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Constraining CMSSM dark matter with direct detection results Chris Savage Oskar Klein Centre for Cosmoparticle Physics Stockholm University with Yashar Akrami, Pat Scott, Jan Conrad & Joakim Edsjö JCAP 1104:012, 2011 [arXiv:1011.4318] JCAP 1107:002,2011 [arXiv:1011.4297]

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Overview 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Direct detection signal N, E k=1..N, S m, , ,... WIMP parameters m , SI,p, SD,p, SD,n Direct detection signal N, E k=1..N, S m, , ,... CMSSM (e.g.) parameters m 0, m 1/2, A 0, tanβ, sign(μ) WIMP parameters m , SI,p, SD,p, SD,n PhenomenologyParticle (SUSY) Theory Messy parameter space: statistical scanning required Well behaved parameter space: analytical methods for constraints? Pheno space not fully mapped out by CMSSM

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Overview 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Direct detection signal N, E k=1..N, S m, , ,... WIMP parameters m , SI,p, SD,p, SD,n Direct detection signal N, E k=1..N, S m, , ,... CMSSM (e.g.) parameters m 0, m 1/2, A 0, tanβ, sign(μ) WIMP parameters m , SI,p, SD,p, SD,n PhenomenologyParticle (SUSY) Theory

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Overview 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Direct detection signal N, E k=1..N, S m, , ,... WIMP parameters m , SI,p, SD,p, SD,n Direct detection signal N, E k=1..N, S m, , ,... CMSSM (e.g.) parameters m 0, m 1/2, A 0, tanβ, sign(μ) WIMP parameters m , SI,p, SD,p, SD,n PhenomenologyParticle (SUSY) Theory Messy parameter space: statistical scanning required Well behaved parameter space: analytical methods for constraints? Pheno space not fully mapped out by CMSSM

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Overview 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Direct detection signal N, E k=1..N, S m, , ,... WIMP parameters m , SI,p, SD,p, SD,n Direct detection signal N, E k=1..N, S m, , ,... CMSSM (e.g.) parameters m 0, m 1/2, A 0, tanβ, sign(μ) WIMP parameters m , SI,p, SD,p, SD,n PhenomenologyParticle (SUSY) Theory This talk Experimental groups Ji-Haeng Huh talk

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Overview How will future direct detection results constrain dark matter from supersymmetric theories? Realistic reconstruction of dark matter properties using CMSSM as case study Outline Basics: CMSSM, direct detection Analysis: likelihoods, statistics and scanning Phenomenological parameter constraints Individual/combined experimental results Statistical/scanning issues Halo model, hadronic uncertainties CMSSM parameter constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Basics and Analysis Procedure

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Basics CMSSM (Constrained Minimal Supersymmetric Standard Model) Simplest SUSY model: four parameters + one sign Complicated parameter space: disconnected regions, sharp peaks,… Results/issues representative of generic SUSY models (e.g. MSSM-7, BMSSM, NMSSM, etc.) Direct detection: future ton-scale experiments XENON1T (Xe, neutron odd) [LUX, PANDA-X] CDMS1T (Ge, neutron odd) [EDELWEISS, CRESST?] COUPP1T (CF 3 I, proton odd) Not included: CoGeNT, CDEX, DAMA, KIMS -like (higher backgrounds) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Detector WIMP Scatter

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Analysis Realistic analysis Typical thresholds and efficiencies Finite energy resolution Backgrounds at target levels (~ 2 events), known spectrum Uncertainties in halo model (density, velocity distribution) Hadronic uncertainties: WIMP-quark → WIMP-nucleon couplings Likelihoods Direct detection Nuisance parameters Halo model Nucleon structure SM parameters …also physicality constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection See paper for technical details COUPP: no spectrum Number of events (Poisson)Event energies (spectrum)

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Likelihoods Direct detection Θ: CMSSM, nuisance parametersP(N, μ): Poisson probability μ: expected number of eventsf(E) dR/dE (energy spectrum) N: observed number of events E i : observed event energies Nuisance parameters 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection CDMS XENON COUPP: no spectrum (Poisson only) Nucleon structureHalo model + SM parameters (not shown) Also: physicality constraints

