Institut Theoretische Teilchenphysik und Kosmologie Dark Matter direct detection and Bayesian statistics BASED ON: • CA, J. Hamann and Y. Wong, JCAP09 (2011) 022 arXiv:1105.5121 [hep-ph] • CA, JPCS of TAUP 2011, arXiv:1110.0313 [hep-ph] • CA, J. Hamann, R. Trotta and Y. Wong arXiv:1111. 3238 [hep-ph], to appear in JCAP Chiara Arina Grenoble, February 16, 2012
Standard Cosmological Model Komatsu et al. ’10, Larson et al. ’10, Bennett et al. ’10 Gravitational hint of Dark Matter (DM) CMB (WMAP) + BAO (clusters) + H0 (SNIa) at all scales + Rotational curves of galaxies and clusters 2 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Standard Cosmological Model Komatsu et al. ’10, Larson et al. ’10, Bennett et al. ’10 Gravitational hint of Dark Matter (DM) CMB (WMAP) + BAO (clusters) + H0 (SNIa) at all scales + Rotational curves of galaxies and clusters 2 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
What do we know about Dark Matter? - Neutral (and massive) - Stable at least on cosmological scale - Thermally (or non-thermally) produced: = 0.227 +- 0.014 - Cluster to account for large scale structures and form halos X X X X Non baryonic Dark Matter (DM) X X X X X X X X X X X X New physics beyond the Standard Model (SM) 3 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMPs: Weakly Interacting Massive Particles Lee & Weinberg ’77, Gunn et al. ’78, Steigman et al. ’78, Kolb & Turner ’81, Ellis et al. ’84, χ + χ ↔ SM + SM Scherrer & Turner ’85, Griest & Seckel ’91 Freeze-out (chemical decoupling): Γ = n < σ A v > ∼ H � 10 − 26 cm 3 s − 1 � Ω DM h 2 ∼ 0 . 3 < σ A v > Example: < σ A v > ∼ g 2 0 . 01 2 (100 GeV) 2 ∼ 8 × 10 − 25 cm 3 s − 1 ∼ m 2 χ GeV TeV scale DM candidates with weak scale interactions WIMPs arise in SUSY theories, Hidden sectors, Kaluza-Klein models (other DM candidates are axions, sterile neutrinos, ...) 4 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
GeV-TeV DM detection 5 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
GeV-TeV DM detection 5 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Outline • Bayesian (brief remind of basic concepts) analysis of direct detection data motivated by (a) tension between experiments (b) experimental systematics (c) astrophysical uncertainties • Bayesian Evidence • Results for model comparison CoGeNT modulation • Conclusions 6 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMP Direct Detection (DD) Goodman & Witten ’85 d 3 v ′ f(v ′ (t)) dR d σ � ρ ⊙ dE = dE v ′ m DM v ′ >v ′ min 7 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMP Direct Detection (DD) Goodman & Witten ’85 d 3 v ′ f(v ′ (t)) dR d σ � ρ ⊙ dE = dE v ′ m DM v ′ >v ′ min � 2 � f p Z + ( A − Z ) f n dE = M N σ SI d σ F 2 ( E ) n 2 µ 2 f 2 n n • For equal coupling to n and p, A^2 dependence: light nuclei more sensitive to light WIMPs and viceversa • spin-independent interaction (SI) 7 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMP Direct Detection (DD) Goodman & Witten ’85 d 3 v ′ f(v ′ (t)) dR d σ � ρ ⊙ dE = dE v ′ m DM v ′ >v ′ min � 2 � f p Z + ( A − Z ) f n dE = M N σ SI d σ F 2 ( E ) n 2 µ 2 f 2 n n • For equal coupling to n and p, A^2 dependence: light nuclei more sensitive to light WIMPs and viceversa • spin-independent interaction (SI) 7 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMP Direct Detection (DD) Goodman & Witten ’85 d 3 v ′ f(v ′ (t)) dR d σ � ρ ⊙ dE = dE v ′ m DM v ′ >v ′ min � 2 � f p Z + ( A − Z ) f n dE = M N σ SI d σ F 2 ( E ) n 2 µ 2 f 2 n n DM velocity distribution + • For equal coupling to n and p, A^2 astrophysical parameters at dependence: light nuclei more sensitive to the Sun position light WIMPs and viceversa � M N E • spin-independent interaction (SI) v ′ min = 2 µ N 7 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
