Can we tell SUSY (from a hole in the ground)? Alan Barr UCL YETI06 11 Jan 2006

Scenario: 2006: New year’s resolutions: End of first year of data taking After careful calibration … ATLAS observes excess of events with: Missing transverse energy Leptons Jets Produces letter Definitely new physics! But what sort of new physics?!? 2006: New year’s resolutions: Give up assumptions Exercise more caution 11 Jan 2005 Alan Barr, UCL

What will we find at the LHC We expect to find: All the Standard Model particles W, Z, top, … Including a Higgs boson We hope to also find: Explanation for the scale of the Higgs mass Supersymmetry? Extra gauge groups? Extra dimensions? ? … but not a one-horse race. Susy in the lead … ? 11 Jan 2005 Alan Barr, UCL

What is supersymmetry? Nature permits only various types of symmetry: Space & time Lorentz transforms Rotations and translations Gauge symmetry e.g. SM: SU(3)c x SU(2)L x U(1) Supersymmetry Anti-commuting (Fermionic) generators Relationship with space-time {Q,Q†} = -2γμPμ 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! 11 Jan 2005 Alan Barr, UCL

(S)particles SM SUSY 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) 11 Jan 2005 Alan Barr, UCL

“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) 11 Jan 2005 Alan Barr, UCL LHC Pt5

Constraining masses Mass constraints Invariant masses in pairs Missing energy Kinematic edges Frequently- studied decay chain Observable: Depends on: Di-lepton invariant mass Extract information about masses from edges in kinematical distributions Limits depend on angles between sparticle decays 11 Jan 2005 Alan Barr, UCL

What particles are we seeing? End points tell us something about masses but not: Are these supersymmetric particles? If so, which particles are participating? Which neutralino? Left or right slepton? What sort of decays were involved? Two or three body? A nice example on how to include ambiguity in one’s analysis Use Markov Chain Monte Carlo to explore the parameter space Calculate likelihood at each point, including ambiguities Able to explore high-dimensional parameter space efficiently Still requires lots of CPU Used for mass-space, unification-space and adding non-universal terms Ambiguities in SUSY parameters from (2) and (3) Lester, Parker, White hep-ph/0508143 11 Jan 2005 Alan Barr, UCL

What particles are we seeing? End points tell us something about masses but not: Are these supersymmetric particles? If so, which particles are participating? Which neutralino? Left or right slepton? What sort of decays were involved? Two or three body? SUSY predicts particles with particular properties: Couplings are SAME as SM partners Spins differ by ½ Unbroken SUSY masses equal to SM partners SUSY breaking terms dominate masses A nice example on how to include ambiguity in one’s analysis Use Markov Chain Monte Carlo to explore the parameter space Calculate likelihood at each point, including ambiguities Able to explore high-dimensional parameter space efficiently Still requires lots of CPU Used for mass-space, unification-space and adding non-universal terms Does anything else look like SUSY? Lester, Parker, White hep-ph/0508143 11 Jan 2005 Alan Barr, UCL

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” 11 Jan 2005 Alan Barr, UCL hep-ph/0205314

UED level-1 spectrum Example decay spectrum Cheng, Matchev hep-ph/0205314 1st excited KK level (example masses) After adding boundary terms -> SUSY-like spectrum Example decay spectrum Stable lightest KK particle (weakly interacting) 11 Jan 2005 Alan Barr, UCL

Similarities and differences SUSY UED One extra particle for each SM particle Tower of extra particles for each SM particle Spins differ by half unit Same spins Same couplings R-parity  particles produced in pairs KK parity  n=1 level particles produced in pairs Weakly interacting Lightest SUSY particle Weakly interacting Lightest KK particle Can have good WIMP relic density Mass spectrum depends on method of SUSY breaking Typically rather degenerate mass spectrum 11 Jan 2005 Alan Barr, UCL

2nd KK mode? If 2nd KK mode light enough we can see it at LHC Datta, Kong, Matchev hep-ph/0509246 If 2nd KK mode light enough we can see it at LHC Can even separate 2 and Z2 Good evidence in favour of UED Problems: May not be seen Could have other interpretations (new gauge bosons?) 11 Jan 2005 Alan Barr, UCL