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Analysis Procedure Select CMSSM models that give particular m and SI,p : benchmark models Generate random experimental results Reconstruct CMSSM model by scanning over CMSSM parameter space DarkSUSY + SuperBayeS (MultiNest) Statistics Scan: Bayesian (SuperBayes) Results: Frequentist or Bayesian Profile likelihood (frequentist) Marginalized PDF (Bayesian) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection www.darksusy.org www.superbayes.org Most experimental analyses

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Benchmark Models 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection BM1: low m , high SI,p O(100-400) signal events BM2: low m , low SI,p O(1-3) signal events BM3: moderate m and SI,p O(20-30) signal events BM4: high m , high SI,p O(20-30) signal events + 2 background events (on average) Benchmarks still below most recent XENON constraints

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Benchmark Models 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Results (Constraints)

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BM1: low m , high SI,p Spin-independent/dependent cross-sections vs. mass XENON: ~ 200 signal events (~ 7 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ true value max likelihood posterior mean

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BM1: low m , high SI,p Spin-independent/dependent cross-sections vs. mass CDMS: ~ 140 signal events (~ 2 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM1: low m , high SI,p Spin-independent/dependent cross-sections vs. mass COUPP: ~ 390 signal events (~ 120 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM1: low m , high SI,p Spin-dependent couplings: neutron vs. proton a n ≈ -a p : CMSSM prediction (not experimental constraint) O(5) [CDMS/XENON] vs. O(100) [COUPP] SD events 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM1: low m , high SI,p Spin-independent/dependent cross-sections vs. mass ~ 140 / 200 / 390 signal events (~ 2 / 7 / 120 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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BM2: low m , low SI,p Spin-independent/dependent cross-sections vs. mass XENON: ~ 2.1 signal events (~ 0 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM2: low m , low SI,p Spin-independent/dependent cross-sections vs. mass CDMS: ~ 1.4 signal events (~ 0 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM2: low m , low SI,p Spin-independent/dependent cross-sections vs. mass COUPP: ~ 3.0 signal events (~ 0.1 SD events) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM2: low m , low SI,p Spin-independent/dependent cross-sections vs. mass ~ 1.4 / 2.1 / 3.0 signal events (~ 0 / 0 / 0.1 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM2: low m , low SI,p Spin-independent/dependent cross-sections vs. mass ~ 1.4 / 2.1 / 3.0 signal events (~ 0 / 0 / 0 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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BM3: moderate m and SI,p Spin-independent/dependent cross-sections vs. mass ~ 17 / 23 / 32 signal events (~ 0 / 0 / 0.6 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM3: moderate m and SI,p Spin-independent/dependent cross-sections vs. mass ~ 17 / 23 / 32 signal events (~ 0 / 0 / 0.6 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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BM4: high m , high SI,p Spin-independent/dependent cross-sections vs. mass ~ 19 / 25 / 36 signal events (~ 0 / 0 / 0.3 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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BM4: high m , high SI,p Spin-independent/dependent cross-sections vs. mass ~ 19 / 25 / 36 signal events (~ 0 / 0 / 0.3 SD) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Issues

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Issue: sampling/coverage Mass constraint from energy spectrum: degeneracy for heavy WIMPs 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Phenomenological parameter scan Pato et al., PRD 83, 083505 (2011) BM3 BM4

