Learning from Dark Matter direct detection Riccardo Catena Chalmers - PowerPoint PPT Presentation

Learning from Dark Matter direct detection Riccardo Catena Chalmers University of Technology September 12, 2019

Measuring the local Dark Matter density at direct detection experiments Riccardo Catena Chalmers University of Technology September 12, 2019

Overview function of the DM-nucleon scattering cross section (the so-called Earth- section, 𝜏 , are degenerate if the DM scattering rate only depends on their product d ℛ d E R = 𝜍 loc B. J. Kavanagh, R. Catena and C. Kouvaris, JCAP 1701 (2017) no.01, 012 | v |> v min Local Dark Matter (DM) density, 𝜍 loc , and DM-nucleon scattering cross d E R However, when DM is lighter than ∼ 0 . 5 GeV, spin-independent DM- crossing efgect ) perimentally allowed For these cross section values, the DM velocity distribution becomes a d 3 v | v | f ( v , t ) d 𝜏 m 𝜓 m T ∫ nucleon scattering cross sections of the order of 10 − 36 cm 2 are still ex- This breaks the degeneracy between 𝜍 loc and 𝜏

Overview If DM lies in this region of parameter space, can we simultaneously measure DM-nucleon scattering cross section and local DM density? R. Agnese et al. [SuperCDMS Collaboration], Phys. Rev. D 95 (2017) no.8, 082002

Outline Earth-crossing efgect Quantitative impact on the local DM velocity distribution Application: Extracting the local DM density from a future signal at direct detection experiments Summary

Earth-crossing efgect in the halo However, before reaching the detector, DM particles have to cross the Earth nuclei, which implies f ≠ f halo . I will refer to this distortion as Earth- crossing efgect In the standard paradigm f = f halo , where f halo is the velocity distribution Detector The Earth-crossing of DM unavoidably distorts f halo if DM interacts with

Earth-crossing efgect Two processes contribute to the Earth-crossing efgect; attenuation and defmection: (a) Attenuation (b) Defmection B B Detector Detector C A A

Earth-crossing efgect As a result, the DM velocity distribution at detector can be written as follows: f ( v , 𝛿) = f A ( v , 𝛿) + f D ( v , 𝛿) 𝛿 = cos − 1 (⟨ ̂ v 𝜓 ⟩ ⋅ ̂ r det ) Key observation : since 𝛿 depends on the detector position and on time, the same is true for f ( v , 𝛿) f A and f D depends on the input f halo , m 𝜓 , 𝜏 , the Earth composition and

Computing the attenuation term, f A For DM particles crossing the Earth with velocity v , the survival probability is given by AB d ℓ 𝜇( r , v )] The velocity distribution of particles enter- ing the Earth with velocity v is related to the free halo distribution f 0 ( v ) = f halo ( v ) by f A ( v , 𝛿) = f 0 ( v ) p surv ( v ) B Detector p surv ( v ) = exp [− ∫ A

Computing the defmection term, f D Rate of particles entering an infjnitesimal inter- action region at C and scattering into the direc- tion v : The rate of defmected particles leaving the inter- action region with velocity v can also be written in terms of f D B Detector [ n 𝜓 f 0 ( v ′ ) v ′ ⋅ d S d 3 v ′ ][ d p scat P ( v ′ → v ) d 3 v ] where d p scat = d ℓ/[𝜇( r , v ′ ) cos 𝛽] . C A n 𝜓 f D ( v , 𝛿) v ⋅ d S d 3 v

Computing the defmection term, f D The contribution to f D ( v , 𝛿) from the interaction point C , and velocities f D ( v , 𝛿) = d ℓ 𝜇( r , v ′ ) v ′ d Ω v , one obtains the dark matter speed distribution at detector after Earth- crossing. around v ′ is v f 0 ( v ′ ) P ( v ′ → v ) d 3 v ′ The fjnal expression for f D is obtained by integrating over d ℓ and d 3 v ′ . Multiplying f ( v , 𝛿) = f A ( v , 𝛿) + f D ( v , 𝛿) by v 2 = | v | 2 , and integrating over Comments: v ′ / v determined by kinematics; f D depends upon 𝜏 through 𝜇 and P ( v ′ → v ) .

Dark matter speed distribution at detector B. J. Kavanagh, R. Catena and C. Kouvaris, JCAP 1701 (2017) no.01, 012 Operator O 1 − m χ = 0 . 5 GeV Operator O 8 − m χ = 0 . 5 GeV Operator O 12 − m χ = 0 . 5 GeV 4 . 0 4 . 0 4 . 0 Free Free Free 3 . 5 3 . 5 3 . 5 f ( v, γ ) [10 − 3 km / s] f ( v, γ ) [10 − 3 km / s] f ( v, γ ) [10 − 3 km / s] γ = 0 γ = 0 γ = 0 3 . 0 3 . 0 3 . 0 γ = π/ 2 γ = π/ 2 γ = π/ 2 2 . 5 2 . 5 2 . 5 γ = π γ = π γ = π 2 . 0 2 . 0 2 . 0 1 . 5 1 . 5 1 . 5 1 . 0 1 . 0 1 . 0 ˜ ˜ ˜ 0 . 5 0 . 5 0 . 5 1 . 1 1 . 2 1 . 1 f ( v, γ ) /f 0 ( v ) f ( v, γ ) /f 0 ( v ) f ( v, γ ) /f 0 ( v ) 1 . 0 1 . 0 1 . 0 0 . 9 0 . 8 0 . 9 0 . 8 0 . 6 0 . 7 0 . 8 ˜ ˜ 0 . 6 ˜ 0 . 4 0 . 7 0 . 5 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800 v [km / s] v [km / s] v [km / s]

