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Global Fits: Making Sense out of What we Will See Global Fits – Motivation & History “SUSY Fits” – where are we today? The future Global Fits – Motivation & History “SUSY Fits” – where are we today? The future Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Oliver Buchmüller Roberto Trotta Imperial College London

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 “Random Scans”: Why we Need Better Tools Points accepted/rejected in a in/out fashion (e.g., 2-sigma cuts) No statistical measure attached to density of points: no probabilistic interpretation of results possible Inefficient/Unfeasible in high dimensional parameters spaces (N>3) Explores only a very limited portion of the parameter space! Gogoladze et al (2008) [one of many such studies]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Statistics in High-D spaces Tom Loredo (cosmostats09 talk) Damien Francois (2005) “Random scans” of a high-dimensional parameter space only probe a very limited sub-volume: this is the concentration of measure. Statistical fact: the norm of d draws from U[0,1] concentrates around (d/3) 1/2 with constant variance

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Geometry in High-D Spaces Volume of cube Volume of sphere Ratio Sphere/Cube 1 1 Geometrical fact: in d dimensions, most of the volume is near the boundary. The volume inside the spherical core of d-dimensional cube is negligible.

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Scanning the New Physics Parameter Space 2 Determining the preferred NP parameter space is a multi-dimensional problem. Even in one of the simplest cases, the CMSSM, there are four NP parameters (M 0, M 1/2, A 0, tanβ) as well as SM parameters like m top or m b. The conventional (now historical) strategy in the field was to carry out “2D scans” by fixing the other relevant parameters to certain values. An arbitrary example: 0106334 [hep-ph] tanβ=10 tanβ=50 2D scans strongly depend on the “fixed NP parameters”

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Scanning the New Physics Parameter Space 3 M top =170 GeVM top =180 GeV There is also a strong dependence on the important SM parameters! (which are known only with a limited accuracy)

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 The Solution to the Problem – Global Fits 5 Valid for all NP and SM parameters Carry out a simultaneous fit of all relevant NP and SM parameter to the experimental data/constraints. Marginalize (= integrate) or maximise along the hidden dimensions so as to obtain results that account for the multi-dimensional nature of the problem. This gives a statistically well- defined answer.

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Wmap blobs today Joint HEP-APP IOP meeting on SUSY - March 24th 2010 The Solution to the Problem – Global Fits 6 WMAP strips a few years ago Another Example: the so-called “WMAP strips” 0306219 [hep-ph] In 2D scans, enforcing the cosmological relic abundance results in narrow “allowed regions” (the “WMAP strips”), whose location changes with the value of the fixed parameters. Once fixed parameters are included and hidden dimensions accounted for, WMAP strips widen to become “WMAP blobs”

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Confronting Theory with Data – Global fits 8 UT FitCKM Fitter LEP EW FIT Comprehensive statistical confrontation of theory and data has always been a very important subject of particle physics phenomenology. Global Fits Prominent Examples are: LEP EW Fit Constraining the SM (EW part) Unitarity Triangle UT Fit vs. CKM Fitter

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Testing Consistency and Predicting Unknowns 9 Probably the most famous example: LEP EW FIT i) Test consistency of theory with data using well-defined statistical procedure. Determine consistency probability - here via “χ 2 ” ii) Predict unknown quantities in the model - here M Higgs

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Different Statistical Approaches ρbar = 0.139 [+0.025 -0.027] ηbar = 0.341[+0.016 -0.015] ρbar = 0.155 [+0.022 -0.022] ηbar = 0.342[+0.014 -0.014] Bayesian vs Frequentist Different answers to different questions CKM triangle Fits Today: Overall good agreement between the two approaches but still differences in the details.

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Marginal Posterior vs Profile Likelihood Marginal posterior:Profile likelihood: In general different if: θ2θ2 θ1θ1 likelihood = “hottest” hypothesis Physical analogy: (thanks to Tom Loredo) Heat: Posterior: Posterior = region with most heat (plot depicts likelihood contours - prior assumed flat over wide range) Bayesian vs Frequentist Relevant for underconstrained system

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Bayesian Statistic on the Rise? 11 As far as I can think back, the frequentist approach has dominated the field of particle physics – it still does but bayesian methodology becomes increasingly more important it seems. In particular there is strong influence from the field of astrophysics:

