum of all energy H (200 GeV) → 4 T l ~10 fb ~102 10-4 deposits in calorimeters (ÆEtmiss) 14 TeV “Needle in haystack” December 11-12, 2007 Antonella De Santo, RHUL 16 December 11-12, 2007 Antonella De Santo, RHUL 17

Search Strategy for Rare Processes Detector Requirements

High-pT physics largely dominated by QCD processes, while interesting physics has EW cross sections Excellent position and momentum resolution in central tracker b-jets, taus Purely hadronic channels essentially hopeless Excellent ECAL performance electrons, photons Must rely on distinctive final state signatures v. good granularity (energy and position measurements) leptons (e, mu and taus) Good HCAL performance photons jets, Etmiss (neutrinos, SUSY stable LSP, etc) b-jets good granularity (energy and position measurements) missing ET good η coverage (hermeticity for Etmiss measurements) Excellent muon identification and momentum resolution Further signal suppression from branching ratios from “combined” muons in external spectrometer + central tracker

December 11-12, 2007 Antonella De Santo, RHUL 18 December 11-12, 2007 Antonella De Santo, RHUL 19 The Detectors ATLAS vs CMS CMS Muon System ATLAS CMS

Air-core toroids + solenoid Solenoid Magnet Calorimetry Calorimeter outside field Calorimeters inside field system B = 2 T (barrel) B = 4 T

Central Si pixel + strips, TRT (e/had) Si pixel+strips -4 -4 tracker σ(pT)/pT~5×10 pT⊕ 0.01 σ(pT)/pT~1.5×10 pT ⊕ 0.005 PbWO crystals Pb + Liquid Ar (LAr) 4 σ /E~3-5%/√E ECAL σ /E~10%/√E (uniform) E E no longitudinal segmentation Magnet system longitudinal segmentation

Fe-scintillator + Cu-LAr (10 λ) Cu-scintillator (5.8 l + catcher) HCAL σE/E~50%/√E ⊕ 0.03 σE/E~65%/√E ⊕ 0.05 Tracking Fe Æσ(p )/p ~5% at 1TeV Air Æσ(p )/p ~7% at 1TeV T T μ−Det T T (“combined” muons) ATLAS (standalone) December 11-12, 2007 Antonella De Santo, RHUL 20 December 11-12, 2007 Antonella De Santo, RHUL 21

Overview of the CMS and ATLAS Triggers ATLAS

Detectors 40 MHz input rate Detectors (bunch crossing)

Lvl-1L1 3.2Front μ ends pipelines Lvl-1L1 2.5 μsFront end pipelines Regions of O(100 kHz) L1 rate Interest (RoIs) Readout buffers Lvl-2L2 ~10 msReadout buffers

Switching network Switching network O(1 kHz) L2 HLTrate (ATLAS only) HLT HLT Processor farms Lvl-3EF ~1 s Processor farms O(100 Hz) output rate (on tape)

CMS – 2 levels ATLAS – 3 levels ( L2 + EF = HLT ) L1: Hardware based (calo+μ’s) (HLT = High-Level Trigger) Event size December 11-12,HLT: 2007 Software based Antonella De Santo, RHUL1-2 MBytes 22 December 11-12, 2007 Antonella De Santo, RHUL 23 CMS

ATLAS

μ

6.920 m

5.635 m

4.645 m

3.850 m

2.950 m

2.864 m

1.840 m 1.320 m CMS

Y CERN, Building 40 ϕ X

Towards Center of LHC

CMS-TS-00079 Transverse View December 11-12, 2007 Antonella De Santo, RHUL 24 December 11-12, 2007 Antonella De Santo, RHUL 25

Electroweak Symmetry Breaking

SU(2)⊗U(1) must be a broken symmetry photon is mass less, W and Z are not Don’t want to destroy gauge invariance of theory (SM) no explicit symmetry breaking term in lagrangian EW SYMMETRY BREAKING Higgs mechanism offers a solution to this

AND HIGGS BOSON Laws of Nature (lagrangian) are left- right symmetric, equilibrium state is not

By choosing one of the two minima, particle breaks l-r symmetry

December 11-12, 2007 Antonella De Santo, RHUL 27 Higgs Mechanism Theoretical Constraints on Higgs Mass

