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DM in the Constrained MSSM - A Bayesian approach Leszek Roszkowski CERN and Astro Particle Theory and Cosmology Group, Sheffield, England with Roberto Ruiz de Austri (Autonoma Madrid), Joe Silk and Roberto Trotta (Oxford) hep-ph/0602028 JHEP06, hep-ph/0611173 JHEP07, arxiv:0705.2012 and arxiv:0707.0622 SuperBayes package, superbayes.org L. Roszkowski, COSMO-07, 22/08/2007 p.1

Outline the Constrained MSSM (CMSSM) limitations of fixed-grid scans Bayesian Analysis of the CMSSM fits of observables mean quality of fit and the CMSSM direct detection of dark matter indirect detection of dark matter summary L. Roszkowski, COSMO-07, 22/08/2007 p.2

Constrained MSSM...aka msugra L. Roszkowski, COSMO-07, 22/08/2007 p.3

Constrained MSSM...aka msugra At M GUT 2 10 16 GeV: gauginos M 1 = M 2 = m eg = m 1/2 (c.f. MSSM) scalars m 2 eq i = me 2 li = m 2 H b = m 2 H t = m 2 0 3 linear soft terms A b = A t = A 0 L. Roszkowski, COSMO-07, 22/08/2007 p.3

Constrained MSSM...aka msugra At M GUT 2 10 16 GeV: gauginos M 1 = M 2 = m eg = m 1/2 (c.f. MSSM) scalars m 2 eq i = me 2 li = m 2 H b = m 2 H t = m 2 0 3 linear soft terms A b = A t = A 0 radiative EWSB µ 2 = m 2 H b +Σ (1) b m 2 H t +Σ (1) t tan 2 β 1 tan 2 β m2 Z 2 five independent parameters: tan β, m 1/2, m 0, A 0, sgn(µ) mass spectra at m Z : run RGEs, 2 loop for g.c. and Y.c, 1-loop for masses some important quantities (µ, m A,...) very sensitive to procedure of computing EWSB & minimizing V H we use SoftSusy and FeynHiggs L. Roszkowski, COSMO-07, 22/08/2007 p.3

CMSSM: allowed regions usual fixed-grid scans L. Roszkowski, COSMO-07, 22/08/2007 p.4

CMSSM: allowed regions tan β < 45 usual fixed-grid scans L. Roszkowski, COSMO-07, 22/08/2007 p.4

CMSSM: allowed regions usual fixed-grid scans tan β < 45 tan β > 45 L. Roszkowski, COSMO-07, 22/08/2007 p.4

CMSSM: allowed regions usual fixed-grid scans tan β < 45 tan β > 45 fixed-grid scans, assuming rigid 1σ or 2σ experimental ranges green: consistent with WMAP-3yr (at 2σ) all the rest excluded by LEP, BR( B X s γ), Ω χ h 2, EWSB, charged LSP,... L. Roszkowski, COSMO-07, 22/08/2007 p.4

Instead, allowed is this: L. Roszkowski, COSMO-07, 22/08/2007 p.5

Instead, allowed is this: Bayesian pdf maps 4 3.5 3 Ruiz, Trotta & Roszkowski (2006) m 0 2.5 2 1.5 1 0.5 0.5 1 1.5 2 m 1/2 L. Roszkowski, COSMO-07, 22/08/2007 p.5

Instead, allowed is this: Bayesian pdf maps 4 Ruiz, Trotta & Roszkowski (2006) fixed-grid scans 3.5 3 m 0 2.5 2 1.5 1 0.5 0.5 1 1.5 2 m 1/2 L. Roszkowski, COSMO-07, 22/08/2007 p.5

Instead, allowed is this: Bayesian pdf maps 4 Ruiz, Trotta & Roszkowski (2006) fixed-grid scans 3.5 3 m 0 2.5 2 1.5 1 0.5 0.5 1 1.5 2 m 1/2 Note: In both an outdated SM value of BR( B X s γ) used. See below. L. Roszkowski, COSMO-07, 22/08/2007 p.5

Bayesian Analysis of the CMSSM Apply to the CMSSM: L. Roszkowski, COSMO-07, 22/08/2007 p.6

Bayesian Analysis of the CMSSM Apply to the CMSSM: m = (θ, ψ): model s all relevant parameters L. Roszkowski, COSMO-07, 22/08/2007 p.6

Bayesian Analysis of the CMSSM Apply to the CMSSM: m = (θ, ψ): model s all relevant parameters θ: CMSSM parameters: m 1/2, m 0, A 0, tan β ψ: relevant SM parameters nuisance parameters ξ = (ξ 1, ξ 2,..., ξ m ): set of derived variables (observables): ξ(m) d: data Bayes theorem: posterior pdf p(θ, ψ d) = p(d ξ)π(θ,ψ) p(d) p(d ξ): likelihood π(θ, ψ): prior pdf p(d): evidence (normalization factor) posterior = likelihood prior normalization factor L. Roszkowski, COSMO-07, 22/08/2007 p.6

Bayesian Analysis of the CMSSM θ = (m 0, m 1/2, A 0, tan β): CMSSM parameters ψ = (M t, m b (m b ) MS, α em (M Z ) MS, α MS s ): SM (nuisance) parameters priors assume flat distributions and ranges as: flat priors: CMSSM parameters 50 GeV < m 0 < 4 TeV 50 GeV < m 1/2 < 4 TeV A 0 < 7 TeV 2 < tan β < 62 flat priors: SM (nuisance) parameters 160 GeV < M t < 190 GeV 4 GeV < m b (m b ) MS < 5 GeV 0.10 < α MS s < 0.13 127.5 < 1/α em (M Z ) MS < 128.5 vary all 8 (CMSSM+SM) parameters simultaneously, scan with MCMC include all relevant theoretical and experimental errors L. Roszkowski, COSMO-07, 22/08/2007 p.7

Experimental Measurements (assume Gaussian distributions) L. Roszkowski, COSMO-07, 22/08/2007 p.8

Experimental Measurements SM (nuisance) parameter Mean Error µ σ (expt) M t 171.4 GeV 2.1 GeV m b (m b ) MS 4.20 GeV 0.07 GeV α MS s 0.1176 0.002 1/α em (M Z ) MS 127.918 0.018 (assume Gaussian distributions) L. Roszkowski, COSMO-07, 22/08/2007 p.8

Experimental Measurements (assume Gaussian distributions) SM (nuisance) parameter Mean Error µ σ (expt) M t 171.4 GeV 2.1 GeV m b (m b ) MS 4.20 GeV 0.07 GeV α MS s 0.1176 0.002 1/α em (M Z ) MS 127.918 0.018 new M W = 80.413 ± 0.048 GeV (Jan 07, not yet included) new M t = 170.9 ± 1.8 GeV (Mar 07, not yet included) BR( B X s γ) 10 4 : new SM: 3.15 ± 0.23 (Misiak & Steinhauser, Sept 06) used here Derived observable Mean Errors µ σ (expt) τ (th) M W 80.392 GeV 29 MeV 15 MeV sin 2 θ eff 0.23153 16 10 5 15 10 5 δa SUSY µ 10 10 28 8.1 1 BR( B X s γ) 10 4 3.55 0.26 0.21 M Bs 17.33 0.12 4.8 Ω χ h 2 0.119 0.009 0.1 Ω χ h 2 take as precisely known: M Z = 91.1876(21) GeV, G F = 1.16637(1) 10 5 GeV 2 L. Roszkowski, COSMO-07, 22/08/2007 p.8

Experimental Limits Derived observable upper/lower Constraints limit ξ lim τ (theor.) BR(B s µ + µ ) UL 1.5 10 7 14% m h LL 114.4 GeV (91.0 GeV) 3 GeV ζ 2 h g2 ZZh /g2 ZZH SM UL f(m h ) 3% m χ LL 50 GeV 5% m χ ± 1 LL 103.5 GeV (92.4 GeV) 5% mẽr LL 100 GeV (73 GeV) 5% m µr LL 95 GeV (73 GeV) 5% m τ1 LL 87 GeV (73 GeV) 5% m ν LL 94 GeV (43 GeV) 5% m t 1 LL 95 GeV (65 GeV) 5% m b1 LL 95 GeV (59 GeV) 5% m q LL 318 GeV 5% m g LL 233 GeV 5% (σ SI p UL WIMP mass dependent 100%) Note: DM direct detection σ SI p not applied due to astroph l uncertainties (eg, local DM density) L. Roszkowski, COSMO-07, 22/08/2007 p.9

The Likelihood: 1-dim case Take a single observable ξ(m) that has been measured (e.g., M W ) L. Roszkowski, COSMO-07, 22/08/2007 p.10

The Likelihood: 1-dim case Take a single observable ξ(m) that has been measured c central value, σ standard exptal error (e.g., M W ) L. Roszkowski, COSMO-07, 22/08/2007 p.10

The Likelihood: 1-dim case Take a single observable ξ(m) that has been measured c central value, σ standard exptal error (e.g., M W ) define χ 2 = [ξ(m) c]2 σ 2 L. Roszkowski, COSMO-07, 22/08/2007 p.10

The Likelihood: 1-dim case Take a single observable ξ(m) that has been measured c central value, σ standard exptal error (e.g., M W ) define χ 2 = [ξ(m) c]2 σ 2 assuming Gaussian distribution (d (c, σ)): L = p(σ, c ξ(m)) = 1 2πσ exp [ χ2 2 when include theoretical error estimate τ (assumed Gaussian): σ s = σ 2 + τ 2 TH error smears out the EXPTAL range ] L. Roszkowski, COSMO-07, 22/08/2007 p.10

Probability maps of the CMSSM L. Roszkowski, COSMO-07, 22/08/2007 p.11

Probability maps of the CMSSM arxiv:0705.2012 4 Roszkowski, Ruiz & Trotta (2007) 3.5 3 MCMC scan Bayesian analysis m 0 2.5 2 1.5 relative probability density fn flat priors 68% total prob. inner contours 1 95% total prob. outer contours 0.5 m 1/2 CMSSM µ>0 0.5 1 1.5 2 2-dim pdf p(m 0, m 1/2 d) favored: m 0 m 1/2 (FP region) Relative probability density 0 0.2 0.4 0.6 0.8 1 L. Roszkowski, COSMO-07, 22/08/2007 p.11

Strategies for WIMP Detection L. Roszkowski, COSMO-07, 22/08/2007 p.12

Strategies for WIMP Detection direct detection (DD): measure WIMPs scattering off a target go underground to beat cosmic ray bgnd L. Roszkowski, COSMO-07, 22/08/2007 p.12

Strategies for WIMP Detection direct detection (DD): measure WIMPs scattering off a target indirect detection (ID): go underground to beat cosmic ray bgnd L. Roszkowski, COSMO-07, 22/08/2007 p.12

Strategies for WIMP Detection direct detection (DD): measure WIMPs scattering off a target indirect detection (ID): HE neutrinos from the Sun (or Earth) go underground to beat cosmic ray bgnd WIMPs get trapped in Sun s core, start pair annihilating, only ν s escape antimatter (e +, p, D) from WIMP pair-annihilation in the MW halo from within a few kpc gamma rays from WIMP pair-annihilation in the Galactic center depending on DM distribution in the GC L. Roszkowski, COSMO-07, 22/08/2007 p.12

Dark matter detection: σ SI p L. Roszkowski, COSMO-07, 22/08/2007 p.13

Dark matter detection: σ SI p MCMC+Bayesian analysis (pb)] Log[σ p SI 4 5 6 7 8 9 Roszkowski, Ruiz & Trotta (2007) CMSSM, µ > 0 ZEPLIN I EDELWEISS I CDMS II XENON 10 10 11 0.2 0.4 0.6 0.8 1 m χ L. Roszkowski, COSMO-07, 22/08/2007 p.13

Dark matter detection: σ SI p MCMC+Bayesian analysis compare: fixed grid scan (pb)] Log[σ p SI 4 5 6 7 8 9 Roszkowski, Ruiz & Trotta (2007) CMSSM, µ > 0 ZEPLIN I EDELWEISS I CDMS II XENON 10 10 11 0.2 0.4 0.6 0.8 1 m χ L. Roszkowski, COSMO-07, 22/08/2007 p.13

Prospects for direct detection: σ SI p (pb)] 4 5 6 7 Roszkowski, Ruiz & Trotta (2007) CMSSM, µ > 0 ZEPLIN I EDELWEISS I CDMS II XENON 10 Bayesian analysis, flat priors (MCMC) Log[σ p SI 8 9 10 11 0.2 0.4 0.6 0.8 1 m χ internal (external): 68% (95%) region L. Roszkowski, COSMO-07, 22/08/2007 p.14

