Map Alan Barr What can we say about what we’ve found? Anything unusual out there Just find SM Higgs Was it really SUSY? How can we discover SUSY at LHC? What can we say about what we’ve found? Why look for SUSY?

Dark Matter Atoms ~ 4% Evidence for Dark Matter from Visible mass Invisible mass Atoms ~ 4% Evidence for Dark Matter from Rotation curves of galaxies Microwave background radiation Galaxy cluster collision Particle physicists should hunt: Weakly Interacting, Stable, Massive Particles

Producing exotics? If exotics can be produced singly they can decay Time standard exotic Time standard exotic If exotics can be produced singly they can decay No good for Dark Matter candidate If they can only be pair-produced they are stable Only disappear on collision (rare) Time standard exotics Time standard exotics Require an even number of exotic legs to/from blobs (Conserved multiplicative quantum number)

How do they then behave? Production part Complete event Decay part Time Complete event standard 2 exotics Time Time standard heavy exotic lighter exotic Decay part Events build from blobs with 2 “exotic legs” A pair of cascade decays results Complicated end result = exotic = standard

Candidates? New particles by a symmetry: Supersymmetry …? Relationship between particles with spins differing by ½h Spatial symmetry With extra dimensions Gauge symmetry Extra force interactions (and often matter particles) electron …? neutrino quarks x3x2 …? _ Force-carriers …? Already observed exotic partners? Related by symmetry

What is supersymmetry? Nature permits various only types of symmetry: Space & time Lorentz transforms Rotations and translations Gauge symmetry SU(3)c x SU(2)L x U(1) Supersymmetry Anti-commuting (Fermionic) generators Relationship with space-time Consequences: Q(fermion)=boson Q(boson)=fermion Equal fermionic and bosonic DF Double particle content of theory Partners not yet observed Must be broken! Otherwise we’d have seen it {Q,Q†} = -2γμPμ

Why SUSY? Higgs mass2 Quadratic loop corrections In SM natural scale top Higgs mass2 Quadratic loop corrections In SM natural scale Λcutoff ~ Mplanck v. high! Need m(h) near electroweak scale Fine tuning Many orders of magnitude stop λ λ λ λ higgs higgs higgs higgs Δm2(h)  Λ2cutoff Enter SUSY 2 x Stop quarks Factor of -1 from Feynman rules Same coupling, λ Quadratic corrections cancel

What does SUSY do for us? Coupling of stop to Higgs RGE corrections Make mHH coupling negative Drives electro-weak symmetry breaking Predicts gauge unification Modifies RGE’s Step towards “higher things” 1/α +SUSY Hit! Log10 (μ / GeV)

(S)particles SM SUSY Spin-1/2 Spin-0 After Mixing  Z0 W± gluon B W0 quarks (L&R) leptons (L&R) neutrinos (L&?) squarks (L&R) sleptons (L&R) sneutrinos (L&?) Spin-1/2 Spin-0 After Mixing  Z0 W± gluon B W0 Bino Wino0 Wino± gluino Spin-1 4 x neutralino Spin-1/2 gluino h0 H0 A0 H± ~ H0 H± ~ 2 x chargino Spin-0 Extended higgs sector (2 doublets)

Proton on Proton at 14 TeV

40 million bunch crossings/minute

Something to see it with

“typical” SUSY spectrum (mSUGRA) General features Mass/GeV Complicated cascade decays Many intermediates Typical signal Jets Squarks and Gluinos Leptons Sleptons and weak gauginos Missing energy Undetected LSP Model dependent Various ways of transmitting SUSY breaking from a hidden sector “typical” SUSY spectrum (mSUGRA)

SUSY event Missing transverse momentum Heavy quarks Jets Leptons

Cross-sections etc “Rediscover” Lower backgrounds “Discover” WW ZZ “Discover” Higher backgrounds

Discovering SUSY with jets SIGNAL topology Select a small number of high PT jets Large signal cross-section Large control statistics Relatively well known SM backgrounds Relatively “model independent” Does not rely on leptonic cascades Does not rely on hadronic cascades BACKGROUND topology (QCD)

Importance of detailed detector understanding Et(miss) Geant simulation showing fake missing energy Lesson from the Tevatron

Suppressing backgrounds QCD SUSY Jet Remove events with missing energy back-to-back with leading jets

Measuring Backgrounds Measure in Z -> μμ Use in Z -> νν R: Z -> nn B: Estimated Example: SUSY BG Missing energy + jets from Z0 to neutrinos Measure in Z -> μμ Use for Z ->  Good match Useful technique Statistics limited Go on to use W => μ to improve

