Learning from WIMPs. Manuel Drees. Bonn University. Learning from WIMPs p. 1/29

Learning from WIMPs Manuel Drees Bonn University Learning from WIMPs p. 1/29

Contents 1 Introduction Learning from WIMPs p. 2/29

Contents 1 Introduction 2 Learning about the early Universe Learning from WIMPs p. 2/29

Contents 1 Introduction 2 Learning about the early Universe 3 Learning about our galaxy Learning from WIMPs p. 2/29

Contents 1 Introduction 2 Learning about the early Universe 3 Learning about our galaxy 4 Summary Learning from WIMPs p. 2/29

Introduction: WIMPs as Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Learning from WIMPs p. 3/29

Introduction: WIMPs as Dark Matter Several observations indicate existence of non-luminous Dark Matter (DM) (more exactly: missing force) Galactic rotation curves imply Ω DM h 2 0.05. Ω: Mass density in units of critical density; Ω = 1 means flat Universe. h: Scaled Hubble constant. Observation: h = 0.72 ± 0.07 (?) Models of structure formation, X ray temperature of clusters of galaxies,... Learning from WIMPs p. 3/29

Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Learning from WIMPs p. 4/29

Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Learning from WIMPs p. 4/29

Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Consistent result: Ω bar h 2 0.02 Learning from WIMPs p. 4/29

Need for non baryonic DM Total baryon density is determined by: Big Bang Nucleosynthesis Analyses of CMB data Consistent result: Ω bar h 2 0.02 = Need non baryonic DM! Learning from WIMPs p. 4/29

Need for exotic particles Only possible non baryonic particle DM in SM: light neutrinos! Learning from WIMPs p. 5/29

Need for exotic particles Only possible non baryonic particle DM in SM: light neutrinos! Make hot DM: do not describe structure formation correctly = Ω ν h 2 < 0.01 Learning from WIMPs p. 5/29

Need for exotic particles Only possible non baryonic particle DM in SM: light neutrinos! Make hot DM: do not describe structure formation correctly = Ω ν h 2 < 0.01 = Need exotic particles as DM! Possible loophole: primordial black holes; not easy to make in sufficient quantity sufficiently early. Learning from WIMPs p. 5/29

What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) Learning from WIMPs p. 6/29

What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) which still survives today (lifetime τ 10 10 yrs) Learning from WIMPs p. 6/29

What we need Since h 2 0.5: Need 20% of critical density in Matter (with negligible pressure, w 0) which still survives today (lifetime τ 10 10 yrs) and has (strongly) suppressed coupling to elm radiation Learning from WIMPs p. 6/29

Weakly Interacting Massive Particles (WIMPs) Exist in well motivated extensions of the SM: SUSY, (Little Higgs with T Parity), ((Universal Extra Dimension)) Learning from WIMPs p. 7/29

Weakly Interacting Massive Particles (WIMPs) Exist in well motivated extensions of the SM: SUSY, (Little Higgs with T Parity), ((Universal Extra Dimension)) Can also (trivially) write down tailor made WIMP models In standard cosmology, roughly weak cross section automatically gives roughly right relic density for thermal WIMPs! (On logarithmic scale) Learning from WIMPs p. 7/29

WIMP production Let χ be a generic DM particle, n χ its number density (unit: GeV 3 ). Assume χ = χ, i.e. χχ SM particles is possible, but single production of χ is forbidden by some symmetry. Evolution of n χ determined by Boltzmann equation: dn χ dt + 3Hn χ = σ ann v ( n 2 χ ) n2 χ, eq + X,Y H = Ṙ/R : Hubble parameter... : Thermal averaging σ ann = σ(χχ SM particles) v : relative velocity between χ s in their cms n χ,eq : χ density in full equilibrium n X Γ(X χ + Y ) Learning from WIMPs p. 8/29

Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Learning from WIMPs p. 9/29

Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H Learning from WIMPs p. 9/29

Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H For T < m χ : n χ n χ, eq T 3/2 e m χ/t, H T 2 Learning from WIMPs p. 9/29