WIMP Direct Detection (DD) Goodman & Witten ’85 d 3 v ′ f(v ′ (t)) dR d σ � ρ ⊙ dE = dE v ′ m DM v ′ >v ′ min � 2 � f p Z + ( A − Z ) f n dE = M N σ SI d σ F 2 ( E ) n 2 µ 2 f 2 n n DM velocity distribution + • For equal coupling to n and p, A^2 astrophysical parameters at dependence: light nuclei more sensitive to the Sun position light WIMPs and viceversa � M N E • spin-independent interaction (SI) v ′ min = 2 µ N Total rate = Integrate over energy times detector mass and exposure time 7 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Experimental Issues � m N • Small recoil energy m DM � 2 �� � E R � ∼ keV GeV m DM + m N lowest threshold possible • Event rate very small large detector mass and long exposure time • Background discrimination -> SYSTEMATICS !! misidentified electrons (surface events) neutrons in the recoil band use of multiple detection techniques (ionization, heat, scintillation) use of signature proper of the a WIMP 8 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Annual Modulation Drukier, Freese and Spergel ’86, Signature of WIMP recoil in the detector Freese, Frieman and Gould ’88 In the Earth’ s rest frame the DM velocity distribution acquires a time dependence, which follows a sinusoidal behavior Projecting along the galactic plane: d 3 v ′ f(v ′ (t)) � η ( E, t ) = v ′ v ′ >v min v 2 = | � v ′ + � v ⊕ | 2 v ⊙ + � v ⊕ = | � ′′ ⊕ , rot | v = v ⊙ + v ′′ ⊕ , rot cos γ cos[2 π ( t − t 0 ) /T ] Bernabei et al. arXiv:1002.1028 γ = 60 ◦ effect of O(10%) 9 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Theoretical Issues • WIMP-nucleon cross-section can span several order of magnitude: model dependent quantity theoretical model parameter together with the WIMP mass • DM velocity distribution depends on the solar neighborhood quantities and properties approximated with Standard Model Halo (SMH), that is a spherically symmetric and isotropic Maxwellian distribution SMH disfavoured by N-body simulations Velocity distribution in a shell 7<R<9 kpc Milky way like galaxy simulated with RAMSES: DM + baryons Ling et al. ’09 10 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Bayesian Inference framework data θ = { θ 1 , ..., θ n , ψ a , ..., ψ z } θ i theoretical model parameters Posterior probability Prior Likelihood function (PDF) nuisance parameters = ψ k (proper of astrophysics and systematics each EXP) 11 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Bayesian Inference framework data θ = { θ 1 , ..., θ n , ψ a , ..., ψ z } θ i theoretical model parameters Posterior probability Prior Likelihood function (PDF) nuisance parameters = ψ k (proper of astrophysics and systematics each EXP) Common prior choices that do not favour any parameter region 11 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Bayesian Inference framework data θ = { θ 1 , ..., θ n , ψ a , ..., ψ z } θ i theoretical model parameters Posterior probability Prior Likelihood function (PDF) nuisance parameters = ψ k (proper of astrophysics and systematics each EXP) Common prior choices that do not favour any parameter region Posterior sampled via MCMC techniques (Markov-Chain Monte Carlo) given the likelihood and the prior and marginalized over nuisance parameters 11 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Bayesian Inference framework data θ = { θ 1 , ..., θ n , ψ a , ..., ψ z } θ i theoretical model parameters Posterior probability Prior Likelihood function (PDF) nuisance parameters = ψ k (proper of astrophysics and systematics each EXP) Common prior choices that do not favour any parameter region Posterior sampled via MCMC techniques (Markov-Chain Monte Carlo) given the likelihood and the prior and marginalized over nuisance parameters Profile Likelihood -> comparison with frequentist approach, prior independent 11 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Construction of DM velocity distribution DD depends on the distribution function (DF) at the sun position arising from the WIMPs phase-space distribution • DF obtained inverting the equation above • Symmetries assumed: density profile spherically symmetric and f(v) isotropic -> DF only function of the energy • f(v) is a function of the gravitational potential (including baryon contribution) • f(v) is a function of the DM density profile 12 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
Construction of DM velocity distribution Spherically symmetric DM density 1000 profiles : Ρ DM � GeV � cm 3 � ρ DM = ρ DM ( c vir , M vir ) NFW 10 Einasto Cored Isothermal 0.1 Burkert R 0.001 � They mostly differ near the galactic center, at the sun 0.001 0.01 0.1 1 10 100 position they give similar behavior for f(v) r � kpc � In what follow only shown comparison between NFW and SMH Likelihood for astrophysical observables (nuisance parameters for ALL EXP) 13 C. Arina (RWTH-Aachen) - Grenoble, February 16, 2012
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