Dark Matter direct detection and Bayesian statistics BASED ON: CA, - - PowerPoint PPT Presentation
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]
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Komatsu et al. ’10, Larson et al. ’10, Bennett et al. ’10
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Komatsu et al. ’10, Larson et al. ’10, Bennett et al. ’10
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Lee & Weinberg ’77, Gunn et al. ’78, Steigman et
Scherrer & Turner ’85, Griest & Seckel ’91
(other DM candidates are axions, sterile neutrinos, ...)
< σAv >∼ g2 m2
χ
∼ 0.012 (100 GeV)2 ∼ 8 × 10−25cm3s−1
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Goodman & Witten ’85
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Goodman & Witten ’85
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Goodman & Witten ’85
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Goodman & Witten ’85
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Goodman & Witten ’85
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Drukier, Freese and Spergel ’86, Freese, Frieman and Gould ’88
′′
⊕,rot|
⊕,rot cos γ cos[2π(t − t0)/T]
Bernabei et al. arXiv:1002.1028
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Ling et al. ’09
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Likelihood (proper of each EXP) Prior Posterior probability function (PDF) data
theoretical model parameters nuisance parameters = astrophysics and systematics
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Likelihood (proper of each EXP) Prior Posterior probability function (PDF) data
theoretical model parameters nuisance parameters = astrophysics and systematics
Common prior choices that do not favour any parameter region
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Likelihood (proper of each EXP) Prior Posterior probability function (PDF) data
theoretical model parameters nuisance parameters = astrophysics and systematics
Posterior sampled via MCMC techniques (Markov-Chain Monte Carlo) given the likelihood and the prior and marginalized over nuisance parameters
Common prior choices that do not favour any parameter region
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Likelihood (proper of each EXP) Prior Posterior probability function (PDF) data
theoretical model parameters nuisance parameters = astrophysics and systematics
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
Common prior choices that do not favour any parameter region
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They mostly differ near the galactic center, at the sun position they give similar behavior for f(v) In what follow only shown comparison between NFW and SMH
R
ρDM = ρDM(cvir, Mvir)
★ Gran Sasso ★ Boulby Mine ★ SNO Lab ★ Soudan Mine
Mini-CLEAN Picasso Zeplin-III Drift-II NaIAD DAMA/LIBRA Xenon10/Xenon100 Warp Cuoricino/Cuore Cresst-II CDMS CoGeNT FermiLab COUPP Anais
ROSEBUD
Modane Laboratory, CERN and Laboratoire subterrain a bas bruit Edelweiss EURECA ArDM SIMPLE MIMAC NEWAGE ULEGe XMASS Tokyo CaF2 MIT DMTPC Homestake mine LUX
★
KIMS
★
TEXONO
★ ★ ★ ★ ★
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2D marginal credible regions at 90 and 99% 1D marginalized posterior PDF Scintillator made by Na and I: quenching factors are nuisance parameters Data given by modulated rate as a function of the energy (13 annual cycles, 1.17 ton x yr) : gaussian likelihood
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the SMH case
effects due to the integration over all possible velocities and density values of the halo at the Sun position
Preferred values for astrophysics:
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(Aalseth et al. arXiv:1106.0650 data courtesy of CoGeNT coll.)
Gaussian likelihood
2D marginal credible regions at 90 and 99% NFW SMH Ge detector, 146 kg days Very low threshold: 0.4 keVee = 2.7 keV
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(same behavior also for SMH) 2D marginal credible regions at 90 and 99%
standard at rest, the escape velocity and density NFW
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Aprile et al. arXiv:1104.2549
experimental set-up
gaussian prior and marginalized over
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2D marginal credible regions at 90% +
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2D marginal credible regions at 90% +
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No nuisance parameters, background accounted for by analytical marginalization
Akerib et al. ’05, Ahmed et al ’09
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1010.4290)
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Preferred values for the astrophysical observables
profiles give very similar results
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E1 0.50.9 keVee
100 200 300 400 500 20 30 40 50 60 t days Counts30days
E2 0.93.0 keVee
100 200 300 400 500 20 40 60 80 100 t days Counts30days
E3 3.04.5 keVee
100 200 300 400 500 10 20 30 40 50 60 t days Counts30days
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Priors on the fractional modulated amplitude predicted from configurations of DM mass and sigma that account for the CoGeNT total rate R(t) = S(t) + B
Sm = R(tmax) − R(tmin) R(tmax) + R(tmin)
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2 4 6 ln(B) 1a 1b 2a 2b
ΔE1 ΔE2 ΔE3 All ΔE
strong evidence for M0 moderate evidence for M0 weak evidence for M0 weak evidence against M0 moderate evidence against M0 strong evidence against M0
0.88 0.57 1.49
0.61
0.0048
2.05
1.50
Non-DM T free Non-DM annual Consistent DM Pheno-DM No modulation
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N
i > ∆χ2 eff)
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N
i > ∆χ2 eff)
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N
i > ∆χ2 eff)
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N
i > ∆χ2 eff)
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N
i > ∆χ2 eff)
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N
i > ∆χ2 eff)
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5 10 15 20 0.01 0.00 0.01 0.02 0.03 0.04 E keVee Averaged SmcpdkgkeVee
0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 20 25 E keVee counts0.05 keV 0.33 kg 56 days
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Assuming equilibrium between gravitational force and pressure: Eddigton formula for spherically symmetric DM density profiles that lead to isotropic f(v) Poisson equation for the gravitational potential including contribution from the bulge and disk: NFW The velocity distribution is translated to the reference frame of the Earth:
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Analytical marginalization over the background:
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from 2 -> 10 KeV and 9 from 10 to 100 keV
arXiv:1011.2482 prior range flat over: Background due to surface events, leakage events and zero-charge events is extrolated below 5 KeV
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Germanium cryogenic detector detector mass 0.33 kg live time 442 days total exposure 145.86 kg days
Total rate : 27 bins of width 0.1 keVee energy range 0.5- 3.2 keVee Modulated rate: 3 nuisance parameters for the non modulating background quenching factor:
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Data analysis
arXiv:1106.0650
Theoretical predictions for elastic spin-independent scattering off nucleus
Differential rate
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(Brown et al. arXiv:1109.2589) Angloher et al., arXiv:1109.0702
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