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Global NP Fits in the LHC (Discovery) Era 13 O. Buchmueller, R. Cavanaugh, A. De Roeck, J.R. Ellis, H.Flacher, S. Heinemeyer, G. Isidori, K.A. Olive, F.J. Ronga, G. Weiglein MasterCode Superbayes Fittino S.S. AbdusSalam, B.C. Allanach, M.J. Dolan, F. Feroz, M.P. Hobson H. Flächer, M. Goebel, J. Haller, A. Höcker, K. Mönig, J. Stelzer P. Bechtle, K. Desch, M. Uhlenbrock, P. Wienemann L. Roszkowski, R. Ruiz de Austri, R. Trotta Sfitter R. Lafaye, M. Rauch, T. Plehn, D. Zerwas GFitter

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Global NP Fits in the LHC (Discovery) Era 14 O. Buchmueller, R. Cavanaugh, A. De Roeck, J.R. Ellis, H.Flacher, S. Heinemeyer, G. Isidori, K.A. Olive, F.J. Ronga, G. Weiglein MasterCode Superbayes Fittino S.S. AbdusSalam, B.C. Allanach, M.J. Dolan, F. Feroz, M.P. Hobson H. Flächer, M. Goebel, J. Haller, A. Höcker, K. Mönig, J. Stelzer P. Bechtle, K. Desch, M. Uhlenbrock, P. Wienemann L. Roszkowski, R. Ruiz de Austri, R. Trotta Sfitter R. Lafaye, M. Rauch, T. Plehn, D. Zerwas GFitter Many different groups of theorists and experimentalists and several different approaches!

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Global NP Fit Methodology in a Nutshell Chose a NP model SUSY as show-case – so far considered models: GUT Scale model: CMSSM, NUHM, AMSB Soft Scale model: pMSSM Chose the measurements Considered (indirect) constraints are collider (EWK, flavour) and non- collider data (g-2, relic density) It is crucial to have a consistent set of calculations for these constraints! Chose your preferred statistical approach to confront model prediction Pi with measurements Mi with cov(Mi,Mi) “χ 2 “ as an example: (M – P) T cov -1 (M – P) [+ limits] Find set of Pi that minimize χ 2 15

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 RGE Non-linear numerical function via SoftSusy 2.0.18 DarkSusy 4.1 MICROMEGAS 2.2 FeynHiggs 2.5.1 Hdecay 3.102 Constrained MSSM Analysis Pipeline 4 CMSSM parameters θ = {m 0, m 1/2, A 0, tanβ} (fixing sign(μ) > 0) 4 SM “nuisance parameters” Ψ={m t, m b,α S, α EM } Observable quantities f i (θ,Ψ) CDM relic abundance BR’s EW observables g-2 Higgs mass sparticle spectrum (gamma-ray, neutrino, antimatter flux, direct detection x-section) Data: Gaussian likelihoods for each of the Ψ j (j=1...4) Data: Gaussian likelihood (CDM, EWO, g-2, b→sγ, ΔM Bs ) other observables have only lower/upper limits Physically acceptable? EWSB, no tachyons, neutralino CDM YES NO Likelihood = 0 SCANNING ALGORITHM Joint likelihood function

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Consistent Set of Predictions: Example MasterCode Consistency Relies on SLHA interface Modularity Compare calculations Add/remove predictions State-of-the-art calculations Direct use of code from experts

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Finding the Favoured Regions Due to the weak nature of constraints, different scanning techniques and statistical methods will generally give different answers (also because the questions being asked are different!) Traditional method: determine best fit parameter (find minimum) Markove Chain Monte Carlos (MCMC) MCMC and Minuit as “afterburner” Simulated annealing Genetic algorithm Determine errors: Local Δ(LogLikelihood) Intelligent sampling of parameter space with MCMC Pseudo Experiment/Toy Experiment sampling 16

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Finding the Favoured Regions Alternatively, one might focus on the probability mass instead (Bayesian) Best fit has no special status: look for the bulk of the posterior probability mass instead Markov Chain Monte Carlo techniques (MCMC) Nested sampling Hamiltonian MC Determine errors: region of parameter space containing e.g. 95% of samples Might depend on measure chosen (prior) Represents degree of knowledge (rather than coverage) 16

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Consistent Set of Predictions: Example MasterCode Consistency Relies on SLHA interface Modularity Compare calculations Add/remove predictions State-of-the-art calculations Direct use of code from experts Confront prediction and data Form statistical metric (e.g.χ 2 ) and use as input to e.g. MCMC or Minuit

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 List of Implemented Observables

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 MasterCode: Constraint List 20 Consistent prediction of more 30 constraints!

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 21 Today: “Weak Constraints” only Biggest problem today – no significant deviation from the SM! Only ~2 to ~3σ evidence and relic density that cannot be explained in the SM. only weakly constraint NP parameter space Ωh 2 =0.1099 ± 0.0066 ± 0.012 Mw Relic density Mw =80.399 ± 0.023 GeV Δa μ =(24.6 ± 8)E-10 g-2 R(B X s γ) = 1.117±0.12 R: Measurement/SM R(B τν) = 1.43±0.43 The main players today

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 22 Today: “Weak Constraints” only Ωh 2 =0.1099 ± 0.0066 ± 0.012 Mw Relic density Mw =80.399 ± 0.023 GeV Δa μ =(24.6 ± 8)E-10 g-2 R(B X s γ) = 1.117±0.12 R: Measurement/SM R(B τν) = 1.43±0.43 The main players today 0808.4128 [hep-ph] Biggest problem today – no significant deviation from the SM! Only ~2 to ~3σ evidence and relic density that cannot be explained in the SM. only weakly constraint NP parameter space

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Where are we today? Details in Frederic Ronga’s and Roberto Ruiz de Austri’s talks Here just a few points...

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM Today – “Frequentist Fits” 24 Fittino uses the constraint calculation from MasterCode but the statistical approach for the global fit as well as the involved people are independent. MasterCode Best fit point (μ>0) MasterCode M 0 =60, M 1/2 =310 A 0 =130, tanβ=11 Fittino M 0 =76, M 1/2 =332 A 0 =383, tanβ=13 0907.2589 [hep-ph] 0907.4468 [hep-ph] 0808.4128 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM – Without Relic Density Constraint 25 MasterCode Note: y and x flipped Not same scale With Ωh 2 95% CL Without Ωh 2 95% CL Without Ωh 2 95% CL With Ωh 2 95% CL M0M0 M0M0 M0M0 M 1/2 M0M0 tanβ 0907.2589 [hep-ph] 0907.4468 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM - Best Fit Spectrum 26 MasterCode 68% 95% Also very good agreement in best fit point sparticle spectrum (and errors)! Both frequentist groups arrive at same conclusion: Today’s constraints prefer light mass SUSY in CMSSM! 0907.2589 [hep-ph] 0907.4468 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM – “Bayesian Fits” 27 (Main) considered prior choices in Bayesian fits today: “flat prior” Uniform in M 0,M 1/2,A 0,tanβ “log prior” Uniform in log(M 0 ), log(M 1/2 ), A 0, tanβ “naturalness prior” Same as flat priors but uniform in B and μ instead of B and tanβ 0807.4512 [hep-ph]0809.3792 [hep-ph]0705.0487 [hep-ph] Posterior distributions “non-informative”“midly-informative”“highly-informative”

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM Today: Frequentist vs. Bayesian 33 “flat prior ” “log prior ” “naturaless prior ” All priors find a “low mass SUSY” solution similar to the prior independent frequentist result. The key question is how constrained is actually this region? Has the frequentist approach missed “high mass” regions? 0705.0487 [hep-ph] 0809.3792 [hep-ph] 0808.4128 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Prior Dependence 28 “flat prior” “log prior” 0809.3792 [hep-ph] Prior dependence of the Bayesian fits results from weak constraints on parameter space. Stronger assumptions (e.g. naturalness priors) lead to posteriors dominated by prior information (rather than data). “flat prior ” “naturalness prior ” “naturalness prior ” “log prior” “flat prior” 0705.0487 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Prior Dependence due to Weak Constraints 29 0705.0487 [hep-ph] 0806.1184 [hep-ph] Global Fit to CMSSM with four parameters: M 0, M 1/2, A 0, tanβ [μ>0] strong prior dependence Global Fit to Large Volume String scenario with only two param.: M 0, tanβ [μ>0] smaller prior dependence “flat prior ” “naturalness prior ” “naturalness prior ” Four (CMSSM) vs. two (LVS) free parameters. “Volume” effects coming from large-D parameter spaces are presently important. The question will remain in the future: i.e., once we’ll have LHC data, the frontier will shift to models in higher dimensions (eg, pMSSM with ~ 20 free parameters)

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 LHC Data (Discoveries) will help a lot 31 Assumed ATLAS covariance matrix for the SU3 benchmark Point at 1/fb If we are really luck we might see these spectacular signatures already very early at the LHC! “flat prior ” “log prior ” M(l + l - ) GeV A ssuming such a spectacular discovery as input reduces the prior dependence of the global bayesian fits to almost negligible levels. 0907.0594 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 LHC Data (Discoveries) will help a lot 32 Assumed ATLAS covariance matrix for the SU3 benchmark Point at 1/fb If we are really luck we might see these spectacular signatures already very early at the LHC! “flat prior ” “log prior ” M(l + l - ) GeV A ssuming such a spectacular discovery as input reduces the prior dependence of the global bayesian fits to almost negligible levels. 0907.0594 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Accelerated Inference from Neural Networks Standard MCMC (SuperBayeS v1.23, 2006) 500 CPU days MultiNest algorithm (SuperBayeS v1.35, 2008) <3 CPU days speed-up factor: 200 SuperBayeS+Neural Networks (Bridges, RT et al, upcoming) 15 CPU minutes speed-up factor: 50’000 We will need faster methods to deal with more complex models and higher dimensional parameter spaces, independently of the statistics used. Neural networks provide a way forward for ultra-fast inference. Computational effort for an 8- parameters global CMSSM fit: Simulated ATLAS data with 1/fb luminosity full MultiNest fit Neural Network

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Profile Likelihood from a Genetic Algorithm GA profile likelihoodNested sampling profile Akrami et al (0910.3950) A genetic algorithm (GA) has been employed by Akrami et al (0910.3950) to map out the profile likelihood - something Bayesian fits struggle somewhat with. This allows to find isolated spikes in the likelihood in high-mass region: the GA is optimised to look for this features, Nested sampling looks rather at the bulk posterior mass. overall best-fit isolated local maxima (1 and 2 sigma regions)

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM Today: Frequentist vs. Bayesian 34 “flat prior ” “log prior ” 0809.3792 [hep-ph] 0907.4468 [hep-ph] Δχ 2 Very comprehensive sampling with more than 25 Mio(!) points reveals no second minima structure in the frequentist approach: “ High mass region” M 0 >1 TeV is disfavored by Δχ 2 > 8 M 1/2 >1 TeV is disfavored by Δχ 2 > 20 Only by fully ignoring g-2 the High-mass region becomes more probable and is only disfavored by Δχ 2 ~ 2. No g-2 With g-2 0907.4468 [hep-ph] MasterCode

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 CMSSM Today: Frequnetist vs. Bayesian 35 “flat prior ” “log prior ” 0809.3792 [hep-ph] 0907.4468 [hep-ph] Δχ 2 Very comprehensive sampling with more than 25 Mio(!) points reveals no second minima structure in the frequentist approach: “ High mass region” M 0 >1 TeV is disfavored by Δχ 2 > 8 M 1/2 >1 TeV is disfavored by Δχ 2 > 10 Only by fully ignoring g-2 the High-mass region becomes more probable and is only disfavored by Δχ 2 ~ 2. Note: The sampling is so detailed that it even resolves clearly the light higgs funnel of m h ~ 2mχ 1 0, which is disfavored by Δχ 2 ~>10. MasterCode

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Other GUT Scale Models

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Connection to Astro(particle)physics

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Direct Dark Matter Searches & LHC 54 Sensitivity Plot: WIMP(LSP) Mass vs. p SI p SI : spin-independent dark matter WIMP elastic scattering cross section on a free proton. A convenient way to illustrate direct and indirect WIMP searches. 0907.4468 [hep-ph] 0809.3792 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Direct Detection Prospects in the CMSSM Predicted reach with 1 tonne detectors Bayesian posteriorProfile likelihood 68% 95% 68% 95% Prospects for WIMP discovery in the CMSSM framework for upcming 1t scale detectors are robust, independently of the choice of statistics.

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Implications of CDMS II for the CMSSM Bertone et al, in prep WITHOUT CDMS IIINCLUDING CDMS II The 2007-2008 run of the CDMS II detector reported 2 candidate events in the WIMP acceptance region. Effective exposure after cuts is 194 kg days. This leads to a 90% upper limit for the spin independent scattering cross section of 7.0 x 10 -44 pb for a 70 GeV WIMP The 2 observed events favour the high mass (focus point) region of the CMSSM and lead to a suppression the probability of the bulk region (corresponding to low mass SUSY) Profile likelihood CDMS II 90% limit

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 The Need for a Multiple Probes Approach Cumberbatch et al (in prep) No single probe can cover the whole favoured parameter space, not even the LHC. Astroparticle probes (direct and indirect detection) can increase the coverage of the favoured parameter space, and deliver increased statistical robustness. High complementarity with direct detection methods. Need to establish a common language (and approach) to Use all this information consistently Global Fits are one possible tool for this.