Upper bound Two independent fields (triviality) : and two independent “motions” ⎛ 4π 2v 2 ⎞ Excitations in one direction (along Λ ≤ M H exp⎜ 2 ⎟ potential) produce physical Higgs ⎝ 3M H ⎠ boson no perturbative unitarity Lower bound Excitations in the “horizontal plane” (vacuum stability) : correspond to gauge transformation: “global” Æ unseen unstable vacuum “local” Æ extra polarization state 2 3GF 2 2 2 M H > 2 F log()Λ / v (gives mass to gauge bosons) 8π

(Λ = cut-off scale at which new physics becomes important)

December 11-12, 2007 Antonella De Santo, RHUL 28 December 11-12, 2007 Antonella De Santo, RHUL 29

Experimental Constraints on Higgs Mass SM Higgs Couplings

mlimit = 144 GeV At LEP-2 :

m ig m g 1 “Higgs-strahlung” f W μν ig m g − i cosθ Z μν v W Direct LEP limit : Different Feynman rules for fermions and gauge bosons, MH >114.4 GeV (95% C.L.) but in all cases Higgs couplings proportional to mass

From http://lepewwg.web.cern.ch/LEPEWWG/ December 11-12, 2007 Antonella De Santo, RHUL 30 December 11-12, 2007 Antonella De Santo, RHUL 31 SM Higgs Production at the LHC SM Higgs Production Cross Sections

Gluon Fusion Vector Boson Fusion

December 11-12,Higgs-strahlung 2007 Antonella De Santo,ttbar RHUL H (“associated” production) 32 December 11-12, 2007 Antonella De Santo, RHUL 33

Standard Model Higgs Decays Low Mass Higgs (MH<140 GeV) – H Æ γγ

Heaviest quark (b-bbar) BR Direct Higgs coupling to γγ forbidden, as dominates at low masses, photon is mass less until there is enough energy to produce gauge boson Low branching ratio (~10-3), but nice mass pairs (WW, ZZ) peak thanks to excellent ECAL energy resolution (both ATLAS and CMS) But b-bbar very difficult due to huge QCD background and limited b-jet resolution S/B ≈1:20 (O(15%))

Despite much lower BR, HÆγγ via intermediate ttbar loop has better Signal/Bkgd −1 ratio for low Higgs mass 100 fb

December 11-12, 2007 Antonella De Santo, RHUL 34 DecemberCMS Physics11-12, 2007 TDR, 2006 Antonella De Santo,Resolution RHUL ~1 GeV at 100 GeV 35 H Æ γγ – Backgrounds High Mass Higgs (MH>2 MZ) – H Æ 4 lep

e+ Z e- * + – + – q H→ZZ →l l l l (l =e,μ) _ H q Z e+ Very little background (ZZ, Zbb, t-ttbar)

e- Irreducible (from physics) – Intrinsically v. similar to signal CMS

q _ γ γ q π0 gluon

Reducible (can be suppressed in principle) –

December 11-12, 2007e.g. increased Antonella calo De segmentation Santo, RHUL 36 DecemberResolution 11-12, <12007 GeV at 100 Antonella GeV De Santo, RHUL 37

Vector Boson Fusion Vector Boson Fusion

Two tagging forward jets Tagging Higgs decay products in central region Forward Jets Lep-lep or lep-had signature for HÆττ

High-pT jet veto

μ− 4σ for 30 fb-1 J2 J1 CMS, HÆττ

− December 11-12, 2007 Antonella De Santo, RHUL 38 December 11-12, e2007H Æ Antonellaττ Æ eμνν De Santo, RHUL 39 SM Higgs – Discovery Potential Higgs Boson Properties

CMS, 30 fb-1 ATLAS, 30 fb-1 Once Higgs boson is discovered, want to measure its properties… Significance vs. MH mass, width spin, CP (SM predicts 0++) coupling to other bosons and to fermions self-coupling

… and check whether it’s a SM Higgs, or if for example it is compatible with theories beyond the SM (e.g. SUSY) in principle there could be more than one Higgs boson “Significance” σ measures how likely it is that observed signal is the product of statistical fluctuations in the data perform direct searches for extra Higgs bosons

For example, σ = S/sqrt(S+B) > 5 usually taken as “threshold” for discovery (S=signal, B=background) December 11-12, 2007 Antonella De Santo, RHUL 40 December 11-12, 2007 Antonella De Santo, RHUL 41

What If No Higgs?...