Prospects for direct detection: σ SI p (pb)] Log[σ p SI 4 5 6 7 8 9 10 11 Roszkowski, Ruiz & Trotta (2007) CMSSM, µ > 0 ZEPLIN I EDELWEISS I CDMS II m χ XENON 10 0.2 0.4 0.6 0.8 1 Bayesian analysis, flat priors XENON-10 (June 07): new limit σp SI < 10 7 pb: explore the FP region (large m 0 m 1/2 ), (MCMC) also CDMS II (?) outside of the LHC reach ultimately: 1 tonne detectors: σp SI < 10 10 pb will cover all 68% region internal (external): 68% (95%) region L. Roszkowski, COSMO-07, 22/08/2007 p.14

CDM Halo Models...not a settled matter L. Roszkowski, COSMO-07, 22/08/2007 p.15

CDM Halo Models fitting DM halo with a semi-heuristic formula: ( r ρ DM (r) = ρ c / a ) γ [ 1 + ( ) r α ] (β γ)/α a...not a settled matter α, β, γ - adjustable parameters ρ c = ρ 0 ` r0a γ h1 + R0 a α i (β γ)/α, ρ0 0.3 GeV/ cm 3 - DM density at r 0 a - scale radius - from num. sim s or to match observations adiabatic compression due to baryon concentration in the GC: likely effect: central cusp becames steeper: model model-c some most popular models: halo model a ( kpc) r 0 ( kpc) (α, β, γ) small r: r γ large r: isothermal cored 3.5 8.5 (2, 2, 0) flat r 2 NFW 20.0 8.0 (1, 3, 1) r 1 r 3 NFW-c 20.0 8.0 (1.5, 3, 1.5) r 1.5 r 3 Moore 28.0 8.0 (1, 3, 1.5) r 1.5 r 3 Moore-c 28.0 8.0 (0.8, 2.7, 1.65) r 1.65 r 2.7 L. Roszkowski, COSMO-07, 22/08/2007 p.15

Gamma Rays from the Galactic Center L. Roszkowski, COSMO-07, 22/08/2007 p.16

Gamma Rays from the Galactic Center in the GC: ρ DM is likely to be larger WIMP pair annihilation χχ SMparticles ρ 2 χ will be enhanced WIMP annihilation final decay products: W W, ZZ, qq,... diffuse γ radiation (and/or γγ, γz) diffuse γ radiation: l.o.s - line of sight dφ γ de γ (E γ, ψ) = X i σ i v 8πm 2 χ dn i γ de γ Z l.o.s. dlρ 2 χ(r(l, ψ)) separate particle physics and astrophysics inputs; define: and J(ψ) = 1 8.5 kpc 1 0.3 GeV/cm 3 Z J( Ω) = (1/ Ω) «2 Z Ω l.o.s. J(ψ)dΩ dl ρ 2 χ (r(l, ψ)) Ω - finite angular resolution of a GR detector L. Roszkowski, COSMO-07, 22/08/2007 p.16

Gamma Rays from the Galactic Center diff l flux from the cone Ω dφ γ X (E γ, Ω) = Φ γ,0 de γ i σ i v 10 29 cm 3 sec 1 «dn i γ de γ «2 100 GeV ` J( Ω) Ω m χ Φ γ,0 = 0.94 10 13 cm 2 sec 1 sr 1 L. Roszkowski, COSMO-07, 22/08/2007 p.17

Gamma Rays from the Galactic Center diff l flux from the cone Ω dφ γ X (E γ, Ω) = Φ γ,0 de γ i σ i v 10 29 cm 3 sec 1 «dn i γ de γ «2 100 GeV ` J( Ω) Ω m χ total flux Φ γ ( Ω) = Z mχ E th Φ γ,0 = 0.94 10 13 cm 2 sec 1 sr 1 de γ dφ γ de γ (E γ, Ω) main bgnd: π 0 s from primary CR int s with interstellar H and He atoms (π 0 γγ) much experimental activity: EGRET, ACT (HESS, Veritas, Cangaroo, etc); GLAST (due to launch in Dec 07): expected major improvement in sensitivity L. Roszkowski, COSMO-07, 22/08/2007 p.17

GRs from the GC in the CMSSM use GLAST parameters Bayesian posterior probability maps L. Roszkowski, COSMO-07, 22/08/2007 p.18