Thermal WIMP Assume χ was in full thermal equilibrium after inflation. Requires n χ σ ann v > H For T < m χ : n χ n χ, eq T 3/2 e m χ/t, H T 2 Inequality cannot be true for arbitrarily small T ; point where inequality becomes (approximate) equality defines decoupling (freeze out) temperature T F. Learning from WIMPs p. 9/29

Thermal WIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders Learning from WIMPs p. 10/29

Thermal WIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders No entropy production after χ decoupled: Not testable at colliders Learning from WIMPs p. 10/29

Thermal WIMPs: Assumptions χ is effectively stable, τ χ τ U : partly testable at colliders No entropy production after χ decoupled: Not testable at colliders H at time of χ decoupling is known: partly testable at colliders Universe must have been sufficiently hot: T R > T F m χ /20 Learning from WIMPs p. 10/29

Low temperature scenario Assume T R < T F, n χ (T R ) = 0 Learning from WIMPs p. 11/29

Low temperature scenario Assume T R < T F, n χ (T R ) = 0 Introduce dimensionless variables Y χ n χ s, x m χ T (s: entropy density). Use non relativistic expansion of cross section: σ ann = a + bv 2 + O(v 4 ) = σ ann v = a + 6b/x Using explicit form of H, Y χ,eq, Boltzmann eq. becomes dy χ dx = f ( a + 6b ) x x 2 ( Yχ 2 cx 3 e 2x). f = 1.32 m χ M Pl g, c = 0.0210gχ 2/g2 Learning from WIMPs p. 11/29

Low temperature scenario (cont. d) For T R T F : Annihilation term Y 2 χ negligible: defines 0 th order solution Y 0 (x), with Y 0 (x ) = fc [ a 2 x Re 2x R + ( a 4 + 3b) e 2x R]. Note: Ω χ h 2 σ ann in this case! For intermediate temperatures, T R < T F : Define 1st order solution Y 1 = Y 0 + δ. δ < 0 describes pure annihilation: dδ dx = f ( a + 6b ) Y0 (x) 2 x. x 2 δ(x) can be calculated analytically: δ σann 3 Learning from WIMPs p. 12/29

Numerical comparison: b = 0 MD, Imminniyaz, Kakizaki, hep-ph/0603165 10-1 Ω χ h 2 exact Ω χ h 2 old Ω χ h 2 new 10 0 Ω χ h 2 exact Ω χ h 2 old Ω χ h 2 new Ω χ h 2 10-2 x F = 23.5 Ω χ h 2 10-1 x F = 21.3 10-3 10 15 20 25 30 x 0 a = 10 8 GeV 2 10-2 10 15 20 25 30 x 0 a = 10 9 GeV 2 Can extend validity of new solution to all T, including T T R, by using Ω χ (T max ) if T R > T max T F Learning from WIMPs p. 13/29

Application: lower bound on T R for thermal WIMP MD, Imminniyaz, Kakizaki, in progress If n χ (T R ) = 0, demanding Ω χ h 2 0.1 imposes lower bound on T R : Learning from WIMPs p. 14/29

Application: lower bound on T R for thermal WIMP MD, Imminniyaz, Kakizaki, in progress If n χ (T R ) = 0, demanding Ω χ h 2 0.1 imposes lower bound on T R : Ω χ h 2 26 Ω χ h 2 26 24 24 0.119 0.079 1 0.1 10-2 22 20 18 x 0 0.119 0.079 1 0.1 10-2 22 20 18 x 0 10-10 10-9 10-8 10-716 10-9 10-8 10-7 10-616 a [GeV -2 ] b [GeV -2 ] Learning from WIMPs p. 14/29

Constraining H(T) Assumptions Learning from WIMPs p. 15/29

Constraining H(T) Assumptions Ω χ h 2 is known (see below) Learning from WIMPs p. 15/29

Constraining H(T) Assumptions Ω χ h 2 is known (see below) a, b are known (from collider experiments) Learning from WIMPs p. 15/29

