Direct Detection and Collider Searches of Dark Matter Lecture 4 Graciela Gelmini - UCLA Dark Matter School, Lund, Sept. 26-30, 2016
Graciela Gelmini-UCLA Content of Lecture 4 • Halo-dependent and halo-independent direct detection data analysis. • The future of direct dark matter detection. • Introduction to search strategies at the LHC Subject is very vast, so idiosyncratic choice of subjects + citations disclaimer Dark Matter School, Lund, Sept. 26-30, 2016 1
Graciela Gelmini-UCLA . Halo-dependent and halo-independent direct detection data analysis Dark Matter School, Lund, Sept. 26-30, 2016 2
Graciela Gelmini-UCLA 𝑒 3 𝑤 2𝑛𝜈 2 𝑈 𝜍𝜃(𝑤 𝑛𝑗𝑜 , 𝑢) 𝑥ℎ𝑓𝑠𝑓 𝑤>𝑤𝑛𝑗𝑜 𝑤, 𝑢) 𝑤 𝑤, 𝑢) : local DM density and 𝑈 ⃗ 𝑤 distribution depend on halo model. NOTICE: ̃ 𝜃(𝑤 𝑛𝑗𝑜 ) = 𝜏 𝑠𝑓𝑔 𝜍𝜃(𝑤 𝑛𝑗𝑜 )/𝑛 contains all the dependence of the rate on Given 𝑛 the plots are in the 𝑤 𝑛𝑗𝑜 , ̃ 𝜃(𝑤 𝑛𝑗𝑜 ) plane: “Halo-Independent” Dark Matter School, Lund, Sept. 26-30, 2016 Halo-Independent direct DM detection data comparison 𝜏 𝑈 (𝐹 𝑆 ) 3 𝑒𝐹 𝑆 𝐷 𝑈 𝑒𝑆 𝑁 𝑈 𝑒𝐹 𝑆 𝑒𝐹 𝑆 𝑤, 𝑢)𝑒 3 𝑤 𝑒𝜏 𝑈 𝑒𝐹 𝑆 Event rate: events/(unit mass of detector)/(keV of recoil energy)/day 2𝜈 2 𝑈 𝑤 2 𝜏 𝑈 (𝐹 𝑆 ) ∼ 𝜏 𝑠𝑓𝑔 𝑒𝑆 × 𝑒𝜏 𝑈 × 𝑜𝑤𝑔( ⃗ = � 𝑈 � = 𝜏 𝑈 (𝐹 𝑆 ) 𝑁 𝑈 𝑔( ⃗ = � 𝜃(𝑤 𝑛𝑗𝑜 , 𝑢) = � - 𝜍 = 𝑜𝑛 , 𝑔( ⃗ Given 𝜍𝜃(𝑤 𝑛𝑗𝑜 ) the plots are in the 𝑛, 𝜏 𝑠𝑓𝑔 plane: usual “Halo-Dependent” the halo and is common to all experiments! Fox, Liu, Weiner 1011.1915
Graciela Gelmini-UCLA Halo-Independent data comparison Dark Matter School, Lund, Sept. 26-30, 2016 Every experiment is sensitive to a “window in velocity space” 2 ] 1 , 𝐹 ′ DEPENDENT response function non zero only 2 ] : EXPERIMENT AND INTERACTION 1 ,𝐹 ′ ℛ [𝐹 ′ 𝜃(𝑤 𝑛𝑗𝑜 ) 2 ] (𝑤 𝑛𝑗𝑜 ) ̃ 1 ,𝐹 ′ 0 ∞ 1 ,𝐹 ′ 𝑆 [𝐹 ′ 2 ] for any cross section as 1 , 𝐹 ′ detected energy interval [𝐹 ′ resolution and efficiency with arbitrary energy dependence, we write the expected rate over a Using instead experimentally accessible quantities, including isotopic composition and energy Gondolo-Gelmini 1202.6359; Del Nobile, Gelmini, Gondolo and Huh, 1306.5273 Halo Independent analysis for ANY interaction 4 Early versions of the method used the recoil spectrum 𝑒𝑆/𝑒𝐹 𝑆 which is not directly accessible to experiments, and SI interactions Fox, Liu, Weiner 1011.1915; Frandsen et al 1111.0292 2 ] = � 𝑒𝑤 𝑛𝑗𝑜 ℛ [𝐹 ′ in an interval in 𝑤 𝑛𝑗𝑜 given an interval [𝐹 ′