Di-jets + MET measurement Dijet inclusive: - No lepton veto - No b-jet veto - No multi-jet veto Keeping it simple >=2 jets ET (J1,2) > 150 GeV; |η1,2| < 2.5 Cambridge “Stransverse mass”

Discovering SUSY with leptons Small Standard Model Backgrounds Golden channel @ Tevatron Particularly important if strongly interacting particles are heavy

 e Top pair backgrounds Leptons from b-decays contribute to background Use track isolation to reduce these

Again: measure the background Measure this background in same-sign leptons in semi-leptonic b-decays

After 10 fb-1 Great discovery potential here… Lots of other channels: signal signal “Standard” SUSY point Very light SUSY point Great discovery potential here… Lots of other channels: M jets + N leptons + missing transverse energy

Reach in cMSSM? Rule out with 1fb-1 WMAP constraints ‘Focus point’ region: annihilation to gauge bosons mSUGRA A0=0, tan(b) = 10, m>0 Slepton Co-annihilation region Rule out with 1fb-1 ‘Bulk’ region: t-channel slepton exchange WMAP constraints

Mass scale? SUSY kinematic variable “MTGEN” Spectrum ET sum / 2

What might we then know? “Discovered supersymmetry?” Can say: Undetected particles produced missing energy Some particles have mass ~ 600 GeV, with couplings similar to QCD MTGEN & cross-section Some of the particles are coloured jets Some of the particles are Majorana excess of like-sign lepton pairs Lepton flavour ~ conserved in first two generations e vs mu numbers Possibly Yukawa-like couplings excess of third generation Some particles contain lepton quantum numbers opposite sign, same family dileptons Perhaps not what we think!

Mapping out the new world LHC Measurement SUSY Extra Dimensions Masses Breaking mechanism Geometry & scale Spins Distinguish from ED Distinguish from SUSY Mixings, Lifetimes Gauge unification? Dark matter candidate? Some measurements make high demands on: Statistics (=> time) Understanding of detector Clever experimental technique

Constraining masses Mass constraints Invariant masses in pairs Missing energy Kinematic edges Frequently- studied decay chain Observable: Depends on: Limits depend on angles between sparticle decays

Mass determination Basic technique Event-by-event likelihood Measure edges Try various masses in equations Variety of edges/variables Basic technique Measure edges Try with different SUSY points Find likelihood of fitting data Event-by-event likelihood In progress Narrow bands in ΔM Wider in mass scale Improve using cross- section information

SUSY mass measurements Try various decay chains Extracting parameters of interest Difficult problem Lots of competing channels Can be difficult to disentangle Ambiguities in interpretation Lots of effort has been made to find good techniques Look for sensitive variables (many of them) Extract masses

SUSY mass measurements: LHC clearly cannot fully constrain all parameters of mSUGRA However it makes good constraints Particularly good at mass differences [O(1%)] Not so good at mass scale [O(10%) from direct measurements] Mass scale possibly best “measured” from cross-sections Often have >1 interpretation What solution to end-point formula is relevant? Which neutralino was in this decay chain? What was the “chirality” of the slepton “ “ “ ? Was it a 2-body or 3-body decay? Long history of calculating masses from kinematical edges at LHC (since TDR) Often can be measured with high experimental precision  experimentally clean In cascades through sleptons, SM Backgrounds can be accurately determined from lepton different-flavour subtraction Analytical expressions contain differences of masses squared Edge variables most sensitive to mass differences (order 1%) than masses (order 10%) Various factors lead to difficulties in interpretation Provide non-trivial constraints on masses and mass-differences of particles The extent to which ambiguities can be solved in LHC-only and LHC-ILC analyses is an area of active investigation

SUSY spin measurements The defining property of supersymmetry Distinguish from e.g. similar-looking Universal Extra Dimensions Difficult to measure @ LHC No polarised beams Missing energy Indeterminate initial state from pp collision Nevertheless, we have some very good chances…

Universal Extra Dimensions TeV-scale universal extra dimension model Kaluza-Klein states of SM particles same QN’s as SM mn2 ≈ m02 + n2/R2 [+ boundary terms] KK parity: From P conservation in extra dimension 1st KK mode pair-produced Lightest KK state stable, and weakly interacting R KK tower of masses n=0,1,… Radius of extra dimension ~ TeV-1 S1/Z2 First KK level looks a lot like SUSY BUT same spin as SM Cheng, Matchev Dubbed “Bosonic Supersymmetry” hep-ph/0205314

SPIN 2 Spin 2 particle: looks same after 180° rotation

SPIN 1 Spin 1 particle : looks same after 360° rotation

SPIN ½ Spin ½ particle : looks different after 360° rotation indistinguishable after 720° rotation

