1. Extraction of SUSY Parameters from Collider Data SUSY 2008 Seoul 06/17/2008 Dirk Zerwas LAL Orsay Introduction Measurements Reconstruction of fundamental Parameters Summary

2. Supersymmetry 3 neutral Higgs bosons: h, A, H 1 charged Higgs boson: H ± and supersymmetric particles spin-0spin-1/2spin-1 squarks: q R, q L q gluino: gg sleptonen: ℓ R, ℓ L ℓ h,H,Aneutralino χ i=1-4 Z, γ H±H± charginos: χ ± i=1-2 W±W± ~~ ~~ ~ Many different models: MSSM (low scale many parameters) mSUGRA (high scale few parameters) DSS (SUSY with heavy scalars) GMSB AMB NMSSM R-parity production of SUSY particles in pairs (Cascade-) decays to the lightest SUSY particle LSP stable, neutral and weakly interacting: neutralino (χ 1 ) experimental signature: missing E T fermion  boson has “no” problems with radiative corrections (quadrat. div.) has a light Higgs Boson (<150GeV) interesting pheno at the TeV scale

3. A typical (optimistic) point gluinos and squarks (not too heavy) light sleptons heavy and light gauginos Higgs boson mass at the LEP limit τ 1 lighter than the lightest χ ± : χ ± BR 100% τν χ 2 BR 90% ττ cascade: q L  χ 2 q  ℓ R ℓ q  ℓ ℓ qχ 1 ~ ~ ~ ~ “Physics Interplay of the LHC and ILC” G. Weiglein et al ~ SPS1aSPS1a’SU3LM1 M 0 (GeV)1007010060 m 1/2 (GeV)250 300250 tanβ10 6 A0 (GeV)-100-300 0

4. Edges at the LHC hard jets with leptons invariant mass: jet-lepton lepton-lepton-jet lepton-lepton less statistics: 1-10fb -1 Improvements over past studies: full simulation and reconstruction realistic detector description (with additional distorsions) early Data: 0.5-10fb -1 SUSY08: Paul de Jong, Peter Wienemann, talks by CMS

5. LHC and ILC measurements SPS1a Linear collider e+e- collisions up to 1TeV LHC: lepton energy scale 0.1% LHC: jet energy scale 1% luminosity 100fb -1 for the following continue with SPS1a as example LHC: from edges/thresholds to masses: toy/fit ILC: direct measurements/threshold scans

6. mass spectra and decays: SOFTSUSY, SUSPECT, FeynHiggs, ISASUSY,SPHENO, SDecay, SUSY-HIT, HDECAY, NMSSMtools,… NLO cross sections from Prospino2.0,… dark matter: micrOMEGAS, DarkSUSY, IsaRED,… Beenakker et al Search for parameter point, determine errors including treatement of error correlations: Pioneers: G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27:263-281,2003) / Allanach et al. hep-ph/0403133 FITTINO: P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46:533-544,2006) SFITTER: R. Lafaye, T. Plehn, M. Rauch, D. Z. (Eur.Phys.J.C54:617-644,2008) GFITTER: M. Goebel, J. Haller, A. Hoecker, K. Moenig, J. Stelzer (EW fit) EW fits plus dark matter: Buchmueller et al, Phys.Lett.B657:87-94,2007 Super-Bayes: R.R. de Austri, R. Trotta, (MCMC, collider observables and dark matter…) CMSSM fits and weather forcasts: B. Allanach, K. Cranmer, C. Lester, A. Weber … Determination of Supersymmetric Parameters from edges, masses (etc) to fundamental parameters: e.g.: mSUGRA m(Smuon) = f(m 0, m 1/2, tanβ) m(Chargino) = f(m 1/2, tanβ,…) correlations exp and theoretical treatment of theory errors!  global ansatz necessary See Allanach arXiv:0805.2088[hep-ph] for complete list

7. Information Extraction from Standard Measurements alone Buchmueller et al: electroweak plus dark matter, b  sγ, b  μμ CMSSM χ 2 slightly better than SM m h =110 +8 -10 ±3GeV Allanach et al: Predict SUSY cross sections at LHC: ~fb μ and B (high scale parameters) Bayesian measure: same order of magnitude for all parameters (no scale imposed nor unification) slightly higher cross sections in non-Bayesian approach (Profile Likelihood ~maximum instead of measure) SUSY08: Sven Heinemeyer

8. Lagrangian@GUT scale: mSUGRA SPS1a Start m0m0 1001TeV m 1/2 2501TeV tanβ1050 A0-1000GeV First question: do we find the right point? mSUGRA advantage: few parameters, testing ground for studies of principles disadvantage: starts at GUT scale and adds RGE extrapolation, not the most general lagrangian Sign(μ) fixed ~300 toy experiments: convergence OK with MINUIT alone for LHC (largest errors)! brute force method GRID: disadvantage: N P advantage: computer industry (OECD?) Hypothesis: SUSY particles discovered and discrete quantum numbers (spin) measured brute force method MINUIT: disadvantage: starting point

9. Lagrangian@GUT scale: mSUGRA SFitter: Markov Chains (efficient sampling in high dimensions, linear in number of parameters) Full dimensional exclusive likelihood map with the possibility of different types of projections: marginalisation (Bayes) introduces a measure profile likelihood (Frequentist approach) Fittino: Simulated annealing Ranked list of minima: secondary minima exist (LHC) discarded by χ 2 alone interplay with top mass (parameter!)

