Towards improved overclosure bounds for WIMP-like dark matter models - PowerPoint PPT Presentation

Towards improved overclosure bounds for WIMP-like dark matter models Simone Biondini Albert Einstein Center - Institute for Theoretical Physics, Universit¨ at Bern Strong and Electroweak Matter Conference, Barcelona Tuesday, June 26 in collaboration with Mikko Laine JHEP 1804 (2018) 072 S. Biondini (AEC) SEWM 2018, Barcelona 1 / 46

Outline 1 Motivation and Introduction 2 Non-relativistic WIMPs in a thermal bath 3 Majorana DM with strongly interacting mediators 4 Conclusions and Outlook S. Biondini (AEC) SEWM 2018, Barcelona 2 / 46

Motivation and Introduction Evidence for Dark Matter Star-velocity distribution in a galaxy V. Rubin and W. Ford (1970) 1 Strong and weak gravitational lensing J. K. Adelman-McCarthy et al. (2005) 2 Even at cosmological scales from the Cosmic Microwave Background P.A.R. Ade et al. 1502.01589 early universe before recombination : baryon-photon fluid oscillations Ω m , Ω b and photons dynamics of the fluid: gravitational collapse vs expansion due to pressure Ω dm h 2 = 0 . 1186 ± 0 . 0020 Ω b h 2 = 0 . 02226 ± 0 . 00023 Ω b consistent with BBN predictions! S. Biondini (AEC) SEWM 2018, Barcelona 3 / 46

Motivation and Introduction Weakly interacting massive particles Many candidates: axions, sterile neutrinos, composite dark matter ... G. Gelmini 1502.01320 WIMPs are attractive for some reasons arise to solve problems within particle physics realm (SUSY, extra dimensions...) relic abundance from freeze-out (Ω dm h 2 today) testable experimentally with direct, indirect and collider searches 10 1 non � pert. ATLAS jets � ETmiss 10 0 XENON100 100 m Η � m Χ � 1 H . E . S . S . 25. ATLAS Monojet 10 � 1 LUX 50. Η � squark 100 No thermal WIMP How reliable is the curve obtained from the 10 � 2 10 2 10 3 cosmological relic abundance? m Χ � GeV � 1403.4634 S. Biondini (AEC) SEWM 2018, Barcelona 4 / 46

Motivation and Introduction Wimp relic density and overclosure bound χ in equilibrium in the early universe: χχ ↔ f ¯ f Recombination f ¯ f → χχ is Boltzmann suppressed at T < M dn χ n 2 χ − n 2 � � dt + 3 Hn χ = −� σ v � χ, eq T / M ⇒ � σ v � ≈ � a + bv 2 + . . . � = a + 3 � σ v � ≈ α 2 � 2 b T v ≈ M + . . . , M 2 new variables Y χ = n χ / s and z = M / T -3 M M = 0.5 TeV, ∆ M = 10 -8 10 λ 3,4,5 = 0 Ω dm h 2 λ 3,4,5 = 1 -10 10 λ 3,4,5 = π overclosure Y -12 10 0 . 1186 -14 10 viable Y eq -16 10 1 2 3 10 10 10 M exp . bounds z = M / T S. Biondini (AEC) SEWM 2018, Barcelona 5 / 46

Non-relativistic WIMPs in a thermal bath Wimp in a thermal bath χ are non-relativistic and have time to experience several interactions in the freeze-out regime it holds M ≫ π T , gT , Mv , Mv 2 a) Mass correction b) Sommerfeld effect c) Interaction rate and bound states How does all this reflect into the χχ annihilation? . . . soft hard S. Biondini (AEC) SEWM 2018, Barcelona 6 / 46

Non-relativistic WIMPs in a thermal bath Factorizing the annihilation rate Annihilation of a heavy pair: DM-DM, with energies ∼ 2 M (forget about T ) O = i c M 2 φ † φ † φφ , c ≈ α 2 (inclusive s-wave annihilation ) G. T. Bodwin, E. Braaten and G. P. Lepage hep-ph/9407339 c M ≫ T ⇒ ∆ x ∼ 1 M ≪ 1 1 k ∼ T local and insensitive to the thermal scales we want to ”thermal-average” . . . � φ † φ † φφ � T soft hard S. Biondini (AEC) SEWM 2018, Barcelona 7 / 46

Non-relativistic WIMPs in a thermal bath Beyond the free case: the spectral function Compare Boltzmann equation with linear response theory ( ∂ t + 3 H ) n = −� σ v � ( n 2 − n 2 eq ) and ( ∂ t + 3 H ) n = − Γ chem ( n − n eq ) � σ v � ≡ Γ chem 2 n eq ⇒ � σ v � = 4 c where γ = � φ † φ † φφ � T M 2 γ n 2 eq D. Bodeker and M. Laine 1205.4987; S. Kim and M. Laine 1602.08105; S. Kim and M. Laine 1609.00474 S. Biondini (AEC) SEWM 2018, Barcelona 8 / 46

Non-relativistic WIMPs in a thermal bath Beyond the free case: the spectral function Compare Boltzmann equation with linear response theory ( ∂ t + 3 H ) n = −� σ v � ( n 2 − n 2 eq ) and ( ∂ t + 3 H ) n = − Γ chem ( n − n eq ) � σ v � ≡ Γ chem 2 n eq ