1 / 80

Bayesian Constraints on Supersymmetric Neutralino Dark Matter

Bayesian Constraints on Supersymmetric Neutralino Dark Matter Roberto Ruiz de Austri IFIC In collaboration with: R. Trotta, L. Roszkowski, M. Hobson, F. Feroz, J. Silk, C. P. de los Heros, A. Casas, M. E. Cabrera. Outline.

pbarber
Download Presentation

Bayesian Constraints on Supersymmetric Neutralino Dark Matter

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Bayesian Constraints on Supersymmetric Neutralino Dark Matter Roberto Ruiz de Austri IFIC In collaboration with: R. Trotta, L. Roszkowski, M. Hobson, F. Feroz, J. Silk, C. P. de los Heros, A. Casas, M. E. Cabrera

  2. Outline There are three kinds of lies: lies, damned lies, and statistics. (Mark Twain, quoting Benjamin Disraeli)‏ • Bayesian approach and SUSY searches • CMSSM forecast for the LHC

  3. The model & data • The general Minimal Supersymmetric Standard Model (MSSM): 105 free parameters! • Need some simplifying assumption: i.e. the Constrained MSSM (CMSSM) reduces the free parameters to just 4 continous variables plus a discrete one (sign(μ))‏ • Present-day data: collider measurements of rare processes, CDM abundance (WMAP), sparticle masses lower limits, EW precision measurements. Soon, LHC sparticle spectrum measurements • Astrophysical direct and indirect detection techniques might also be competitive: neutrino (IceCUBE), gamma-rays (Fermi), antimatter (PAMELA), direct detection (XENON, CDMS, Eureca, Zeplin)‏ • Goal: inference of the model parameters but it is difficult problem

  4. Why is this a difficult problem? • Inherently 8-dimensional: reducing the dimensionality over-simplifies the problem. Nuisance parameters (in particular mt) cannot be fixed! • Likelihood discontinuous and multi-modal due to physicality conditions • RGE connect input parameters to observables in highly non-linear fashion: only indirect (sometimes weak) constraints on the quantities of interest (-> prior volume effects are difficult to keep under control)‏ • Mild discrepancies between observables (in particular, g-2 and b→sγ) tend to pull constraints in different directions

  5. Impact of nuisance parameters

  6. Random scans • 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)‏

  7. The accessible “surface” Scan from the prior with no likelihood except physicality constraints

  8. Bayesian parameter inference

  9. The Bayesian approach • Bayesian approach led by two groups (early work by Baltz & Gondolo, 2004): • Ben Allanach (DAMPT) et al (Allanach & Lester, 2006 onwards, Cranmer, and others) • RdA, Roszkowski & Roberto Trotta (2006 onwards) SuperBayeS public code (available from: superbayes.org) + Feroz & Hobson (MultiNest), + Silk (indirect detection), + de los Heros (IceCube)‏, + Casas et al. (Naturalness) + Bertone et al. (pmssm) ‏

  10. Bayes’ theorem H: hypothesis d: data I: external information • Prior: what we know about H (given information I) before seeing the data • Likelihood: the probability of obtaining data d if hypothesis H is true • Posterior: our state of knowledge about H after we have seen data d • Evidence: normalization constant (independent of H), crucial for model comparison

  11. Continuous parameters Bayesian evidence: average of the likelihood over the prior For parameter inference it is sufficient to consider posterior ∝ likelihood x prior

  12. ... • Ignoring the prior and identifying • implicitly amounts to • But e. g.

  13. But • If data are good enough to select a small region of {θ} then the prior p(θ) becomes irrelevant

  14. Priors • There is a vast literature on priors: Jeffreys’, conjugate, non-informative, ignorance, reference, ... • In simple problems, “good” priors are dictated by symmetry properties • Flat: All values of θ equally probable • Logarithmic: All magnitudes of θ equally probable

  15. Key advantages • Efficiency: computational effort scales ~ N rather than k^N as in grid-scanning methods. Orders of magnitude improvement over previously used techniques. • Marginalisation: integration over hidden dimensions comes for free Suppose we have and are interested in • Inclusion of nuisance parameters: simply include them in the scan and marginalise over them. Notice: nuisance parameters in this context must be well constrained using independent data. • Derived quantities: probabilities distributions can be derived for any function of the input variables (crucial for DD/ID/LHC predictions).

  16. Analysis pipeline

  17. Posterior Samplers • MCMC:A Markov Chain is a list of samples θ1, θ2, θ3,... whose density reflects the (unnormalized) value of the posterior • Crucial property: a Markov Chain converges to a stationary distribution, i.e. one that does not change with time. In our case, the posterior • Different algorithms: MH, Gibbs... all need a proposal distribution => difficult to find a good one in complex problems • Nested: New technique for efficient evidence evaluation (and posterior samples) (Skilling 2004)‏ • MultiNest: Also an extremely efficient sampler for multi-modal likelihoods ! Feroz & Hobson (2007), RT et al (2008), Feroz et al (2008)‏

  18. The Multinest Algorithm • MultiNest: Also an extremely efficient sampler for multi-modal likelihoods! Feroz & Hobson (2007), RT et al (2008), Feroz et al (2008)‏

  19. Marginal Posterior vs Profile likelihood

  20. The SuperBayeS package (superbayes.org)‏ • Supersymmetry Parameters Extraction Routines for Bayesian Statistics • Implements the CMSSM, but can be easily extended to the general MSSM • Currently linked to SoftSusy 2.0.18, DarkSusy 4.1, MICROMEGAS 2.2, FeynHiggs 2.5.1, Hdecay 3.102. New release (v 1.5)‏ • Includes up-to-date constraints from all observables • Fully parallelized, MPI-ready, user-friendly interface a la cosmomc (thanks Sarah Bridle & Antony Lewis)‏, plotting routines • Bayesian MCMC, MULTI-MODAL NESTED SAMPLING or grid scan mode • MULTI-MODAL NESTED SAMPLING (Feroz & Hobson 2008), efficiency increased by a factor 200. A full 8D scan now takes 3 days on a single CPU (previously: 6 weeks on 10 CPUs)‏

  21. Global CMSSM constraints

  22. Variables of the scan From Robertos' talk

  23. Samples from priors only • No data in the likelihood, non-physical points discarged priors • => flat prior on log means

  24. Samples from priors only • Volume effect from the non-physical regions

  25. Priors distributions from observables • Priors are quite informative regardless the quantities being constrained !!!

  26. Data included Indirect observablesSM parameters

  27. Parameter inference (all data included)‏ Flat priors Log priors

  28. 2D posterior vs profile likelihood Posterior Profile likelihood

  29. The model Universality at High Scale supported for FCNC constraints

  30. Goal • Scan the model evaluating Forecast map for LHC

  31. Towards a more refineanalysis • Recall an usual assumption should be • In order to get a Natural Electroweak symmetry Breaking (with no fine-tunings)

  32. Bayesian and Naturalness

  33. ... • Instead solving in terms of and the other soft-terms and, treat as another exp. Data • Approximate the likelihood as

  34. ... • Use to marginalize (Barbieri Gudice measure of fine-tunning)‏ • Probability of cancellation between the various contributions to get

  35. At practical level • Besides, we have done a similar analysis for the fermion masses • And traded

  36. Putting all the pieces together

  37. Finally • For the prior we take the two basic possibilities: flat logarithmic

  38. brings SUSY to the LHC region • We may vary up to the results do not depend on the range choosen • This suggests that large soft-masses are disfavoured

  39. Data Included

  40. Adding g-2 using (e+ e- data) Preferred region clearly within the LHC reach

  41. Adding [and notg-2]

  42. Adding all Events with more or equal to 2 jets[Baer et al 0907.1922]

  43. Comparison with Likelihood based inference Buchmueller et al. (2009) Cabrera et al. (2009)‏

  44. ATLAS will solve the prior dependency • Projected constraints from ATLAS, (dilepton and lepton+jets edges, 1 fb-1 luminosity)‏

  45. Residual dependency on the statistics • Marginal posterior and profile likelihood will remain somewhat discrepant using ATLAS alone. Much better agreement from ATLAS+Planck CDM determination.

  46. ... • For the results are similar with an important difference: • Now SUSY produces contributions to in the wrong direction • So adding (using e+ e- data) does not help in this case to bring the preferred region to the LHC • And, of course, gets strongly disfavoured with respect to

  47. Astrophysical probes • Direct detection: underground detectors looking for nuclear recoils from WIMP scattering. It is fundamental to account for the uncertainty in the local WIMP distribution. • Indirect detection: detection of annihilation products from WIMP-WIMP annihilation. • Gamma ray(galactic centre, galactic halo, diffuse extragalactic sources, nearby dwarf galaxies). • Antimatter (positrons, anti-proton) from local clumps. • Neutrinosfrom the center of the Sun/Earth.

  48. Direct and indirect detection prospects

  49. Direct detection prospects

More Related