GRs from the GC in the CMSSM use GLAST parameters Bayesian posterior probability maps total flux vs. m χ 4 Roszkowski, Ruiz, Silk & Trotta (2007) Moore adiab. comp. Φ γ from GC Log[Φ γ (cm 2 s 1 )] 6 8 10 NFW adiab. comp. NFW Moore CMSSM, µ > 0 GLAST reach (1yr) 12 14 iso. cored m χ Ω = 10 5 sr E > 1 GeV thr 0.2 0.4 0.6 0.8 1 Relative probability density 0 0.2 0.4 0.6 0.8 1 L. Roszkowski, COSMO-07, 22/08/2007 p.18

GRs from the GC in the CMSSM use GLAST parameters total flux vs. m χ Log[Φ γ (cm 2 s 1 )] 4 6 8 Roszkowski, Ruiz, Silk & Trotta (2007) Moore adiab. comp. NFW adiab. comp. NFW iso. cored Moore m χ Φ γ from GC CMSSM, µ > 0 GLAST reach (1yr) 10 12 Ω = 10 5 sr E > 1 GeV thr 14 0.2 0.4 0.6 0.8 1 Relative probability density 0 0.2 0.4 0.6 0.8 1 Bayesian posterior probability maps γ-ray energy spectrum: example (E 2 dφ/de) γ (GeV cm 2 s 1 ) 3 Roszkowski, Ruiz, Silk & Trotta (2007) 10 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 (E 2 dφ/de) γ from GC CMSSM, µ > 0 NFW adiab. comp. GLAST reach (1 yr) 159 GeV < m χ < 493 GeV (68% range) EGRET π 0 bgnd 10 1 10 0 10 1 10 2 E γ (GeV) m χ (GeV) 200 250 300 350 400 450 159 GeV < m χ < 493 GeV (68% range) L. Roszkowski, COSMO-07, 22/08/2007 p.18

GRs from the GC in the CMSSM use GLAST parameters Bayesian posterior probability maps total flux vs. m χ Log[Φ γ (cm 2 s 1 )] 4 6 8 10 12 14 Roszkowski, Ruiz, Silk & Trotta (2007) Moore adiab. comp. NFW adiab. comp. NFW iso. cored Moore m χ Φ γ from GC CMSSM, µ > 0 GLAST reach (1yr) Ω = 10 5 sr E thr > 1 GeV 0.2 0.4 0.6 0.8 1 Relative probability density 0 0.2 0.4 0.6 0.8 1 γ-ray energy spectrum: example (E 2 dφ/de) γ (GeV cm 2 s 1 ) 3 Roszkowski, Ruiz, Silk & Trotta (2007) 10 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 (E 2 dφ/de) γ from GC CMSSM, µ > 0 NFW adiab. comp. GLAST reach (1 yr) 159 GeV < m χ < 493 GeV (68% range) EGRET π 0 bgnd 10 1 10 0 10 1 10 2 E γ (GeV) m χ (GeV) 200 250 300 350 400 450 159 GeV < m χ < 493 GeV (68% range) GLAST prospects critically depend on how cuspy is the GC if more cuspy than NFW: all 95% CMSSM range will be explored (at 95% CL) even if signal detected: much uncertainty in determining m χ L. Roszkowski, COSMO-07, 22/08/2007 p.18

Positron flux and PAMELA L. Roszkowski, COSMO-07, 22/08/2007 p.19

Positron flux and PAMELA E e + from from DM annihilations propagate in interstellar magnetic field K(ɛ) = 2.1 10 28 ɛ 0.6 cm 2 sec 1 much less halo model dependence ɛ = E e +/1 GeV loose energy via inverse Compton scattering b(ɛ) = ɛ2 τ E 10 16 ɛ 2 sec 1 τ E = 10 16 sec 1 diffusion zone: infinite slab of height L = 4 kpc, free escape BC s NFW + adiab. compression Φ e+ /(Φ e+ +Φ e ) 10 1 10 2 10 3 10 4 10 5 Roszkowski, Ruiz, Silk & Trotta (2007) CMSSM, µ > 0 NFW adiab. comp. Moore adiab. comp. 159 GeV < m χ < 493 GeV (68% range) 10 1 10 0 10 1 10 2 E e+ (GeV) m χ (GeV) BF=1 bgnd CAPRICE 94 HEAT 94+95 HEAT 00 200 250 300 350 400 450 (scales linearly with boost factor) L. Roszkowski, COSMO-07, 22/08/2007 p.19