If no Higgs boson is found at the TeV scale, new mechanism is required to avoid divergencies at high energy

Study of the WW cross section may hold the key in this case, as WW scattering becomes strong at the TeV scale in the absence of a light Higgs SUPERSYMMETRY

No further discussion here

December 11-12, 2007 Antonella De Santo, RHUL 42 Why go Beyond the ? Hierarchy Problem and Naturalness

Despite its many successes, Standard Model is widely In SM, loop corrections to Higgs bosonδ mass: α believed to be only an effective theory, valid up to a scale 2 ⎛ ⎞ 2 m H = O⎜ ⎟ Λ Λ << M Planck ⎝ π ⎠ Theory cut-off Natural scale of scalar mass is very large! Gravity not included in SM

Hierarchy/naturalness problem: These corrections, which are large, give rise to fundamental problems when requiring that: MEW << MPlanck Fine-tuning mH << fundamental mass scale (i.e. MPlanck) (hierarchy problem) 2 2 Unification of couplings Corrections δmH to Higgs mass should not be >> mH (naturalness) Need a more fundamental theory of which SM is only a Need either fine-tuning or protective symmetry! low-energy approximation December 11-12, 2007 Antonella De Santo, RHUL 44 December 11-12, 2007 Antonella De Santo, RHUL 45

Unification of Coupling Constants in the SM Supersymmetry (SUSY)

Space-time symmetry that relates fermions (matter) and bosons (interactions) Q boson = fermion and Q boson = fermion

Further doubling of the particle spectrum Every SM field has a “superpartner” with same mass Spin differs by 1/2 between SUSY and SM partners Identical gauge numbers Or lack of it… Identical couplings Superpartners have not been observed SUSY must be a broken symmetry But SUSY-breaking terms in Lagrangian must not re-introduce Slope of 1/α lines depends on matter and couplings of entire theory quadratic divergences in theory !

December 11-12, 2007 Antonella De Santo, RHUL 46 December 11-12, 2007 Antonella De Santo, RHUL 47 Minimal Supersymmetric Standard Model Minimal Supersymmetric Standard Model – II

Supersymmetric Partners Standard Model Particles Standard and Fields Model Spin Superpartners Spin Interaction Mass Particles Eigenstates Eigenstates Symbol Name Symbol Name Symbol Name quarks 1/2 squarks 0 quark ~ ~ squark q~ ,q~ squark q = u,d,c, s,t,b qL ,qR 1 2 ~ ~ ~ ~ l = e, μ, τ lepton slepton l1, l2 slepton leptons 1/2 sleptons 0 lR , lL μ ~ ~ l =ν e , ν , ντ neutrino ν sneutrino ν sneutrino ~ gauge g gluon g gluino g~ gluino 1 gauginos 1/2 ± ~ ± bosons W W-boson W wino ~± χ1,2 + − chargino Higgs charged ~ + ~ − charged Hu , H d H , H 0 higgsinos 1/2 Higgs boson u d higgsino bosons ~ B B-field B bino 0 W W0-field ~ 0 wino ~0 Gauginos and higgsinos mix 2 charginos and 4 neutralinos W χ1,2,3,4 neutralino ~ ~ ± 0 0 neutral Higgs H 0 , H 0 neutral Two Higgs doublets 5 physical Higgs bosons (h,H; A; H ) Hu , H d u d December 11-12, 2007boson Antonella De Santo,higgsino RHUL 48 December 11-12, 2007 Antonella De Santo, RHUL 49

Supersymmetric Solution to Divergencies Unification of Coupling Constants in MSSM

Now two diagrams, one bosonic and one fermionic, give equal and opposite contributions:δ f S HH π H

π 2 2 α ⎛ g f ⎞ ⎛ g ⎞ ⎛ ⎞ m2 = ⎜ ⎟ ()Λ2 + m2 − ⎜ S ⎟ ()Λ2 + m2 = O⎜ ⎟ m2 − m2 H ⎜ 2 ⎟ f ⎜ 2 ⎟ S S f ⎝16 ⎠ ⎝16 ⎠ ⎝ 4 π ⎠

If #boson = #fermions and they have equal masses and couplings, the quadratic divergencies cancel

2 2 m2 − m2 <~ TeV2 Higgs mass correction δ m H < m H if S f

Gauge boson contribution cancelled by gaugino contribution Now unification of strong, weak and e.m. forces achieved at ~MGUT