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Conclusions Global fits are needed as tool to interpret new physics discoveries from multiple probes. Can be used to explore connections between particle and astroparticle physics as well as cosmology. Two independent statistical approaches: ought to give the same result (eventually, when data are constraining enough!) In the meantime, different questions could give different answer if problem is underconstrained (as it is today) The statistical frontier is a moving target and as we will make progress in understanding the first discoveries our questions will again be more complex! More details now in the next two talks!

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Supplementary material after this slide

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Global NP Fit Methodology in a Nutshell Chose a NP model SUSY as show-case – so far considered models: GUT Scale model: CMSSM, NUHM, AMSB Soft Scale model: pMSSM Chose the measurements Considered (indirect) constraints are collider (EWK, flavour) and non- collider data (g-2, relic density) It is crucial to have a consistent set of calculations for these constraints! Chose your preferred statistical approach to confront model prediction Pi with measurements Mi with cov(Mi,Mi) “χ 2 “ as an example: (M – P) T cov -1 (M – P) [+ limits] Find set of Pi that minimize χ 2 15

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 RGE Non-linear numerical function via SoftSusy 2.0.18 DarkSusy 4.1 MICROMEGAS 2.2 FeynHiggs 2.5.1 Hdecay 3.102 Constrained MSSM Analysis Pipeline 4 CMSSM parameters θ = {m 0, m 1/2, A 0, tanβ} (fixing sign(μ) > 0) 4 SM “nuisance parameters” Ψ={m t, m b,α S, α EM } Observable quantities f i (θ,Ψ) CDM relic abundance BR’s EW observables g-2 Higgs mass sparticle spectrum (gamma-ray, neutrino, antimatter flux, direct detection x-section) Data: Gaussian likelihoods for each of the Ψ j (j=1...4) Data: Gaussian likelihood (CDM, EWO, g-2, b→sγ, ΔM Bs ) other observables have only lower/upper limits Physically acceptable? EWSB, no tachyons, neutralino CDM YES NO Likelihood = 0 SCANNING ALGORITHM Joint likelihood function

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 AMSB & GMSB 37 “log prior” “naturalness prior” “flat prior” “naturalness prior” 0906.0957 [hep-ph] AMSB M 0, M 3/2, tanβ GMSB M mess, Λ, tanβ If Ωh2 is only used as upper bound AMSB seems favored.

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Non-Universal Higgs Models 38 0903.1279 [hep-ph] 0907.4468 [hep-ph] “flat prior”“log prior” NUHM II M 0, M 1/2, A 0, tanβ, M Hu 2, M Hd 2 NUHM I M 0, M 1/2, A 0, tanβ, M H 2 [M Hu 2 = M Hd 2] Also for NUHM I the frequentist approach clearly favors low mass SUSY! MasterCode

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Closer to the Experiment “Soft Scale Models”

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 40 A Bottom-up Approach So far we have been far up at the GUT scale but for the first interpretation of the hopefully soon forthcoming LHC discoveries it will be beneficial to also consider “soft scale” models with parameters much closer to the experimental measurements/sensitivities (e.g. masses).

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 41 “Soft SUSY breaking” MSSM L

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 42 Gaugino’s and their masses M 3, M 2, M 1 “Soft SUSY breaking” MSSM L

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 43 Squarks and sleptons, and their masses “Soft SUSY breaking” MSSM L

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 44 Tri-linear couplings A “Soft SUSY breaking” MSSM L

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 45 Higgs sector: 2 complex doublets (1 for u-type, 1 for d-type) “Soft SUSY breaking” MSSM L

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 How Much Parameters are Reasonable? 46 pMSSM: 20 NP parameter Wow! 0903.1279 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 “Fitting the Soft Scale” 47 Bayesian fit In general very strong prior dependence – not surprising with 20+ parameters and only indirect constraints 0903.1279 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 48 Frequentist fit to 18+ parameters but now assuming LHC input from 300/fb of data. MSSM18 LHC 300/fb “Fitting the Soft Scale” 0907.2589 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 49 Frequentist fit to 18+ parameters but now assuming LHC input from 300/fb of data. MSSM18 LHC 300/fb “Fitting the Soft Scale” 0907.2589 [hep-ph] Fitting “soft scale” parameters that are much closer to the experimental measurements is an interesting approach but at least initially we need to reduce the set of parameters. Question: Can we define a meaningful set Of 4 to 5 NP “soft scale” parameters?

