Extraction of Parameters from Collider Data? NPF 2009 Heidelberg 02/26/2009 Klaus Desch and Dirk Zerwas Uni Bonn and LAL Orsay Introduction Finding the right parameter set getting the errors right other applications Open questions Definition 1: mSUGRA=toy (Klaus left to hide from Tilman) Definition 2: MSSM=oset 4711

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 treatment of error correlations: Pioneers: G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27: ,2003) / Allanach et al. hep-ph/ FITTINO: P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46: ,2006) SFITTER: R. Lafaye, T. Plehn, M. Rauch, D. Z. (Eur.Phys.J.C54: ,2008) GFITTER: M. Goebel, J. Haller, A. Hoecker, K. Moenig, J. Stelzer (EW fit) Master Code: Buchmueller et al, Phys.Lett.B657:87-94,2007 (my name is Vader, Dirk Vader) 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 (from Klaus to Tilman with love) 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: [hep-ph] for complete list

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) m 1/2 (GeV) tanβ10 6 A0 (GeV) Forced to talk about SPS1a(‘) by genetic pre-disposition (quote from Mihoko)

SUSY already discovered? Global mSugra fit to measured things… (to compare with Buchmüller ea – consistent) dominated by g-2 and  h 2 DM - but encouraging…

From LE fit: predicted mass spectra no (g-2)  no  h 2 DM Prediction driven by g-2 and Ωh 2

LHC measurements SPS1a LHC: lepton energy scale 0.1% LHC: jet energy scale 1% luminosity 100fb -1 LHC: from edges/thresholds to masses: toy/fit NPF: Shoji, Dan

scale: mSUGRA SPS1a Start m0m0 1001TeV m 1/2 2501TeV tanβ1050 A0-1000GeV First question: do we find the right point? 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 Hypothesis: SUSY particles discovered and non-discrete quantum numbers to be measured brute force method MINUIT: disadvantage: starting point

Model discrimination What are fits to mSugra are good for after all? - rule out the most simple assumptions (degenerate masses…) - discriminate between different „digital“ assumptions, e.g. sgn  = -1 sgn  = +1 with 1 fb -1 : correct model (sgn  =+) preferred with 96% probability misinterpreation of edge replace with 1 fb -1 : correct model preferred with 77% probability

scale: mSUGRA 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) Simulated annealing Ranked list of minima: secondary minima exist (LHC) discarded by χ 2 alone interplay with top mass (parameter!)

Fittino: error determination from Toy Fits Parameter fits:  2 distribution as reliable „quality control“ for derived uncertainties - simulated annealing  find global minimum - Toy MC  map out spread of parameters when observables vary within their expt. errors MC Toy fits:

mSUGRA: Theory Errors and Standard Model 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%

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)

MSSM18 Tilman doesn‘t like mSugra – so could we fit (much) more general models? LHC: 300 fb -1 But remember: this maybe possible in the „best of all worlds“ (=SPS1a-like point) Much less will be possible if e.g. no dilepton edge is visible

MSSM Running up to the GUT scale: G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27: ,2003) P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46: ,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

The Higgs sector Measurements Theory Errors Experimental Errors Applying same techniques: Likelihood map with reduction of dimensions either Bayesian of Profile Likelihood (more appropriate here in absence of true secondary minima) Thanks Gavin SFitter+Michael Duehrssen

Profile likelihood 30fb-1 theory errors ZH/WH absent ZH/WH full sensitivity ZH/WH half sensitivity

Questions for discussion Several methods to scan n-dimensional parameter space. Enough? Agree on error treatment (esp theory errors)? extension from SUSY model A to SUSY model B easy Higgs sector study ok other non-susy models? How to communicate (spectrum/observables) without re-inventing the wheel? Do these models Z’, UED etc need n-dimensional scan tools? Is it a particularity of SUSY that a measurement depends on N parameters? Is the theoretical precision sufficient everywhere? Inclusion of exclusion? observed rates: clearly, how to predict N (SUSY pars) for fits? how to implement in fits? interfacing to theory codes: SLHA quite good – problems if > 1 code is used in a fit (e.g. separate RGE running in SPheno + mastercode) fast (parametrized) rate calculator – any ideas? stability of Markov chain MCs (dependence on start values, alg. parameters, statistics,…)

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

backup: LE input

backup: MSSM18 fitted model parameters

backup: LHC inputs note: - all inputs based on +- recent ATLAS/CMS simulation - of course „correct“ interpretation of the edges is assumed / wrong assignment has to be tested separately