December 11-12, 2007 Antonella De Santo, RHUL 50 December 11-12, 2007 Antonella De Santo, RHUL 51 R-parity R-parity

MSSM contains L- ad B-violating terms, which could in principle allow proton decay via sparticle diagrams: In the following, assume R-parity conservation

3(B−L)+2S This can be prevented by introducing a new symmetry in the theory, R ()1 called R-parity: = − R = ()−1 3 (B−L)+2S R=+1 (SM particles), R=-1 (SUSY particles) Stable LSP (neutralino) Two important consequences: LSP (=Lightest SUSY Particle) is stable – typically neutralino Sparticles can only be produced in pairs (in scattering of SM particles)

December 11-12, 2007 Antonella De Santo, RHUL 52 December 11-12, 2007 Antonella De Santo, RHUL 53

Neutralino as Dark Matter Constituent SUSY Soft Breaking

WMAP Empirically we know that SUSY must be a broken symmetry (no 0.094 < Ω h2 < 0.136 (95% CL) CDM sparticles with same mass as particles) Spontaneous breaking not possible in MSSM otherwise sparticles with mass less than their SM partners would exist (Ferrara-Girardello-Palumbo) SUSY breaking must be confined to a hidden sector, which communicates indirectly with the visible one via flavour-blind interactions (i.e. gravity)

Neutralino LSP is a good DM candidate stable electrically neutral SUSY-breaking lagrangian terms do not re-introduce quadratic weakly and gravitationally interacting divergencies (“soft” breaking) December 11-12, 2007 Antonella De Santo, RHUL 54 December 11-12, 2007 Antonella De Santo, RHUL 55 mSUGRA (or CMSSM) RGE Evolution

Soft SUSY breaking mediated by gravitational interaction at GUT Universal boundary conditions at some high scale (GUT) scale Evolution down to EW scale through Renormalisation Group Equations (RGE) Only five parameters:

m0 — universal scalar mass gluino, m1/2 — universal gaugino mass squarks

A0 — trilinear soft breaking parameter at GUT scale tanβ — ratio of Higgs vevs Universal sgn(μ) — sign of SUSY Higgs mass term gaugino mass charginos, (|μ|determined by EW symmetry breaking) neutralinos, Universal sleptons scalar mass

Highly predictive – masses determined mainly by m0 and m1/2 Useful framework to provide benchmark scenarios

December 11-12, 2007 Antonella De Santo, RHUL 56 December 11-12, 2007 Antonella De Santo, RHUL 57

mSUGRA Parameter Space SUSY Cross-Sections

Four regions compatible with WMAP value for h2, different mechanisms for Ω Cross-section dominated by production of neutralino annihilation: coloured particles (pb) bulk tot

3000 neutralino mostly bino, annihilation σ to ff via sfermion exchange

focus point (GeV) neutralino has strong higgsino component, annihilation to WW, ZZ co-annihilation pure bino, small NLSP-LSP mass difference, typically coannihilation with stau 100 Higgs funnel m (GeV) decay to fermion pair through ~0 resonant A exchange ( m A ≈ 2 χ 1 ) – 250 350 high tanβ December 11-12, 2007(GeV) Antonella De Santo, RHUL 58 December 11-12, 2007 Antonella De Santo, RHUL 59 Production Mechanisms Possible Final States

Squark/Gluino Production

Direct Gaugino

December 11-12, 2007 Antonella De Santo, RHULProduction 60 December 11-12, 2007 Antonella De Santo, RHUL 61

Inclusive Searches The “Needle in the Haystack”…

p p ~ ~ χ0 ~ q ~0 ~ 1 g χ 2 l q q l l

miss ( j) In most scenarios, squark and gluino production Meff = ET +∑ET jets dominates Squarks and gluinos typically heaviest particles (heavier than sleptons, gauginos, etc) Complex long decay chains to undetected neutralino (stable in RPC models) – Inclusive search:

high multiplicity of high-pT jets miss large ET (from escaping LSP) ≥ 0 (high-pT) leptons December 11-12, 2007 Antonella De Santo, RHUL 62 December 11-12, 2007 Antonella De Santo, RHUL 63 … a SUSY event in ATLAS… … and one in CMS