Earth-crossing efgect / position dependence Isotropic scattering Backward scattering Forward scattering B. J. Kavanagh, R. Catena and C. Kouvaris, JCAP 1701 (2017) no.01, 012 In the following, N pert = N f A + f D ,𝜏 and N free = N f halo ,𝜏 m χ = 0 . 5 GeV 1 . 2 1 . 1 1 . 0 N pert /N free 0 . 9 0 . 8 O 1 ✛ O 8 ✛ 0 . 7 O 12 ✛ Atten. only 0 . 6 Atten.+Defl. π π 3 π 0 π 4 2 4 γ = cos − 1 ( � ˆ v χ � · ˆ r det )

Earth-crossing efgect / time dependence B. J. Kavanagh, R. Catena and C. Kouvaris, JCAP 1701 (2017) no.01, 012 1 . 2 1 . 2 LNGS (42.5 ◦ N) CJPL (28.2 ◦ N) 1 . 1 1 . 1 N pert /N free N pert /N free 1 . 0 1 . 0 O 1 O 1 Atten. only O 8 O 8 Atten.+Defl. O 12 O 12 0 . 9 0 . 9 0 6 12 18 24 0 6 12 18 24 time [hours] time [hours] 1 . 2 1 . 2 INO (9.7 ◦ N) SUPL (37.1 ◦ S) 1 . 1 1 . 1 1 . 0 N pert /N free N pert /N free 0 . 9 1 . 0 0 . 8 0 . 7 0 . 9 O 1 O 1 O 8 0 . 6 O 8 O 12 O 12 0 . 8 0 . 5 0 6 12 18 24 0 6 12 18 24 time [hours] time [hours]

Comparison with the MC code DAMASCUS T. Emken and C. Kouvaris, JCAP 1710 (2017) no.10, 031

Comparison with the MC code DAMASCUS T. Emken and C. Kouvaris, JCAP 1710 (2017) no.10, 031

Reconstructing 𝜍 loc and 𝜏 from a future signal If DM lies in this region of parameter space, can we simultaneously measure DM-nucleon scattering cross section and local DM density? R. Agnese et al. [SuperCDMS Collaboration], Phys. Rev. D 95 (2017) no.8, 082002

R. Catena, T. Emken and B. Kavanagh, in preparation Reconstructing 𝜍 loc and 𝜏 : 1D profjle likelihood 1 1 1 N pert ∼ 60 N pert ∼ 200 N pert ∼ 2000 0.8 0.8 0.8 Probability Probability Probability 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 4 4.5 5 5.5 6 6.5 5 10 15 20 2 4 6 8 10 12 σ SI [pb] σ SI [pb] σ SI [pb] 1 1 1 N pert ∼ 60 N pert ∼ 200 N pert ∼ 2000 0.8 0.8 0.8 Probability Probability Probability 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0.35 0.4 0.45 0.5 0.5 1 1.5 0.2 0.4 0.6 0.8 1 1.2 ρ loc [GeV/cm 3 ] ρ loc [GeV/cm 3 ] ρ loc [GeV/cm 3 ]

R. Catena, T. Emken and B. Kavanagh, in preparation Reconstructing 𝜍 loc and 𝜏 : 2D profjle likelihood 1 1 1.2 Profile likelihood Profile likelihood 0.9 1.4 0.9 1.1 N pert ∼ 60 N pert ∼ 200 0.8 1 0.8 1.2 0.7 0.9 0.7 ρ loc [GeV/cm 3 ] ρ loc [GeV/cm 3 ] 1 0.6 0.8 0.6 0.5 0.7 0.5 0.8 0.4 0.6 0.4 0.6 0.3 0.5 0.3 0.4 0.2 0.4 0.2 0.3 0.1 0.1 0.2 0.2 0 0 5 10 15 20 2 4 6 8 10 12 σ SI [pb] σ SI [pb] 1 0.52 Profile likelihood 0.9 0.5 N pert ∼ 2000 0.8 0.48 0.7 0.46 ρ loc [GeV/cm 3 ] 0.6 0.44 0.5 0.42 0.4 0.4 0.38 0.3 0.36 0.2 0.34 0.1 0.32 0 4 4.5 5 5.5 6 6.5 σ SI [pb]

Summary Analytic and MC calculations of Earth-scattering efgects can be used to simultaneously extract local DM density and DM-nucleon scattering cross section from data 200 signal events is of about 50 % ; and for ∼ 2000 signal events is of about 10 % For ∼ 60 signal events, the relative error on 𝜍 loc is of a factor of 2; for ∼