Direct and Indirect Detection of Dark Matter Zhao-Huan Yu School of - PowerPoint PPT Presentation

Dark Matter Direct Detection Indirect Detection Direct and Indirect Detection of Dark Matter Zhao-Huan Yu （余钊焕） School of Physics, Sun Yat-Sen University http://yzhxxzxy.github.io June 18, 2019 Zhao-Huan Yu (SYSU) Direct and Indirect Detection of Dark Matter June 2019 1 / 56

Dark Matter Cluster Abell 2218 June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) as suggested by astrophysical and cosmological observations Dark matter (DM) makes up most of the matter component in the Universe, CMB CMB Cluster Abell 2218 Spiral galaxy M33 Direct Detection Spiral galaxy M33 Bullet Cluster Bullet Cluster Dark Matter in the Universe Indirect Detection 2 / 56 M33 dark matter halo stellar disk gas

Dark Matter Direct Detection Indirect Detection Inferred Properties of Dark Matter Dark (electrically neutral): no light emitted from it Nonbaryonic: BBN & CMB observations Long lived: survived from early eras of the Universe to now Colorless: otherwise, it would bind with nuclei Cold: structure formation theory Zhao-Huan Yu (SYSU) Direct and Indirect Detection of Dark Matter June 2019 3 / 56 Abundance: more than 80% of all matter in the Universe ρ DM ∼ 0.3 − 0.4 GeV / cm 3 near the earth

Dark Matter Direct Detection June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Weakly interacting massive particles (WIMPs) A very attractive class of DM candidates: Assuming the annihilation process consists of two weak interaction vertices with would be determined by the annihilation 4 / 56 Indirect Detection DM Relic Abundance If DM particles ( χ ) were thermally produced DM freeze out, m χ = 100 GeV, g * = 86 10 -7 10 -7 10 3 10 3 in the early Universe, their relic abundance 10 -8 10 -8 10 2 10 2 10 -9 10 -9 cross section 〈 σ ann v 〉 : 10 1 10 1 Y = n / s 10 -10 10 -10 3 × 10 -27 Ω χ h 2 Ω χ h 2 ≃ 3 × 10 − 27 cm 3 s − 1 10 0 10 0 10 -11 10 -11 〈 σ v 〉 = 3 × 10 -26 cm 3 /s 10 -1 10 -1 〈 σ ann v 〉 10 -12 10 -12 3 × 10 -25 10 -2 10 -2 Observation value Ω χ h 2 ≃ 0.1 10 -13 10 -13 Equilibrium 10 -3 10 -3 10 -14 10 -14 〈 σ ann v 〉 ≃ 3 × 10 − 26 cm 3 s − 1 ⇒ 10 10 1 1 0.1 0.1 T (GeV) the SU ( 2 ) L gauge coupling g ≃ 0.64 , for m χ ∼ O ( TeV ) we have g 4 ∼ O ( 10 − 26 ) cm 3 s − 1 〈 σ ann v 〉 ∼ 16 π 2 m 2 χ ⇒

Dark Matter physics June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Collider detection Inirect detection Direct detection Unknown Direct Detection SM SM DM DM Experimental Approaches to Dark Matter Indirect Detection 5 / 56

Dark Matter Direct Detection Indirect Detection WIMP Scattering ofg Atomic Nuclei Zhao-Huan Yu (SYSU) Direct and Indirect Detection of Dark Matter June 2019 6 / 56

Dark Matter Direct Detection Indirect Detection Direct Detection [Bing-Lin Young, Front. Phys. 12, 121201 (2017)] Zhao-Huan Yu (SYSU) Direct and Indirect Detection of Dark Matter June 2019 7 / 56

Dark Matter Direct Detection June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Velocity dispersion: [Binney & Tremaine, Galactic Dynamics , Chapter 4] equals to the rotational speed of the Sun : 8 / 56 WIMP Velocity Distribution Indirect Detection Maxwell-Boltzmann velocity distribution in the Galactic rest frame : [Credit: ESO/L. Calçada] During the collapse process which formed the Galaxy, WIMP velocities were Galactic disk and dark halo “thermalized” by fmuctuations in the gravitational potential, and WIMPs have a � v 2 � v 2 / v 2 � 3 / 2 v = e − ˜ � m χ m χ ˜ 0 ≡ 2 k B T 0 ˜ v ) d 3 ˜ d 3 ˜ d 3 ˜ v 2 f ( ˜ v = exp − v , π 3 / 2 v 3 2 π k B T 2 k B T m χ 0 v = 3 v 2 ˜ ∫ v ˜ � v 2 � ∫ v ) d 3 ˜ v ) d 3 ˜ 2 v 2 〈 ˜ v 〉 = f ( ˜ v = 0 , = f ( ˜ ˜ ˜ ˜ 0 v 2 4˜ v 2 / v 2 Speed distribution: ˜ e − ˜ 0 d ˜ f ( ˜ v ) d ˜ v = v � π v 3 0 For an isothermal halo, the local value of v 0 v 0 = v ⊙ ≃ 220km / s � � 〈 ˜ v 2 〉 = 3 / 2 v 0 ≃ 270km / s