Multi-jet event Multi-jet event in with large Bulk Region missing ET 6 jets 2 high-pt muons Large missing E December 11-12, 2007T Antonella De Santo, RHUL 64 December 11-12, 2007 Antonella De Santo, RHUL 65

SUSY Mass Scale ATLAS mSUGRA Reach

10 fb−1 reach — Etmiss signature — (GeV) SUSY mass scale defined as cross-section tanβ=10, μ>0, A=0 (GeV) tanβ=10, μ>0, A=0 1/2 1/2 g(2500)

weighted mean of masses of initial SUSY m g(2500) m particles produced in pp collision

Effective SUSY mass scale MeffSUSY takes into q(2500) account mass of undetected LSP (neutralino) For ideal case q(2500)of perfectly understood (mb/400 GeV) (mb/400 eff Meff a good estimator for MeffSUSY backgrounds and detector effects !! /dM σ d

SUSY 2 2 Meff (GeV/c ) vs. Meff (GeV/c ) g(1000) g(1000) Meff (GeV) q(1000) q(1000)

2 ⎛ M~0 ⎞ MSUSY = ⎜M − χ1 ⎟ eff ⎜ SUSY M ⎟ ⎝ SUSY ⎠

m (GeV) December 11-12, 2007 Antonella De Santo, RHUL 66 December 11-12, 2007 Antonella0 De Santo, RHULm0 (GeV) 67 If Only Life Were That Easy… Example of Data-Driven Bkgd Estimation

Significant discrepancy observed Z+jets (ZÆνν) background from Drell-Yan (ZÆee, μμ) between PS (e.g. Pythia) and ME (e.g. ALPGEN) calculations of multiparton emission amplitudes μ Background rate larger in ME ν μ generator, which also predicts a ν more similar shape to that of signal

Reliance on MC simulated events must be minimized and backgrounds estimated using data- driven techniques

Also need good understanding of detector response December 11-12, 2007 Antonella De Santo, RHUL 68 December 11-12, 2007 Antonella De Santo, RHUL 69

Example of Data-Driven Bkgd Estimation Dilepton Edge

μ ν ~0 ~0 μ ν χ2 can undergo chain two-body decay to χ 1 : ~ m ~0 l ~0 χ2 χ1 l ± l m

Sharp Same-Flavour Opposite-Sign Red: Z Æ νν (SFOS) dilepton invariant mass edge sensitive to sparticle mass differences Blue: Estimated χ ~ M 2 (lχ) M 2 (χ~0 ) M max = M( ~0 ) 1− R 1− 1 ll 2 2 ~0 2 ~ M ( 2 ) M (lR )

December 11-12, 2007 Antonella De Santo, RHUL 70 December 11-12, 2007 Antonella De Santo, RHUL 71 lq edge More Decay Chains (and edges) llq edge Exclusive Channels – An ATLAS Example

Decay chains originating from squarks: Trilepton signal (from direct chargino-neutralino production and decay) two different points in the mSUGRA parameter space q~ ~0 L χ2 ~ m “SU2” — Focus Point l ~0 χ Heavy scalars 3000 ± 1 q No decays through l m l intermediate sleptons (GeV)

lq edge “SU3” — Bulk Region llq edge “Typical” spectrum Consider invariant mass combination of lepton and jets Decays through intermediate 100 sleptons are allowed Combine constraints from different decay chains to extract information 250 350 of individual sparticle masses (GeV)

December 11-12, 2007 Antonella De Santo, RHUL 72 December 11-12, 2007 Antonella De Santo, RHUL 73

ATLAS Example – SU2 and SU3 Points Direct Gaugino Production – Focus Point (SU2)

SU2 – ~0 No intermediate χ1 m0 = 3550 GeV SU2 m0 = 100 GeV SU3 sleptons

m1/2 = 300 GeV m1/2 = 300 GeV l + A = 0 σ = 4.9 pb A = -300 GeV σ = 18.6 pb χ~0 2 SFOS i * tanβ = 10 tanβ = 6 Z l − leptons m > 0 m > 0 missing ± * ET SM bkgd from Mass spectrum of sparticles at the SU2 point Mass spectrum of sparticles at the SU3 point ~ ± W β μ m =100, m =300, A =-300, tanβ=6, μ>0 m =3550, m =300, A =0, tan =10, >0 4 0 1/2 0 χ ± ZW, ZZ, ttbar, 104 0 1/2 0 10 j Higgsino0_u component l another Higgsino0_u component Z/W+jets Higgsino0_d component Higgsino0_d component lepton Mass /GeV Mass /GeV Wino component Wino component ν 3 3 10 Bino component 10 Bino component ~0 m(χ0) =103, 160, 180, 296 GeV χ1 ± 2 m(χ ) =149, 288 GeV 102 10