Constraining H(T) Assumptions Ω χ h 2 is known (see below) a, b are known (from collider experiments) Only thermal χ production (otherwise no constraint) Learning from WIMPs p. 15/29

Constraining H(T) Assumptions Ω χ h 2 is known (see below) a, b are known (from collider experiments) Only thermal χ production (otherwise no constraint) Parameterize modified expansion history: A(z) = H st (z)/h(z), z = T/m χ Around decoupling: z 1 = use Taylor expansion A(z) = A(z F,st )+(z z F,st )A (z F,st )+(z z F,st ) 2 A (z F,st )/2 Learning from WIMPs p. 15/29

Constraining H(T) (cont.d) Assume T R T F = Ω χ h 2 1 R zf A(z)(a+6bz) dz 0 Learning from WIMPs p. 16/29

Constraining H(T) (cont.d) Assume T R T F = Ω χ h 2 1 R zf A(z)(a+6bz) dz 0 Ω χ h 2 400 300 a = 2*10-9 GeV -2 b = 0 k = 1 x F,st - x 0 = 4 A (z F ) 200 100 0 0.12 0.10 0.08-100 0 1 2 3 4 5 6 7 A(z F ) Learning from WIMPs p. 16/29

The case A (z F,st ) = 0 1.3 1.2 Ω χ h 2 a = 2*10-9 GeV -2 b = 0 x F,st - x 0 = 10 1.1 0.08 k 1 0.10 0.9 0.12 0.8 0.7 0 0.5 1 1.5 2 A(z F ) Learning from WIMPs p. 17/29

The case A (z F,st ) = 0 1.3 1.2 Ω χ h 2 a = 2*10-9 GeV -2 b = 0 x F,st - x 0 = 10 1.1 0.08 k 1 0.10 0.9 0.12 0.8 0.7 0 0.5 1 1.5 2 A(z F ) Relative constraint on A(z F,st ) weaker than that on Ω χ h 2. Learning from WIMPs p. 17/29

Direct WIMP detection WIMPs are everywhere! Learning from WIMPs p. 18/29

Direct WIMP detection WIMPs are everywhere! Can elastically scatter on nucleus in detector: χ + N χ + N Measured quantity: recoil energy of N Learning from WIMPs p. 18/29

Direct WIMP detection WIMPs are everywhere! Can elastically scatter on nucleus in detector: χ + N χ + N Measured quantity: recoil energy of N Detection needs ultrapure materials in deep underground location; way to distinguish recoils from β,γ events; neutron screening;... Learning from WIMPs p. 18/29

Direct WIMP detection: theory Counting rate given by dr dq = AF 2 (Q) v esc Q: recoil energy f 1 (v) v min v A= ρσ 0 /(2m χ m r ) = const.: encodes particle physics F(Q): nuclear form factor v: WIMP velocity in lab frame v 2 min = m NQ/(2m 2 r ) v esc : Escape velocity from galaxy f 1 (v): normalized one dimensional WIMP velocity distribution dv Learning from WIMPs p. 19/29

Direct reconstruction of f 1 MD & C.L. Shan, in progress f 1 (v) = N { 2Q d dq [ 1 F 2 (Q) ]} dr dq Q=2m 2 rv 2 /m N Learning from WIMPs p. 20/29

Direct reconstruction of f 1 MD & C.L. Shan, in progress f 1 (v) = N { 2Q d dq [ 1 F 2 (Q) ]} dr dq Q=2m 2 rv 2 /m N N : Normalization ( 0 f 1 (v)dv = 1). Learning from WIMPs p. 20/29

Direct reconstruction of f 1 MD & C.L. Shan, in progress f 1 (v) = N { 2Q d dq [ 1 F 2 (Q) ]} dr dq Q=2m 2 rv 2 /m N N : Normalization ( 0 f 1 (v)dv = 1). Need to know form factor = stick to spin independent scattering. Need to know m χ, but do not need σ 0,ρ. Learning from WIMPs p. 20/29

Determining the logarithmic slope of dr/dq Good local observable: Average energy transfer Q i in i th bin Learning from WIMPs p. 21/29