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Global Fits and Discoveries A few Projections

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 LHC Data (Discoveries) will help a lot 51 If we are really luck we might see these spectacular signatures already very early at the LHC! M(l + l - ) GeV 0907.0594 [hep-ph] Including a ”edge discovery” 0808.4128 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 More Detailed Studies 52 Use MCMC for likelihood maps Note SPS1a is close to the minima found by global fits (at lease MasterCode and Fittino) Test running! SPS1a

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Connection to Astro(particle)physics

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Direct Dark Matter Searches & LHC 54 Sensitivity Plot: WIMP(LSP) Mass vs. p SI p SI : spin-independent dark matter WIMP elastic scattering cross section on a free proton. A convenient way to illustrate direct and indirect WIMP searches. 0907.4468 [hep-ph] 0809.3792 [hep-ph]

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Conclusion Global NP Fits: Still in a tool and methodology development phase – getting ready for the LHC Bayesian vs. Frequentist: Two competing schools? Weakly constraint NP parameter space leads to strong prior dependences of the bayesian results. The frequentist fits yield consistent results favoring light mass SUSY. Fair question – implies the prior dependence of the bayesian fits that the frequentist results are not conclusive too? I don’t think so! In any case the LHC will takes us to “statistic nirvana” (Bob Cousin) “Soft Scale” Fits: Botton-up approach is a very interesting idea. Certainly closer to the experimental measurements! How many parameters can we use and which ones? Can simplified (OSET) models be a guidance?

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Conclusion Global NP Fits @ LHC: Like in the past (e.g. EW fit, CKM fit), global fits will be an important tool for the interpretation of (LHC) discoveries – hence crucial for establishing the true underlying theory of NP. SUSY is a show-case and we eventually will also have to consider other NP models – BUT will we have a consistent set of calculations for the various collider and non-collider observable in these NP models? I would like to thank B. Allanach, R.Trotta, A. De Roeck, F. Ronga, the Fittion, MasterCode, Superbayes groups (and many others) for input and very useful discussions!

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 MasterCode:O. Buchmueller, R. Cavanaugh, A. De Roeck, J.R. Ellis, H. Flacher, S. Heinemeyer, G. Isidori, K.A. Olive, F.J. Ronga, G. Weiglein Fittino: P. Bechtle, K. Desch, M. Uhlenbrock, P. Wienemann Sfitter: Remi Lafaye, Michael Rauch, Tilman Plehn, Dirk Zerwas S.S. AbdusSalam, B.C. Allanach, M.J. Dolan, F. Feroz, M.P. Hobson Gfitter: H. Flächer, M. Goebel, J. Haller, A. Höcker, K. Mönig, J. Stelzer Superbayes: L. Roszkowski, R. Ruiz de Austri, R. Trotta 57

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Bayesian vs. Frequentist – no math. 58 Bayesian approach. This perspective on probabilities, says that a probability is a measure of a person’s degree of belief in an event, given the information available. Thus, probabilities refer to a state of knowledge held by an individual, rather than to the properties of a sequence of events. The use of subjective probability in calculations of the expected value of actions is called subjective expected utility. Frequentist approach. They understand probability as a long-run frequency of a ‘repeatable’ event and developed a notion of confidence intervals. Probability would be a measurable frequency of events determined from repeated experiments. Reichenbach, Giere or Mayo have defended that approach from a philosophical point of view, referred to by Mayo (1997) as the ‘error statistical view” (as opposed to the Bayesian or “evidential-relation view”).

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Posterior & Profile Likelihood 59 Slide from R. Trotta

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Constraints 60

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Posterior vs. Profile Likelihood 61 PosteriorProfile Likelihood “flat prior” “log prior” 0809.3792 [hep-ph] Profile Likelihood (PL) should not depend on prior assumptions (in contrast to the Posterior pdf) but when translating the prior dependent MCMC sampling into PLs the used sampling statistic is often not sufficient – thus resulting in a also “prior dependent” PL result – this should vanish with a complete sampling

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Naturalness Prior 62 Usually Higgs potential parameter B and μ are treated for Mz and tanβ using: Thus leading to the following “flat” prior assumption” Not using the EWK symmetry breaking conditions enables uniform prior assumptions in the more fundamental parameters B and μ: “Naturalness prior” See e.g. 075.0487 [hep-ph]

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Higgs Sector 63

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Higgs Sector 64

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Joint HEP-APP IOP meeting on SUSY - March 24th 2010 Higgs Sector 65

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