0 ∼± ∼0 ∼± ~ ~ ~ ∼χ χ ~g ~q ~ h,H,A Relatively low-pT leptons due to small mass differences χ χ g q l h,H,A l 0123456 0123456 Preliminary results indicate discovery possible with few 100s fb-1 December 11-12, 2007 Antonella De Santo, RHUL 74 December 11-12, 2007 Antonella De Santo, RHUL 75 Direct Gaugino Production – Bulk (SU3) Trileptons +jets (+ Etmiss) signature

± 0 l 2 SFOS m(χ ) =116, 224, 460, 478 GeV q leptons m(χ±) =224, 476 GeV l m q,q′ ~0 m(l ) =152, 232 GeV χi R,L ~ ~ ± 0 g ~ ~ χ 0 ± l χ1 missing q ~ ~ Jets L 2 , χ1 ET ± * ~ ± W χ j ± another q~ 1,2>=3 leptons leptons + l lepton L q,q′ Etmiss(+Etmiss) (x2) ν χ~0 ~ ± 2 , χ1 ~0 χ1 Decays through intermediate sleptons are now allowed Relevant for “low-mass” SUSY (SU3, SU4), not in Focus Point region Preliminary results show that the statistics needed for discovery in this An interesting channel for mass edges, but largest background is from channel (SU3) would be prohibitive (1000s fb-1 !) December 11-12, 2007 Antonella De Santo, RHUL 76 SUSYDecember itself 11-12, Æ 2007explore discovery Antonella potential De Santo, RHULof inclusive 3-lep search ! 77

Trileptons +jets (Bulk region, SU3) – Inclusive Trilepton Inclusive – SU3

Signal = any decay originating from SUSY particles that gives 45

-1 SUSY07 40 ATLAS Preliminary 3 leptons (+ jets + Etmiss) in the final state Signal only Signal only 35 SU3 Simple cut flow: 30 Events/10 fb 3 isolated leptons (including e,μ from taus) – not necessarily SFOS 25 ATLAS preliminary at least 1 high-pt jet (>200 GeV) 20 15 high Etmiss requirement can help, but not crucial theoretical endpoint at 10 ~ 100 GeV Preliminary results for 5s discovery reach: 5 -1 0 SU2 (“focus point”) : O(10-15 fb ) 0 50 100 150 200 250 300 M_SFOS /Gev SU3 (“bulk”) : O(1-2 fb-1) OSSF Dilepton Edge (GeV)

December 11-12, 2007 Antonella De Santo, RHUL 78 December 11-12, 2007 Antonella De Santo, RHUL 79 Models of Extra Dimensions

Plenty of models on the market cannot possibly discuss all of them in detail

BEYOND SUSY – Two “popular” examples: EXTRA DIMENSIONS ADD (Arkani-Hamed, Dimopoulos, Dvali) [Phys Lett B429 (98)]

RS (Randall-Sundrum) [Phys Rev Lett 83 (99)]

December 11-12, 2007 Antonella De Santo, RHUL 81

Motivations Motivations

-17 -17 The hierarchy problem (MEW /MPlanck~10 ), which we saw can be The hierarchy problem (MEW /MPlanck~10 ), which we saw can be solved in the context of supersymmetry, could also be addressed by solved in the context of supersymmetry, could also be addressed by exploiting the geometry of space-time exploiting the geometry of space-time

The three spatial dimensions in which we live could be a three-spatial- The three spatial dimensions in which we live could be a three-spatial- dimensional “membrane” embedded in a much larger extra dimensional dimensional “membrane” embedded in a much larger extra dimensional space space

December 11-12, 2007 Antonella De Santo, RHUL 82 December 11-12, 2007 Antonella De Santo, RHUL 83 Motivations Motivations – Cont’d