Measuring spins of particles Basic recipe: Produce polarised particle Look at angular distributions in its decay spin θ

Revisit “Typical” sparticle spectrum Left Squarks -> strongly interacting -> large production -> chiral couplings LHC point 5 20 = neutralino2 –> (mostly) partner of SM W0 Right slepton (selectron or smuon) -> Production/decay produce lepton -> chiral couplings mass/GeV 10 = neutralino1 –> Stable -> weakly interacting 10 –> Stable -> weakly interacting Some sparticles omitted

Spin projection factors Chiral coupling Approximate SM particles as massless -> okay since m « p

Spin projection factors Σ=0 S Spin-0 Produces polarised neutralino Approximate SM particles as massless -> okay since m « p

Spin projection factors Fermion θ* p S Scalar Polarised fermion Approximate SM particles as massless -> okay since m « p

Spin projection factors mql – measure invariant mass θ* p S Approximate SM particles as massless -> okay since m « p

lnearq invariant mass (1) Back to back in 20 frame quark Probability θ* l+ lepton Phase space Invariant mass l- m/mmax = sin ½θ* Phase space -> factor of sin ½θ* Spin projection factor in |M|2: l+q -> sin2 ½θ* l-q -> cos2 ½θ*

After detector simulation Change in shape due to charge- blind cuts l- parton-level * 0.6 Events Charge asymmetry, spin-0 l+ SUSY detector-level Invariant mass -> Charge asymmetry survives detector simulation -> Same shape as parton level (but with BG and smearing)

Distinguishing between models dP/dSin (θ*/2) Sin (θ*/2) No spin Universal Extra Dim. SUSY ql- or ql+ Sin (θ*/2) dP/dSin (θ*/2) SUSY No spin Universal Extra Dim. ql+ or ql- _ As expected, UED differs from all-scalar (no-spin) and from SUSY Smillie et al.

What else can we do? Measure the invisible particle mass (WIMP mass) Measure couplings from rates and branching ratios Predict WIMP relic density

Summary Discovering something new is an important step Need to understand backgrounds and detector very well Finding out what we have discovered is even more interesting! Masses Spins Branching Ratios These tell us about SUSY vs Extra Dimensions Dark Matter Unification SUSY breaking

Extras

How is SUSY broken? Direct breaking in visible sector not possible Weak coupling (mediation) Direct breaking in visible sector not possible Would require squarks/sleptons with mass < mSM Not observed! Must be strongly broken “elsewhere” and then mediated Soft breaking terms enter in visible sector (>100 parameters) Strongly broken sector Soft SUSY- breaking terms enter lagrangian in visible sector Various models offer different mediation

mSUGRA – “super gravity” A.K.A. cMSSM Gravity mediated SUSY breaking Flavour-blind (no FCNCs) Strong expt. limits Unification at high scales Reduce SUSY parameter space Common scalar mass M0 squarks, sleptons Common fermionic mass M½ Gauginos Common trilinear couplings A0 Susy equivalent of Yukawas 1016 GeV Unification of couplings Iterate using Renormalisation Group Equations EW scale Correct MZ, MW, … Programs include e.g. ISASUSY, SOFTSUSY

Note opposite shapes in distributions Production Asymmetry Twice as much squark as anti-squark pp collider  Good news! Squark Anti-squark Note opposite shapes in distributions

Other suggestions Gauge mediation Anomaly mediation Gauge (SM) fields in extra dimensions mediate SUSY breaking Automatic diagonal couplings  no EWSB No direct gravitino mass until Mpl Lightest SUSY particle is gravitino Next-to-lightest can be long-lived (e.g. stau or neutralino) Anomaly mediation Sequestered sector (via extra dimension) Loop diagram in scalar part of graviton mediates SUSY breaking Dominates in absence of direct couplings Leads to SUSY breaking  RGE β-functions Neutral Wino LSP Charged Wino near-degenerate with LSP  lifetime Interesting track signatures Not exhaustive!