Similarities and differences SUSY UED One extra particle for each SM particle Tower of extra particles for each SM particle Spins differ by half unit Same spins Same couplings R-parity  particles produced in pairs KK parity  n=1 level particles produced in pairs Weakly interacting Lightest SUSY particle Weakly interacting Lightest KK particle Can have good WIMP relic density Mass spectrum depends on method of SUSY breaking Typically rather degenerate mass spectrum 11 Jan 2005 Alan Barr, UCL

SPIN 2 Spin 2 particle : looks same after 180° rotation 11 Jan 2005 Alan Barr, UCL

SPIN 1 Spin 1 particle : looks same after 360° rotation 11 Jan 2005 Alan Barr, UCL

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 Two methods for measuring SUSY particle spins @LHC so far… 11 Jan 2005 Alan Barr, UCL

Method 1 : 20 spin Use particular decay chain (right) AJB hep-ph/0405052 Method 1 : 20 spin Use particular decay chain (right) Make use of chiral couplings of Wino Consider invariant mass of quark with lepton Measure Angle Mostly Wino: Polarised 11 Jan 2005 Alan Barr, UCL

Spin projection factors Chiral coupling Approximate SM particles as massless -> okay since m « p 11 Jan 2005 Alan Barr, UCL

Spin projection factors Σ=0 S Spin-0 Produces polarised neutralino Approximate SM particles as massless -> okay since m « p 11 Jan 2005 Alan Barr, UCL

Spin projection factors Fermion θ* p S Scalar Polarised fermion Approximate SM particles as massless -> okay since m « p 11 Jan 2005 Alan Barr, UCL

Spin projection factors mql – measure invariant mass θ* p S Approximate SM particles as massless -> okay since m « p 11 Jan 2005 Alan Barr, UCL

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* 11 Jan 2005 Alan Barr, UCL

Experimental issues? How to distinguish between leptons? Measure Inv Mass How to distinguish between leptons? Cant – becomes a combinatorial background What about anti-squarks? Asymmetry is reversed Effect would cancel However at pp collider more squark than anti-squark produced! 11 Jan 2005 Alan Barr, UCL

AJB hep-ph/0405052 Charge asymmetry ATLFAST-level Charge asymmetry, spin-0 SUSY PS SUSY “data” Demonstration that spin determination is possible @ LHC Encouraging… but Relies on presence of particular chain Not a general technique. UED has similar shape for asymmetry… After cuts, detector simulation etc… 11 Jan 2005 Alan Barr, UCL

SUSY vs UED: Helicity structure Neutralino spin Smillie, Webber hep-ph/0507170 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 SUSY case UED case 11 Jan 2005 Alan Barr, UCL

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 11 Jan 2005 Alan Barr, UCL

Range of Validity Limits: Relatively small area of validity Neutralino spin Range of Validity Allanach & Mahmoudi To appear in proceedings Les Houches 05 Sleptons too heavy Universal SUSY fermion mass, m½ Universal SUSY scalar mass, m0 Limits: Decay chain must exist Sparticles must be fairly light Relatively small area of validity ~ red + orange areas in plot after cuts LEP excluded 11 Jan 2005 Alan Barr, UCL

Summary of spin method 1 Sensitive to neutralino-2 spin Workable in some regions of parameter space But those regions are not very large Can give slepton mixing information Sensitive to more than just spin Works best when sparticles non-degenerate (SUSY-like) Not workable when masses are near-degenerate (UED-like) Similar shape for UED and SUSY Size of asymmetry must be experimentally measured, not simply shape 11 Jan 2005 Alan Barr, UCL

Method 2: Angular distributions in direct slepton pair production Z/ is polarised along the ±z axis For slepton production Measure m=0 at angle θ from direction where l=1, m=±1 Average over initial states Sum over final states P ~ 1 – cos2 θ Favours θ ~ 90° Slepton Beam θ Beam Slepton Incoming (anti-)quark spins? + or + Z/ spin? or Final state spin? No component along slepton axis (m=0) 11 Jan 2005 Alan Barr, UCL

KK lepton pair production + or Relativistic limit: With KK-lepton masses: m=±1 m=0 KK lepton Beam θ Beam KK lepton Incoming (anti-)quark spins? + or + Z/ spin? or Final state spin? … 11 Jan 2005 Alan Barr, UCL

Angular distributions in direct slepton pair production Normalised angular distributions SUSY : qq  slepton pair : “Perpendicular” UED : qq  KK lepton pair : “Parallel” Phase Space : “Flat” Beam θ Slepton 11 Jan 2005 Alan Barr, UCL

