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

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

3. 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) Producing exotics? Time standard exotic Time standard exotic Time standard exotics Time standard exotics Require an even number of exotic legs to/from blobs (Conserved multiplicative quantum number) Require an even number of exotic legs to/from blobs (Conserved multiplicative quantum number)

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

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

6. 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 † } = -2 γ μ P μ

7. Why SUSY? Higgs mass 2 –Quadratic loop corrections –In SM natural scale Λ cutoff ~ M planck v. high! –Need m(h) near electroweak scale Fine tuning Many orders of magnitude top Δm 2 (h)  Λ 2 cutoff higgs stop higgs Enter SUSY –2 x Stop quarks –Factor of -1 from Feynman rules –Same coupling, λ –Quadratic corrections cancel λλ λλ

8. 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” stop higgs +SUSY Log 10 (μ / GeV) Hit! 1/α

9. Extended higgs sector (2 doublets) (S)particles SMSUSY quarks (L&R) leptons (L&R) neutrinos (L&?) squarks (L&R) sleptons (L&R) sneutrinos (L&?)  Z 0 W ± gluon BW0BW0 h0H0A0H±h0H0A0H± H0H±H0H± 4 x neutralino 2 x chargino After Mixing gluino Spin-1/2 Spin-1 Spin-0 Spin-1/2 Spin-0 Bino Wino 0 Wino ± gluino ~ ~

10. Proton on Proton at 14 TeV

11. 40 million bunch crossings/minute

12. Something to see it with

13. General features Mass/GeV “typical” SUSY spectrum (mSUGRA) 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

14. SUSY event Jets Missing transverse momentum Leptons Heavy quarks

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

16. Discovering SUSY with jets Select a small number of high P T 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 SIGNAL topology BACKGROUND topology (QCD)

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

18. Suppressing backgrounds QCDSUSY Jet Remove events with missing energy back-to-back with leading jets

19. Measuring Backgrounds Example: SUSY BG –Missing energy + jets from Z 0 to neutrinos –Measure in Z -> μμ –Use for Z -> Good match –Useful technique Statistics limited –Go on to use W => μ to improve   Measure in Z -> μμ Use in Z -> νν R: Z  B: Estimated R: Z  B: Estimated

20. Di-jets + MET measurement Keeping it simple –>=2 jets –E T (J 1,2 ) > 150 GeV; | η 1,2 | < 2.5 Cambridge “Stransverse mass” Dijet inclusive: - No lepton veto - No b-jet veto - No multi-jet veto Dijet inclusive: - No lepton veto - No b-jet veto - No multi-jet veto

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

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

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

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

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

26. Mass scale? Spectrum SUSY kinematic variable “M TGEN ” E T sum / 2

27. 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 M TGEN & 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!

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

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

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

31. SUSY mass measurements 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 Try various decay chains Look for sensitive variables (many of them) Extract masses

32. 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?

33. 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…

34. Universal Extra Dimensions TeV-scale universal extra dimension model Kaluza-Klein states of SM particles –same QN’s as SM –m n 2 ≈ m 0 2 + n 2 /R 2 [+ boundary terms] –KK parity: From P conservation in extra dimension 1 st KK mode pair-produced Lightest KK state stable, and weakly interacting First KK level looks a lot like SUSY BUT same spin as SM hep-ph/0205314 Cheng, Matchev Radius of extra dimension ~ TeV -1 KK tower of masses n=0,1,… Dubbed “Bosonic Supersymmetry” R S 1 /Z 2

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

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

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

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

39. Left Squarks -> strongly interacting -> large production -> chiral couplings mass/GeV Revisit “Typical” sparticle spectrum Some sparticles omitted  1 0 –> Stable -> weakly interacting Right slepton (selectron or smuon) -> Production/decay produce lepton -> chiral couplings LHC point 5  2 0 = neutralino 2 –> (mostly) partner of SM W 0  1 0 = neutralino 1 –> Stable -> weakly interacting

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

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

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

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

44. l near q invariant mass (1) m/m max = sin ½ θ* Back to back in  2 0 frame θ*θ* quark lepton Phase space -> factor of sin ½ θ* Spin projection factor in |M| 2 : l + q -> sin 2 ½ θ* l - q -> cos 2 ½ θ* l+l+ l-l- Phase space Probability Invariant mass

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

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

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

48. 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 SpinsBranching Ratios These tell us about –SUSY vs Extra Dimensions –Dark Matter –Unification –SUSY breaking

49. Extras

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

51. 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 M 0 squarks, sleptons –Common fermionic mass M ½ Gauginos –Common trilinear couplings A 0 Susy equivalent of Yukawas Programs include e.g. ISASUSY, SOFTSUSY 10 16 GeV EW scale Iterate using Renormalisation Group Equations Unification of couplings Correct M Z, M W, …

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

53. Other suggestions Gauge mediation –Gauge (SM) fields in extra dimensions mediate SUSY breaking Automatic diagonal couplings  no EWSB –No direct gravitino mass until M pl 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!

54. R-Parity Unrestricted couplings lead to proton decay: L-violatingB-violatingL-violating General soft breaking terms include: Proton u d uu _ e-e- Λ” 112 Λ’ 112 s ~ _ Pion Unacceptably high rate compared to experimental limits (proton lifetime > 10 33 years) Strong limits on products of couplings Impose R P = (-1) 3B+L+2S (by hand) –Distinguishes SM from SUSY partners –Leads to stable LSP Required for dark matter –Sparticles produced in pairs

55. 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

56. 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

57. R-hadrons in detectors Signatures: 1.High energy tracks (charged hadrons) 2.High ionisation in tracker (slow, charged) 3.Characteristic energy deposition in calorimeters 4.Large time-of-flight (muon chambers) 5.Charge may flip Trigger: 1.Calorimeter: etsum or etmiss 2.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)

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

59. Sensitive variables? cos θ lab –Good for linear e + e - collider –Not boost invariant Missing energy means Z boost not known @ LHC Not sensitive @ LHC cos θ ll * –1-D function of Δη: –Boost invariant –Interpretation as angle in boosted frame –Easier to compare with theory N.B. ignore azimuthal angle boost AJB hep-ph/0511115 l1l1 l2l2 θ 2 lab θ 1 lab cos θ lab l1l1 l2l2 η 2 lab η 1 lab Δη l1l1 l2l2 θl*θl* θl*θl* cos θ* ll

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

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

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

63. Neutralino spinSmillie, 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

64. 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 Neutralino spinGoto, Kawagoe, Nojiri hep-ph/0406317

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

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

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

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

69. Need to isolate individual components…

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

71. Dark matter relic density consistency? Use LHC measurements to predict relic density of observed LSPs Caveats: –Can’t tell about lifetimes beyond detector To remove mSUGRA assumption need extra constraints: 1.All neutralino masses Use as inputs to gaugino & higgsino content of LSP 2.Lightest stau mass Is stau-coannihilation important? 3.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) mSUGRA assumed