10. mSUGRA: Errors RFit Scheme: Höcker, Lacker, Laplace, Lediberder use edges not masses (improvement: 10x)! e-scale correlations at LHC 25-50% impact on error remember the standard model (top quark mass 1GeV at LHC) 10%. No information within theory errors: flat distribution Higgssleptonssquarks,gluinosneutralinos, charginos 3GeV1%3%1%

11. mSUGRA: Errors LHC and ILC SPA project: precision of the theoretical calculations Eur.Phys.J.C46:43-60,2006 ILC improves by 3-4x on LHC LHC+ILC better than any machine alone theory errors impact the expected precision at all machines also at LHC Fittino: the beginning 1 fb -1 1 year low lumi 10 fb-1 3 years nominal 300 fb-1 and then the ILC: SFitter

12. The LHC neutralino enigma Exchanging χ 3 and χ 4 leads to a secondary minimum M0 and M1/2 ok, but tanβ and A0 more than 2-3σ from nominal values so in principle need ILC to see which neutralino are present…. the predicted mass of χ 4 is about 400GeV the predicted branching ratios would lead us to expect more χ 4 than χ 3 in the measurement channel in disagrement with the observation general rule: beware of the “hidden” measurements…… SPS1a LHC masses ΔLHC masses LHC edges ΔLHC edges m0m0 10099.64100.32.6 m 1/2 250250.11.7248.82.1 tanβ108.10.87.70.73 A0-100-19630-18639 top175 1175.50.75 χ 2 /p.d.f0-0.2/16-2/11 χ1χ1 97.24.8 χ2χ2 180.84.7 χ3χ3 -- χ4χ4 381.95.1 The uniqueness problem: LHC measures the neutralino index in SPS1a? permute: χ 4 with χ 3

13. MSSM 19 parameters at the EW scale no unification of the 1 st and 2 nd generation 3 neutralino masses at LHC M1, M2, μ 8 fold ambiguity in Gaugino- Higgsino subspace at the LHC! mix techniques: markov flat full Parameter space MINUIT in 5 best points Markov flat gaugino-higgsino space MINUIT on 15 best points BW pdf on remaining parameters MINUIT on 5 best solutions (all parameters) LHC+ILC: all parameters determined several parameters improved

14. MSSM Running up to the GUT scale: G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27:263-281,2003) P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46:533-544,2006) SPS1a (SPA1): dashed bands: today’s theory errors included unification measured from low energy (TeV) data from LHC+ILC remember: all results valid within a well defined model/hypothesis

15. A difficult example: SUSY with heavy scalars N. Bernal, A. Djouadi, P. Slavich JHEP 0707:016,2007 E. Turlay et al. (Proceedings BSM-SUSY les Houches 2007) DSS parameters: M S : decoupling scale, scalar masses m1/2: gaugino mass parameter μ: Higgs mass parameter At: trilinear coupling at MS tanβ: mixing angle between Higgs at MS Phenomenology: scalar Mass scale 10 4 to 16 GeV scalars are at M S fermions O(TeV) SM Higgs h effective theory below MS at MS matching with complete theory and standard RGE Parameter determination at LHC possible Arkani-Hamed & Dimopoulos 2004 Giudice, Romanino 2004 ATLAS/CMS talks: Paul de Jong, Tapas Sarangi, Daniel Teyssier

16. Connection Colliders-Cosmology Measurement of the fluctuations of the cosmic microwave background WMAP Ω CDM h 2 =0.127±0.01 (astro-ph/0603449) Planck Ω CDM h 2 ~ 2% SUSY breaking parameters (determined) spectrum and couplings (deduced) darkSUSY, isaRed or micrOMEGAs Ω CDM h 2 =n LSP *m LSP (relic density) MSUGRA SPS1a (central value irrelevant) LHC : Ωh 2 = 0.1906  0.0033 LHC+ILC: Ωh 2 = 0.1910  0.0003 % precision at LHC, permil LHC+ILC theory errors! NASA/WMAP science team Temperature range: ±200μK E. Baltz,M.Battaglia, M.Peskin, T.Wizansky: Phys.Rev.D74:103521,2006 Nojiri et al/Dutta et al Comparable precision of CMB and Collider data possible SPS1a’

17. Summary LHC alone could provide a wealth of measurements for SUSY LHC+ILC is the dream team will collider dark matter property predictions be comparable to WMAP/Planck? LHC is starting now, is SUSY just around the corner? Thank you: Klaus Desch, Remi Lafaye, Tilman Plehn, Michael Rauch, Laurent Serin, Mathias Uhlenbrock, Peter Wienemann Hope to start testing grand unification soon! SFitter+Suspect

18. MSSM LHC: can assign errors on badly measured parameters LHC+ILC: all parameters determined several parameters improved