Determining the logarithmic slope of dr/dq Good local observable: Average energy transfer Q i in i th bin Stat. error on slope (bin width) 1.5 = need large bins Learning from WIMPs p. 21/29

Determining the logarithmic slope of dr/dq Good local observable: Average energy transfer Q i in i th bin Stat. error on slope (bin width) 1.5 = need large bins To maximize information: use overlapping bins ( windows ) Learning from WIMPs p. 21/29

Recoil spectrum: prediction and simulated measurement 0.004 χ 2 /dof = 0.73 500 events, 5 bins, up to 3 bins per window 0.003 f 1 (v) [s/km] 0.002 0.001 input distribution 0 0 100 200 300 400 500 600 700 v [km/s] Learning from WIMPs p. 22/29

Recoil spectrum: prediction and simulated measurement 0.004 5,000 events, 10 bins, up to 4 bins per window χ 2 /dof = 0.98 f 1 (v) [s/km] 0.003 0.002 input distribution 0.001 0 0 100 200 300 400 500 600 700 v [km/s] Learning from WIMPs p. 23/29

Statistical exclusion of constant f 1 0.1 Average over 1,000 experiments Probability 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 1e-09 median mean 1e-10 100 1000 N ev Learning from WIMPs p. 24/29

Statistical exclusion of constant f 1 0.1 Average over 1,000 experiments Probability 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 1e-09 median mean 1e-10 100 1000 N ev Need several hundred events to begin direct reconstruction! Learning from WIMPs p. 24/29

Determining moments of f 1 v n 0 v n f 1 (v)dv Learning from WIMPs p. 25/29

Determining moments of f 1 v n 0 v n f 1 (v)dv 0 Q (n 1)/2 1 F 2 (Q) dr dq dq Learning from WIMPs p. 25/29

Determining moments of f 1 v n 0 v n f 1 (v)dv 0 Q (n 1)/2 1 F 2 (Q) events a Q(n 1)/2 a F 2 (Q a ) dr dq dq Learning from WIMPs p. 25/29

Determining moments of f 1 v n 0 v n f 1 (v)dv 0 Q (n 1)/2 1 F 2 (Q) events a Q(n 1)/2 a F 2 (Q a ) dr dq dq Can incorporate finite energy (hence velocity) threshold Learning from WIMPs p. 25/29

Determining moments of f 1 v n 0 v n f 1 (v)dv 0 Q (n 1)/2 1 F 2 (Q) events a Q(n 1)/2 a F 2 (Q a ) dr dq dq Can incorporate finite energy (hence velocity) threshold Moments are strongly correlated! High moments, and their errors, are underestimated in typical experiment: get large contribution from large Q Learning from WIMPs p. 25/29

Determination of first 10 moments v n / v n exact 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 100 events 0 2 4 6 8 10 n Learning from WIMPs p. 26/29

Constraining a late infall component 1000 25 events, fit moments n = -1, 1, 2 800 χ 2 = 1 χ 2 = 4 v c [km/s] 600 400 200 0 0 0.2 0.4 0.6 0.8 1 N l Learning from WIMPs p. 27/29

Constraining a late infall component 1000 800 100 events, fit moments n = -1, 1, 2, 3 χ 2 = 1 χ 2 = 4 v c [km/s] 600 400 200 0 0 0.2 0.4 0.6 0.8 1 N l Learning from WIMPs p. 28/29

Summary Learning about the Early Universe: Learning from WIMPs p. 29/29

Summary Learning about the Early Universe: If all DM is thermal WIMPs: T R m χ /23 10 4 T BBN Learning from WIMPs p. 29/29

Summary Learning about the Early Universe: If all DM is thermal WIMPs: T R m χ /23 10 4 T BBN Error on Hubble parameter during WIMP freeze out somewhat bigger than that on Ω χ h 2 Learning about our galaxy Direct reconstruction of f 1 (v) needs several hundred events Non trivial statements about moments of f 1 possible with few dozen events Learning from WIMPs p. 29/29