What we see experimentally Invisible particle LSP or LKP +ve lepton Slepton or KK lepton (very short-lived) Beam θ Beam Observables: Pair of opposite sign, same family leptons Sum of PT of invisibles: PTMISS Invisible particle LSP or LKP -ve lepton Leptons “inherit” some knowledge of θ from their slepton or KK lepton mother 11 Jan 2005 Alan Barr, UCL

How to measure it? cos θlab cos θll* 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 11 Jan 2005 Alan Barr, UCL

slepton  lepton correlations Production angle Observable angle Slepton/KK lepton production angle not measurable Lepton inherits from boost of slepton parent Good correlation in plots above Observable cos θ*ll smaller for SUSY than UED 11 Jan 2005 Alan Barr, UCL

Cuts and acceptance Need to beat down SM backgrounds l+l- + missing energy signature Z0Z0 background Cut on l+l- invariant mass (not near Z) W+W- background Use mT2 variable to reduce this Pseudorapidity of leptons Detector acceptance: |η| < 2.5 11 Jan 2005 Alan Barr, UCL

Slepton spin – LHC pt 5 Statistically measurable “Data” = inclusive SUSY after cuts Statistically measurable Relatively large luminosity required Study of systematics in progress SM background determination SUSY BG determination Experimental systematics No show-stoppers so far 11 Jan 2005 Alan Barr, UCL

Similar results at various SPS benchmark points AJB hep-ph/0511115 SPS1a SPS1b Similar results at various SPS benchmark points 200-300 fb-1 (2-3 years at design lumi) Includes stat error from SM and SUSY BG subtraction No systematic uncertainty in backgrounds SPS3 SPS5 11 Jan 2005 Alan Barr, UCL

Required luminosity? 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 11 Jan 2005 Alan Barr, UCL

Summary of spin method 2 Sensitive to slepton spin A more general method than method 1 Works at various SPS points Sensitive when both: sleptons are light  reasonable x-sec slepton-LSP mass difference is > mW (for either slepton)  separate from WW Possible extensions Clean environment for measuring slepton pair production cross-section Very useful constraint esp. if mass scale can be independently measured 11 Jan 2005 Alan Barr, UCL

So what can we tell from a hole in the ground? LHC Observation Importance for (SUSY) Phenomenology New particles “Death” of the Standard Model Spin SUSY or not SUSY? Kinematical end points Masses  How is SUSY broken? Missing energy Possible dark matter candidate Branching ratios Detailed mass studies Is LSP the major contribution to dark matter? Etc… Extra excavations can extract: Direct dark matter searches Cosmologically stable LSP? ILC measurements (when available) Detailed properties of SUSY breaking, masses etc 11 Jan 2005 Alan Barr, UCL

Questions? 11 Jan 2005 Alan Barr, UCL

Paper trail Phys.Rev. D64 (2001) 035002 Bounds On Universal Extra Dimensions hep-ph/0110108 Spin Correlations In Monte Carlo Simulations hep-ph/0205314 Bosonic Supersymmetry? Getting Fooled At The LHC Phys.Lett. B596 (2004) 205 Determining the Spin of Supersymmetric Particles at the LHC Using Lepton Charge Asymmetry hep-ph/0406317 Study of the slepton non-universality at the CERN Large Hadronic Collider hep-ph/0502031 Probing Universal Extra Dimension at the International Linear Collider JHEP 0507 (2005) 033 Contrasting Supersymmetry and Universal Extra Dimensions at the CLIC Multi-TeV e+ e- Collider hep-ph/0507170 Distinguishing Spins In Supersymmetric and Universal Extra Dimension Models at the Large Hadron Collider hep-ph/0509246 Discrimination of Supersymmetry and Universal Extra Dimensions at Hadron Colliders hep-ph/0511115 Measuring Slepton Spin at the LHC 11 Jan 2005 Alan Barr, UCL

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 11 Jan 2005 Alan Barr, UCL

Result of LHC analyses could be a supersymmetric sudoku puzzle! True masses Trial Masses Wino Bino Slepton Squark Higgsino Constraints from cross-sections (observables) Ambiguities in where to place gauginos, LR sleptons etc After Arkani-Hamed, Kane, Thaler, Wang hep-ph/0512190 11 Jan 2005 Alan Barr, UCL

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 scales [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 11 Jan 2005 Alan Barr, UCL