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Issue: sampling/coverage Scan points without DD likelihood BM4 in poorly sampled region BM3 in higher sampled region Degeneracy: BM3 & BM4 should give similar DD signals (N, E i ) BM4 scan: Good fit around BM3 Nothing to draw scan towards BM4 region Too few models to properly evaluate profile likelihood 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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Issue: sampling/coverage Real priors and/or effective priors affect scan region Scan may miss some regions of interest or cover them too coarsely Can lead to significant over/under-coverage of confidence regions (frequentist) or credible regions (Bayesian) Possibly improved by higher statistics …if higher statistics gives sharper likelihood contours (can overcome real/effective priors) Not for previous case 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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Issue: nuisance parameters Halo model Local density, velocity distribution Standard Halo Model (SHM): isothermal sphere 3 velocity parameters: v 0, v obs, v esc Structure? Annual modulation (DAMA, CoGeNT) Directional detection (DRIFT) Hadronic matrix elements Used in calculating SI & SD from -quark couplings 6 relevant matrix elements (only 3 are important) Affect CMSSM constraints, not pheno constraints (at least not directly) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Halo models + direct detection: see Strigari & Trotta (2009) and various works by A. Green See Ellis, Olive & CS, PRD 77, 065026 (2008)

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Local Halo: m - reconstruction Strigari & Trotta, JCAP 11, 019 (2009) Reconstructing mass and cross-section with/without including halo uncertainties (what if assumed local density is off by 2?) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Actual 0, 3, 7 astrophysical parameters in fit density assumed to be 0.5, 1, 2 of actual

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Halo model uncertainties With / without uncertainties in halo model (nuisance parameters) Local DM density most significant See e.g. Strigari & Trotta, JCAP 11, 019 (2009) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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Halo model uncertainties With / without uncertainties in halo model (nuisance parameters) Local DM density most significant See e.g. Strigari & Trotta, JCAP 11, 019 (2009) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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Hadronic uncertainties With / without hadronic uncertainties (nuisance parameters) No change: affects only CMSSM parameter constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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Hadronic uncertainties With / without hadronic uncertainties (nuisance parameters) No change: affects only CMSSM parameter constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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Hadronic uncertainties With / without hadronic uncertainties (nuisance parameters) Only directly affects CMSSM parameter constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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Hadronic uncertainties With / without hadronic uncertainties (nuisance parameters) Only directly affects CMSSM parameter constraints 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection CMSSM Constraints

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CMSSM constraints No direct detection likelihood (priors and nuisance only) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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CMSSM constraints (BM1) With direct detection likelihood Gaugino mass (m 1/2 ) best constrained (related to m ) Weaker constraints on m 0, A 0, tanβ 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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CMSSM constraints No direct detection likelihood (priors and nuisance only) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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CMSSM constraints (BM1) With direct detection likelihood Gaugino mass (m 1/2 ) best constrained (related to m ) Weaker constraints on m 0, A 0, tanβ 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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CMSSM constraints No direct detection likelihood (priors and nuisance only) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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CMSSM constraints (BM1) With direct detection likelihood Gaugino mass (m 1/2 ) best constrained (related to m ) tanβ poorly constrained (not shown) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Profile likelihood: ■ 1σ ■ 2σ

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CMSSM constraints No direct detection likelihood (priors and nuisance only) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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CMSSM constraints (BM1) With direct detection likelihood Gaugino mass (m 1/2 ) best constrained (related to m ) tanβ poorly constrained (not shown) 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Marginalized PDF: — 1σ / 2σ

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CMSSM constraints Can combine with other observational data: Indirect detection: cosmic-rays, neutrinos Accelerators Relic density, etc. 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection -rays (Fermi-LAT) Segue 1 analysis Scott et al. (2009) Neutrinos (IceCube) IC collab + Edsjö, Scott, CS, in prep. Accelerator (LHC: ATLAS) SU3 benchmark analysis Bridges et al. (2010) See Trotta et al., JHEP 0812:024 (2008)

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Summary Examined realistic reconstruction of dark matter properties in SUSY (e.g. CMSSM) theories using direct detection results Can reconstruct WIMP properties reasonably well in some cases, not so well in others Coverage, sampling issues: Accuracy affected by scanning technique Nuisance parameters Combine DD results with other observations to better constrain SUSY theory parameters 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection Backup Slides

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TO DO Update slides: Additional slides: 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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Blank 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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Blank 9/27/2011C Savage - DSU 2011 - CMSSM and Direct Detection

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