Graciela Gelmini-UCLA 𝑆 𝑚𝑗𝑛𝑗𝑢 Halo Independent analysis ̃ 𝜃 is a non decreasing function of 𝑤 𝑛𝑗𝑜 : the smallest possible with value � 𝜃 . Thus, compute the rate with this downward step function and ask for this rate to be at most equal to the measured limit for � 𝜃 0 𝑚𝑗𝑛 . [𝐹 ′ 1 ,𝐹 ′ 1 ,𝐹 ′ � 𝜃 𝑚𝑗𝑛𝑗𝑢 0 𝑤 0 0 [𝐹 ′ 1 ,𝐹 ′ 2 ] (𝑤 𝑛𝑗𝑜 ) Dark Matter School, Lund, Sept. 26-30, 2016 2 ] (𝑤 𝑛𝑗𝑜 ) Upper limits: 𝜃 with weight ℛ [𝐹 ′ ∞ Gondolo-Gelmini 1202.6359, Del Nobile, Gelmini, Gondolo and Huh, 1306.5273 - Rate measurements: translated into weighted averages of the ̃ 𝜃 function: 𝑆 𝑛𝑓𝑏𝑡𝑣𝑠𝑓𝑒 [𝐹 ′ 1 ,𝐹 ′ 2 ] � 𝜃 [𝐹 ′ 2 ] : weighted average of ̃ 1 ,𝐹 ′ 0 2 ] (𝑤 𝑛𝑗𝑜 ) 1 ,𝐹 ′ 𝜃 [𝐹 ′ � ‾ 5 1 ,𝐹 ′ = ‾ 𝑒𝑤 𝑛𝑗𝑜 ℛ [𝐹 ′ 2 ] � 𝜃 0 at 𝑤 𝑛𝑗𝑜 = 𝑤 0 is � 𝜃 0 Θ(𝑤 0 − 𝑤 𝑛𝑗𝑜 ) ≤ ̃ 𝜃 0 = � 2 ] = (𝑤 0 ) � 𝑒𝑤 𝑛𝑗𝑜 ℛ 𝑇𝐽
Graciela Gelmini-UCLA Signals compatible with all limits? Assuming the SHM Elastic contact Isospin Conserving (IC) or Violating (IV) Spin-Independent (SI)? Figs. from Del Nobile, Gelmini, Gondolo, Huh 1405.5582 and Gelmini, Georgescu, Huh 1404.7484 IV makes CDMS-II-Si compatible with all 90%CL upper limits, not with DAMA or CoGeNT. Dark Matter School, Lund, Sept. 26-30, 2016 6
Graciela Gelmini-UCLA Halo Dependent vs Independent comparisons for elastic SI IC Rate only crosses, � LEFT: CDMS-II-SI rejected by SuperCDSM bound in the SHM. RIGHT: 𝑛 = 9 GeV. CDMS-II-Si Dark Matter School, Lund, Sept. 26-30, 2016 7 𝜃 0 Del Nobile, Gelmini, Gondolo, Huh 1304.6183, 1311.4247, 1405.5582 rate (red) crosses are forbidden by the SuperCDMS limit in any halo model.
Graciela Gelmini-UCLA Halo Dependent and Independent upper limits Notice the shape of the limits. Generic Halo-Dependent limit (here the SHM): What about a Halo-Independent limit? Dark Matter School, Lund, Sept. 26-30, 2016 8
Graciela Gelmini-UCLA Halo Dependent vs Independent comparison for elastic SI IV Del Nobile, Gelmini, Gondolo, Huh 1304.6183, 1311.4247, 1405.5582 LEFT: Part of the 90%CL CDMS-II-Si region survives all 90%CL limits. Dark Matter School, Lund, Sept. 26-30, 2016 9 RIGHT: 𝑛 = 9 GeV. CDMS-II-Si rate small for CoGeNT/DAMA mod. CoGeNT annual mod. compatible with zero at ≃ 1𝜏 , with best fit phase of DAMA- Comparison of crosses and limits???
