Direct Detection Lecture 1: Introduction to Dark Matter Homework - PowerPoint PPT Presentation

Basics Frontiers in Dark Matter, Neutrinos, and Particle Physics July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) July 27-28, 2017 Sun Yat-Sen University, Guangzhou Theoretical Physics Summer School http://yzhxxzxy.github.io Experiments School of Physics, the University of Melbourne ARC Centre of Excellence for Particle Physics at the Terascale, Zhao-Huan Yu （余钊焕） Direct Detection Lecture 1: Introduction to Dark Matter Homework Efgective Lagrangians 1 / 37

Basics Spiral galaxy M33 July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) as suggested by astrophysical and cosmological observations Dark matter (DM) makes up most of the matter component in the Universe, [1502.01589] Planck 2015 Experiments CMB CMB Spiral galaxy M33 Bullet Cluster Efgective Lagrangians Homework Dark Matter in the Universe 2 / 37 Bullet Cluster M33 dark matter halo stellar disk gas Cold DM ( 25.8% ) Ω c h 2 = 0.1186 ± 0.0020 Baryons ( 4.8% ) Ω b h 2 = 0.02226 ± 0.00023 Dark energy ( 69.3% ) Ω Λ = 0.692 ± 0.012

Basics Experiments July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Weakly interacting massive particles (WIMPs) A very attractive class of DM candidates: Assuming the annihilation process consists of two weak interaction vertices with 3 / 37 Efgective Lagrangians would be determined by the annihilation Homework DM Relic Abundance [Feng, arXiv:1003.0904] If DM particles ( χ ) were thermally produced in the early Universe, their relic abundance cross section 〈 σ ann v 〉 : Ω χ h 2 ≃ 3 × 10 − 27 cm 3 s − 1 〈 σ ann v 〉 Observation value Ω χ h 2 ≃ 0.1 〈 σ ann v 〉 ≃ 3 × 10 − 26 cm 3 s − 1 ⇒ 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 ⇒

Basics physics July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Collider detection Inirect detection Direct detection Unknown Experiments SM SM DM DM Experimental Approaches to WIMP Dark Matter Homework Efgective Lagrangians 4 / 37

Basics Experiments Efgective Lagrangians Homework WIMP Scattering ofg Atomic Nuclei Zhao-Huan Yu (Melbourne) Dark Matter Direct Detection July 2017 5 / 37

Basics Experiments Efgective Lagrangians Homework Direct Detection [Bing-Lin Young, Front. Phys. 12, 121201 (2017)] Zhao-Huan Yu (Melbourne) Dark Matter Direct Detection July 2017 6 / 37

Basics Maxwell-Boltzmann velocity distribution in the Galactic rest frame : July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Velocity dispersion: [Binney & Tremaine, Galactic Dynamics , Chapter 4] Experiments 7 / 37 “thermalized” by fmuctuations in the gravitational potential, and WIMPs have a WIMP Velocity Distribution During the collapse process which formed the Galaxy, WIMP velocities were Homework Efgective Lagrangians Galactic disk and dark halo [Credit: ESO/L. Calçada] � 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 equals to the rotational speed of the Sun : v 0 = v ⊙ ≃ 220km / s � � 〈 ˜ v 2 〉 = 3 / 2 v 0 ≃ 270km / s

Basics Experiments July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) 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 8 / 37 Efgective Lagrangians Earth Rest Frame Homework The WIMP velocity distribution f ( v ) seen Earth June WIMP wind 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 3.5 3.5 v 2 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 ) ⇒

Basics Energy conservation: July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Experiments Momentum conservation: 9 / 37 Nuclear Recoil Homework Efgective Lagrangians 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

Basics Energy conservation: July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Experiments Momentum conservation: 9 / 37 Efgective Lagrangians Homework 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 ,

Basics Astrophysics factors July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Experiments Detector factors Particle physics factors 10 / 37 Event rate per unit time per unit energy interval: Efgective Lagrangians Homework Event Rate ∫ v max d σ χ A dR ρ ⊕ d 3 v f ( v ) v = N A dE R m χ dE R v min N A : target nucleus number ρ ⊕ ≃ 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] )

Basics Experiments July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) Spins of nucleons tend to cancel out among themselves: Strong coherent enhancement for heavy nuclei 11 / 37 There are two kinds of DM-nucleus scattering Cross Section Dependence on Nucleus Spin Homework Efgective Lagrangians 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

Basics DM-nucleon interaction July 2017 Dark Matter Direct Detection Zhao-Huan Yu (Melbourne) 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 Experiments 12 / 37 Three Levels of Interaction Homework DM-parton interaction Efgective Lagrangians 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 )

Basics Experiments Efgective Lagrangians Homework Technologies and Detector Material [From M. Lindner’s talk (2016)] Zhao-Huan Yu (Melbourne) Dark Matter Direct Detection July 2017 13 / 37

Basics Experiments Efgective Lagrangians Homework Technologies and Detector Material [From M. Lindner’s talk (2016)] Zhao-Huan Yu (Melbourne) Dark Matter Direct Detection July 2017 14 / 37