Positron flux and PAMELA E e + from from DM annihilations propagate in interstellar magnetic field K(ɛ) = 2.1 10 28 ɛ 0.6 cm 2 sec 1 much less halo model dependence ɛ = E e +/1 GeV loose energy via inverse Compton scattering b(ɛ) = ɛ2 τ E 10 16 ɛ 2 sec 1 τ E = 10 16 sec 1 diffusion zone: infinite slab of height L = 4 kpc, free escape BC s NFW + adiab. compression Φ e+ /(Φ e+ +Φ e ) 10 1 10 2 10 3 10 4 10 5 Roszkowski, Ruiz, Silk & Trotta (2007) CMSSM, µ > 0 NFW adiab. comp. Moore adiab. comp. 159 GeV < m χ < 493 GeV (68% range) 10 1 10 0 10 1 10 2 E e+ (GeV) m χ (GeV) BF=1 bgnd CAPRICE 94 HEAT 94+95 HEAT 00 200 250 300 350 400 450 159 GeV < m χ < 493 GeV (68% range) L. Roszkowski, COSMO-07, 22/08/2007 p.19

Positron flux and PAMELA E e + from from DM annihilations propagate in interstellar magnetic field K(ɛ) = 2.1 10 28 ɛ 0.6 cm 2 sec 1 much less halo model dependence ɛ = E e +/1 GeV loose energy via inverse Compton scattering b(ɛ) = ɛ2 τ E 10 16 ɛ 2 sec 1 τ E = 10 16 sec 1 diffusion zone: infinite slab of height L = 4 kpc, free escape BC s NFW + adiab. compression Φ e+ /(Φ e+ +Φ e ) 10 1 10 2 10 3 10 4 10 5 Roszkowski, Ruiz, Silk & Trotta (2007) CMSSM, µ > 0 NFW adiab. comp. Moore adiab. comp. 159 GeV < m χ < 493 GeV (68% range) 10 1 10 0 10 1 10 2 E e+ (GeV) m χ (GeV) BF=1 bgnd CAPRICE 94 HEAT 94+95 HEAT 00 200 250 300 350 400 450 prospects for PAMELA rather poor (...unless large boost factor) L. Roszkowski, COSMO-07, 22/08/2007 p.19

Summary L. Roszkowski, COSMO-07, 22/08/2007 p.20

Summary MCMC + Bayesian statistics: a powerful tool to properly analyze multi-dim. new physics models like SUSY L. Roszkowski, COSMO-07, 22/08/2007 p.20

Summary MCMC + Bayesian statistics: a powerful tool to properly analyze multi-dim. new physics models like SUSY new tool: SuperBayes package, superbayes.org L. Roszkowski, COSMO-07, 22/08/2007 p.20

Summary MCMC + Bayesian statistics: a powerful tool to properly analyze multi-dim. new physics models like SUSY new tool: SuperBayes package, superbayes.org easily adaptable to other models, frameworks,... CMSSM: direct detection of neutralino DM 2.8 10 10 pb < σ SI p < 3.9 10 8 pb (68%) can be probed at 95% CL with planned 1 tonne detectors µ > 0 with 4 fb 1 /expt: 3σ evidence over 95% CL m h range DM direct detection: expt now probing favored 68% CL region some already probed with XENON-10 etc. γ-rays from the GC: DM signal guaranteed at GLAST if halo cuspy enough (NFW profile - borderline case) L. Roszkowski, COSMO-07, 22/08/2007 p.20

Backup L. Roszkowski, COSMO-07, 22/08/2007 p.21

Fits of Observables Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) good fits: M t, α s, Ω χ h 2, BR( B X s γ) (for µ < 0!) not so good: M W, sin 2 θ eff, BR( B X s γ) (for µ > 0!) bad: a SUSY µ (for both signs of µ!) L. Roszkowski, COSMO-07, 22/08/2007 p.22

The Likelihood incorporates information about the observational data the mapping ξ(m) comes with uncertainties experimental uncertainty σ i theoretical uncertainty τ i introduce exact mapping ˆξ(θ, χ) the likelihood: where p(ˆξ ξ) = p(d ξ) = R p(d ˆξ)p(ˆξ ξ)d m ˆξ 1 exp 1 (2π) m/2 C 1/2 2 (ξ ˆξ)C 1 (ξ ˆξ) T p(d ˆξ) = total error for each observable: s i = C: m m covariance matrix if uncorrelated: C = diag `τ1 2,..., τ m 2 1 exp 1 (2π) m/2 D 1/2 2 (d ˆξ)D 1 (d ˆξ) T q σ 2 i + τ 2 i if uncorrelated: D = diag `σ1 2,..., σ2 m L. Roszkowski, COSMO-07, 22/08/2007 p.23