Dark Matter Direct Detection June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Annual modulation signal peaked on June 2 [Freese et al. , PRD 37, 3388 (1988)] Speed distribution: by an observer on the Earth can be derived 9 / 56 Indirect Detection Earth Rest Frame The WIMP velocity distribution f ( v ) seen Earth e WIMP wind n u J δ = 30.7 ◦ via Galilean transformation Cygnus v = v + v obs , ˜ v obs = v ⊙ + v ⊕ v ⊙ ≃ 220 km / s Sun r v ⊕ = 30 km / s e b m Velocity distribution: f ( v ) = ˜ f ( v + v obs ) e c e D v 2 + v 2 Speed distributions � � 4 v 2 4.0 4.0 obs − f ( v ) dv = � π v 3 exp v obs = 0 v 2 3.5 3.5 v obs = 205 km/s 0 0 v obs = 235 km/s 3.0 3.0 f ( v ) (10 -3 km -1 s) v 2 � � ˜ 2 vv obs 0 2.5 2.5 × sinh dv v 2 2 vv obs 2.0 2.0 0 1.5 1.5 Since v ⊕ ≪ v ⊙ , we have ( ω = 2 π/ year) 1.0 1.0 0.5 0.5 v obs ( t ) ≃ v ⊙ + v ⊕ sin δ cos [ ω ( t − t 0 )] 0.0 0.0 0 0 100 100 200 200 300 300 400 400 500 500 600 600 700 700 800 800 ≃ 220 km / s + 15 km / s · cos [ ω ( t − t 0 )] v (km s -1 ) ⇒

Dark Matter Energy conservation: June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Direct Detection Momentum conservation: 10 / 56 Nuclear Recoil Indirect Detection v χ 1 2 m χ v 2 = 1 χ + 1 χ 2 m χ v 2 2 m A v 2 R Nucleus WIMP χ A θ χ v m χ v = m χ v χ cos θ χ + m A v R cos θ R m χ v χ sin θ χ = m A v R sin θ R θ R 2 m χ v cos θ R A v R ⇒ Recoil velocity v R = m χ + m A ⇒ Recoil momentum (momentum transfer) q R = m A v R = 2 µ χ A v cos θ R  for m χ ≫ m A m A ,   m χ m A  1 Reduced mass of the χ A system µ χ A ≡ = 2 m χ , for m χ = m A m χ + m A    m χ , for m χ ≪ m A maximal momentum transfer q max Forward scattering ( θ R = 0 ) ⇒ = 2 µ χ A v R

Dark Matter Energy conservation: June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Direct Detection Momentum conservation: 10 / 56 Indirect Detection Nuclear Recoil v χ 1 2 m χ v 2 = 1 χ + 1 χ 2 m χ v 2 2 m A v 2 R Nucleus WIMP χ A θ χ v m χ v = m χ v χ cos θ χ + m A v R cos θ R m χ v χ sin θ χ = m A v R sin θ R θ R 2 m χ v cos θ R A v R ⇒ Recoil velocity v R = m χ + m A ⇒ Recoil momentum (momentum transfer) q R = m A v R = 2 µ χ A v cos θ R 2 µ 2 q 2 χ A R v 2 cos 2 θ R ⇒ Kinetic energy of the recoiled nucleus E R = = 2 m A m A As v ∼ 10 − 3 c , for m χ = m A ≃ 100 GeV and θ R = 0 , E R = 1 2 m χ v 2 ∼ 50 keV q R = m χ v ∼ 100 MeV ,

Dark Matter Astrophysics factors June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Direct Detection Detector factors Particle physics factors 11 / 56 Event Rate Indirect Detection Event rate per unit time per unit energy interval: ∫ v max d σ χ A dR ρ ⊕ d 3 v f ( v ) v = N T dE R m χ dE R v min N T : target nucleus number ρ ⊕ ≃ 0.3 − 0.4 GeV / cm 3 : DM mass density around the Earth ( ρ ⊕ / m χ is the DM particle number density around the Earth) σ χ A : DM-nucleus scattering cross section � 1 / 2 � m A E th R Minimal velocity v min = 2 µ 2 : determined by the detector threshold χ A of nuclear recoil energy, E th R Maximal velocity v max : determined by the DM escape velocity v esc ( v esc ≃ 544 km / s [Smith et al. , MNRAS 379, 755] )

Dark Matter Direct Detection June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) Spins of nucleons tend to cancel out among themselves: Strong coherent enhancement for heavy nuclei 12 / 56 There are two kinds of DM-nucleus scattering Cross Section Dependence on Nucleus Spin Indirect Detection Spin-independent (SI) cross section: σ SI χ A ∝ µ 2 χ A [ ZG p + ( A − Z ) G n ] 2 J A + 1 Spin-dependent (SD) cross section: σ SD χ A ∝ µ 2 ( S A p G ′ p + S A n G ′ n ) 2 χ A J A Nucleus properties: mass number A , atomic number Z , spin J A , expectation value of the proton (neutron) spin content in the nucleus S A p ( S A n ) G ( ′ ) and G ( ′ ) p n : DM efgective couplings to the proton and the neutron Z ≃ A / 2 ⇒ σ SI χ A ∝ A 2 [( G p + G n ) / 2 ] 2 S A N ≃ 1 / 2 ( N = p or n ) for a nucleus with an odd number of N S A N ≃ 0 for a nucleus with an even number of N

Dark Matter DM-nucleon interaction June 2019 Direct and Indirect Detection of Dark Matter Zhao-Huan Yu (SYSU) gluons Relevant partons involve not only valence quarks, but also sea quarks and which describe the probabilities of fjnding partons inside nucleons The DM-nucleon level is related to the DM-parton level via form factors , are usually compared with each other at the DM-nucleon level As a variety of target nuclei are used in direct detection experiments, results DM-nucleus interaction Direct Detection 13 / 56 DM-parton interaction Indirect Detection Three Levels of Interaction p , n χ q χ χ A Mediator Mediator Mediator ⇒ ⇒ p , n χ q χ χ A M ( χ q → χ q ) M ( χ N → χ N ) M ( χ A → χ A )