The hierarchy problem (M /M ~10-17), which we saw can be Our knowledge of the weak and strong force extends down to scales of EW Planck -1 -15 solved in the context of supersymmetry, could also be addressed by ~(100 GeV) ~O(10 m) exploiting the geometry of space-time Our knowledge of the gravitational force (based on mechanically limited torsion-balance experiments, e.g. Cavendish expt), is limited to The three spatial dimensions in which we live could be a three-spatial- distances not smaller than ~1 mm dimensional “membrane” embedded in a much larger extra dimensional space It is hence conceivable that gravity may diverge from Newton’s law at small distances

In this scenario, the hierarchy that we observe between the 1 m m 1 m m gravitational and the EW scale is generated by the geometry of the V()r = 1 2 → 1 2 additional dimensions, rather than by an intrinsic smallness of the 2 [] 3 + n n+2 n+1 MPl r ()M r gravitational coupling constant Pl Matter and non-gravitational forces may be “confined” to our 3-dim Such ideas have led to extra dimensional theories whose space (“brane”), while gravity may propagate throughout the full n+3 spatial volume of a higher dimensional (D=3+n+1) volume, the “bulk” consequences can be verified at LHC energies

December 11-12, 2007 Antonella De Santo, RHUL 84 December 11-12, 2007 Antonella De Santo, RHUL 85

Compactification ADD Model

Modified Newton’s law ruled out for large ED, but not excluded for sufficiently small, compactified ED of size R <

3 n effective Planck scale 1 m1m2 []+ V ()r ∝ for r >> R M Pl = for n extra dim. []3+n n+2 R nr ()M Pl Intrinsically strong gravitational force diluted by bulk volume

[ 3 + n ] n + 2 2 n ()M Pl ∝ M Pl R For n>1, fundamental Planck scale could be as low as 1 TeV (n=2 disfavoured by cosmological arguments):

⎧8 × 10 12 m , n = 1 2 / n ⎪ 1 ⎛ M ⎞ ⎪0 .7 mm , n = 2 R = ⎜ Pl ⎟ ∝ ⎨ 2 π M [ 3 + n ] ⎜ M [ 3 + n ] ⎟ 3 nm , n = 3 Pl ⎝ Pl ⎠ ⎪ Mobius Strip II (Escher, 1963) Relativity (Escher, 1953) ⎪6 × 10 −12 m , n = 4 December 11-12, 2007 Antonella De Santo, RHUL 86 December 11-12, 2007 Antonella De Santo, RHUL⎩ 87 ADD Collider Signatures – Real Graviton Emission ADD Collider Signatures – Virtual Graviton Emission G G Graviton emitted in association with jet or gauge boson g,q g, f,V Jet + jet,V q g,q Etmiss g,q f,V Excess over dilepton continuum from SM processes such as q-qbar, ggÆ l+l-

December 11-12, 2007 Antonella De Santo, RHUL 88 December 11-12, 2007 Antonella De Santo, RHUL 89

RS Models

A small, highly curved (“warped”) extra dimension connects the SM brane (at O(TeV)) to the Planck scale brane

Gravity small in our space because warped dimension decreases exponentially between the two branes

Series of narrow, high-mass resonances: qq, gg → G → + − ,γγ , j + j … AND A LOT MORE… (only first peak visible at LHC, due to PDFs) KK400 600l 800l 1000

10-2 Mll (GeV)

/dM 700 GeV KK Graviton at the σ 10-4 (pb/GeV) d Tevatron 1 k/M10Pl-6 = 1,0.7,0.5,0.3,0.2,0.1 from0.5 Spin analysis to top to-8 bottom 0.1 distinguish spin-2 Drell-Yan10 at the LHC G from spin-1 Z’ 0.05 resonance 10-10 0.01 1000 3000 5000 December 11-12, 2007 Antonella De Santo, RHULDileptonM llmass(GeV) 90 More Physics at the LHC More Physics at the LHC

Standard Model Standard Model

B-physics B-physics day Heavy Ions Heavy Ions Not To Diffractive physics Diffractive physics

December 11-12, 2007 Antonella De Santo, RHUL 92 December 11-12, 2007 Antonella De Santo, RHUL 93

With the LHC turn on, physics at the TeV scale will become accessible experimentally at an accelerator for the first time

High expectations to be able to shed light on the origin of CONCLUSIONS mass and the mechanism for EW symmetry breaking

Serious possibility to observe “dark matter in a laboratory”, and even to test gravity

A new golden age for particle physics may be ahead of us!

December 11-12, 2007 Antonella De Santo, RHUL 95