Probability maps of the CMSSM µ > 0: 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 3.5 2 3 m 0 2.5 2 1.5 m 1/2 1.5 1 1 0.5 CMSSM µ>0 0.5 1 1.5 2 m 1/2 0.5 CMSSM µ>0 4 2 0 2 4 6 A 0 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 3.5 2 3 m 0 2.5 2 1.5 m 1/2 1.5 1 1 0.5 CMSSM µ>0 0.5 CMSSM µ>0 10 20 30 40 50 60 10 20 30 40 50 60 tanβ tanβ 4 3.5 Roszkowski, Ruiz & Trotta (2007) 6 Roszkowski, Ruiz & Trotta (2007) 3 4 m 0 2.5 2 1.5 A 0 2 0 1 2 0.5 CMSSM µ>0 4 2 0 2 4 6 A 0 4 tanβ CMSSM µ>0 10 20 30 40 50 60 L. Roszkowski, COSMO-07, 22/08/2007 p.24

Probability maps of the CMSSM µ > 0: µ < 0: 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 3.5 2 3.5 2 3 3 m 0 2.5 2 1.5 m 1/2 1.5 1 m 0 2.5 2 1.5 m 1/2 1.5 1 1 0.5 CMSSM µ>0 0.5 CMSSM µ>0 1 0.5 CMSSM µ<0 0.5 CMSSM µ<0 0.5 1 1.5 2 4 2 0 2 4 6 0.5 1 1.5 2 4 2 0 2 4 6 m 1/2 A 0 m 1/2 A 0 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 4 Roszkowski, Ruiz & Trotta (2007) Roszkowski, Ruiz & Trotta (2007) 3.5 2 3.5 2 3 3 m 0 2.5 2 1.5 m 1/2 1.5 1 m 0 2.5 2 1.5 m 1/2 1.5 1 1 0.5 CMSSM µ>0 0.5 CMSSM µ>0 1 0.5 CMSSM µ<0 0.5 CMSSM µ<0 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 tanβ tanβ tanβ tanβ 4 3.5 Roszkowski, Ruiz & Trotta (2007) 6 Roszkowski, Ruiz & Trotta (2007) 4 3.5 Roszkowski, Ruiz & Trotta (2007) 6 Roszkowski, Ruiz & Trotta (2007) 3 4 3 4 m 0 2.5 2 1.5 1 0.5 CMSSM µ>0 A 0 2 0 2 4 CMSSM µ>0 m 0 2.5 2 1.5 1 0.5 CMSSM µ<0 A 0 2 0 2 4 CMSSM µ<0 4 2 0 2 4 6 10 20 30 40 50 60 4 2 0 2 4 6 10 20 30 40 50 60 A 0 tanβ A 0 tanβ L. Roszkowski, COSMO-07, 22/08/2007 p.24

Posterior pdf vs. mean qof: µ < 0 L. Roszkowski, COSMO-07, 22/08/2007 p.25

Posterior pdf vs. mean qof: µ < 0 posterior pdf 4 Roszkowski, Ruiz & Trotta (2007) 3.5 3 m 0 2.5 2 1.5 1 0.5 m 1/2 CMSSM µ<0 0.5 1 1.5 2 Relative probability density 0 0.2 0.4 0.6 0.8 1 L. Roszkowski, COSMO-07, 22/08/2007 p.25

Posterior pdf vs. mean qof: µ < 0 posterior pdf 4 3.5 3 Roszkowski, Ruiz & Trotta (2007) 4 3.5 3 Roszkowski, Ruiz & Trotta (2007) mean qof m 0 2.5 2 1.5 m 0 2.5 2 1.5 1 1 0.5 CMSSM µ<0 0.5 CMSSM µ<0 0.5 1 1.5 2 0.5 1 1.5 2 m 1/2 m 1/2 Relative probability density 0 0.2 0.4 0.6 0.8 1 Mean quality of fit 0 0.2 0.4 0.6 0.8 1 µ < 0 generally poorer fit to the data L. Roszkowski, COSMO-07, 22/08/2007 p.25