Graciela Gelmini-UCLA Halo Dependent vs Halo Independent comparison for LEFT: DAMA, CoGeNT and CDMS-Si overlap! RIGHT: CDMS-Si rate too small for CoGeNT/DAMA modulations. Both: rejected by SuperCDMS, but importance of CDMSLite limit depends on the halo model Dark Matter School, Lund, Sept. 26-30, 2016 10 Magnetic Dipole DM Del Nobile, Gelmini, Gondolo, Huh 1401.4508
Graciela Gelmini-UCLA Halo Dependent vs Independent comparison for Inelastic LEFT: DAMA, CoGeNT and CDMS-SI disjoint! RIGHT: 𝑛 = 3.5 GeV. CDMS-Si rate too small for CoGeNT and DAMA modulations (which overlap) Both: CDMS-Si allowed by all bounds Dark Matter School, Lund, Sept. 26-30, 2016 11 Exothermic SI “Ge-Phobic” DM Gelmini, Georgescu, Huh 1404.7484 Exothermic 𝜀 = −50 keV weakens Xe bounds, “Ge-Phobic” 𝑔 𝑜 /𝑔 𝑞 = −0.8 weakens Ge bounds.
Graciela Gelmini-UCLA Halo Dependent vs Independent comparison for Inelastic Ge bounds. LEFT: signal regions disjoint! RIGHT: 𝑛 = 1.3 GeV. CDMS-Si rate too small for CoGeNT and DAMA modulations (which overlap). Both: CDMS-Si allowed by all bounds Dark Matter School, Lund, Sept. 26-30, 2016 12 Exothermic SI “Ge-Phobic” DM Gelmini, Georgescu, Huh 1404.7484 LEFT: Exothermic 𝜀 = −200 keV weakens Xe bounds, “Ge-Phobic” 𝑔 𝑜 /𝑔 𝑞 = −0.8 weakens
Graciela Gelmini-UCLA EHI- Extendent likelihood Halo Independent method Fox, Kahn and Dark Matter School, Lund, Sept. 26-30, 2016 (Gelmini, Georgescu, Gondolo and Huh, 1507.03902) - a statistically meaningful two-sided point-wise band at a chosen CL. maximization conditions, (Fox, Kahn and McCullough 1403.6830) 𝜃(𝑤 𝑛𝑗𝑜 ) , by extending to functionals the Karush-Kuhn-Tucker (KKT) one can find 𝑏 | 𝐹 ′ =𝐹 ′ | | 𝑒𝐹 ′ 13 𝑏=1 � 𝑂 𝑃 𝜃] 𝜃(𝑤 𝑛𝑗𝑜 )] ≡ 𝑓 −𝑂 𝐹 [ ̃ ℒ 𝐹𝐼𝐽 [ ̃ With unbinned data (as in CDMS-II-Si) a statistically meaningful analysis can be made. 𝜃(𝑤 𝑛𝑗𝑜 ) values with upper bounds does not have a clear statistic meaning. ̃ Comparing average McCullough 1403.6830; Gelmini, Georgescu, Gondolo and Huh, 1507.03902 Starting with an extended likelihood for UNBINNED DATA 𝑁𝑈 𝑒𝑆 𝑢𝑝𝑢 - a best fit ̃
Graciela Gelmini-UCLA EHI- Extendent likelihood Halo Independent method Fox, Kahn and McCullough 1403.6830; Gelmini, Georgescu, Gondolo and Huh, 1507.03902 LEFT: halo dependent Figs. from Del Nobile, Gelmini, Gondolo, Huh 1405.5582 RIGHT: halo independent 90%CL bounds and the 68% and 90%CL regions (Left) and confidence confidence bands (Right) Dark Matter School, Lund, Sept. 26-30, 2016 14 for CDMS-II-Si, 𝑛 = 9 GeV elastic SI and 𝑔 𝑜 /𝑔 𝑞 = 1 . No continuous part of the bands allowed
Graciela Gelmini-UCLA EHI- Extendent likelihood Halo Independent method Fox, Kahn and McCullough 1403.6830; Gelmini, Georgescu, Gondolo and Huh, 1507.03902 LEFT: halo dependent Figs. from Gelmini, Georgescu, Huh 1404.7484 RIGHT: halo independent 90%CL bounds and the 68% and 90%CL regions and confidence bands for CDMS-II-Si, 𝑛 = 9 GeV elastic SI 𝑔 𝑜 /𝑔 𝑞 =−0.7 . A continuous part of the bands (so any ̃ 𝜃 contained in it) is allowed Dark Matter School, Lund, Sept. 26-30, 2016 15
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