R-Parity Unrestricted couplings lead to proton decay: e- General soft breaking terms include: L-violating B-violating L-violating Unrestricted couplings lead to proton decay: u Unacceptably high rate compared to experimental limits (proton lifetime > 1033 years) _ _ Pion Proton u ~ u s d Strong limits on products of couplings e- Λ”112 Λ’112 Impose RP = (-1)3B+L+2S (by hand) Distinguishes SM from SUSY partners Leads to stable LSP Required for dark matter Sparticles produced in pairs

Gauge Mediated SUSY Breaking Signature depends on Next to Lightest SUSY Particle (NLSP) lifetime Interesting cases: Non-pointing photons Long lived staus Extraction of masses possible from full event reconstruction More detailed studies in progress by both detectors

R-hadrons Motivated by e.g. “split SUSY” Heavy scalars Gluino decay through heavy virtual squark very suppressed R-parity conserved Gluinos long-lived Lots of interesting nuclear physics in interactions Charge flipping, mass degeneracy, … Importance here is that signal is very different from standard SUSY

R-hadrons in detectors Signatures: High energy tracks (charged hadrons) High ionisation in tracker (slow, charged) Characteristic energy deposition in calorimeters Large time-of-flight (muon chambers) Charge may flip Trigger: Calorimeter: etsum or etmiss Time-of-flight in muon system Overall high selection efficiency Reach up to mass of 1.8 TeV at 30 fb-1 GEANT simulation of pair of R-hadrons (gluino pair production)

Method 2: Angular distributions in direct slepton pair production SUSY : qq  slepton pair Normalised cross-sections UED : qq  KK lepton pair Phase Space : AJB hep-ph/0511115

Sensitive variables? cos θlab cos θll* Good for linear e+e- collider AJB hep-ph/0511115 cos θlab Good for linear e+e- collider Not boost invariant Missing energy means Z boost not known @ LHC Not sensitive @ LHC cos θll* 1-D function of Δη: Boost invariant Interpretation as angle in boosted frame Easier to compare with theory l1 l2 θ2lab θ1lab cos θlab l1 l2 η2lab η1lab Δη boost l1 Δη l2 θl* cos θ*ll N.B. ignore azimuthal angle

Slepton spin – LHC pt 5 Statistically measurable AJB hep-ph/0511115 Slepton spin – LHC pt 5 “Data” = inclusive SUSY after cuts Statistically measurable Relatively large luminosity required Study of systematics in progress SM background determination SUSY BG determination Experimental systematics

Snowmass points Slepton spin AJB hep-ph/0511115 SPS1a, SPS1b, SPS5 mSUGRA “Bulk” points Good sensitivity SPS3 sensitive Co-annihilation point (stau-1 close to LSP) Signal from left-sleptons SPS4 – non-universal cMSSM Larger mass LSP Softer leptons Signal lost in WW background Analysis fails in “focus point” region (SPS2). No surprise: Sleptons > 1TeV  no xsection Statistical significance of spin measurement LHC design luminosity ≈ 100 fb-1 / year

SUSY vs UED: Helicity structure Neutralino spin Smillie, Webber hep-ph/0507170 See also: Battaglia, Datta, De Roeck, Kong, Matchev hep-ph/0507284 SUSY vs UED: Helicity structure SUSY case Both prefer quark and lepton back-to-back Both favour large (ql-) invariant mass Shape of asymmetry plots similar UED case

For UED masses not measureable For SUSY masses, measurable @ SPS1a Neutralino spin Smillie, Webber hep-ph/0507170 For UED masses not measureable Near-degenerate masses  little asymmetry For SUSY masses, measurable @ SPS1a but shape is similar need to measure size as well as shape of asymmetry

Lepton non-universality Neutralino spin Goto, Kawagoe, Nojiri hep-ph/0406317 Lepton non-universality Lepton Yukawa’s lead to differences in slepton mixing Mixing measurable in this decay chain Not easy, but there is sensitivity at e.g. SPS1a Biggest effect for taus – but they are the most difficult experimentally

Range of Validity Limits: Relatively small area of validity Neutralino spin Range of Validity Allanach & Mahmoudi To appear in proceedings Les Houches 05 Decay chain kinematically forbidden Spin Significance at the parton level – no cuts etc Limits: Decay chain must exist Sparticles must be fairly light Relatively small area of validity ~ red + orange areas in plot after cuts

Precise measurement of SM backgrounds: the problem SM backgrounds are not small There are uncertainties in Cross sections Kinematical distributions Detector response

W contribution to no-lepton BG Oe, Okawa, Asai Use visible leptons from W’s to estimate background to no-lepton SUSY search

Normalising not necessarily good enough Distributions are biased by lepton selection 

Need to isolate individual components…

Then possible to get it right… Similar story for other backgrounds – control needs careful selection

Dark matter relic density consistency? Use LHC measurements to predict relic density of observed LSPs Caveats: Can’t tell about lifetimes beyond detector mSUGRA assumed To remove mSUGRA assumption need extra constraints: All neutralino masses Use as inputs to gaugino & higgsino content of LSP Lightest stau mass Is stau-coannihilation important? Heavy Higgs boson mass Is Higgs co-annihilation important? More work is in progress Probably not all achievable at LHC ILC would help lots (if in reach)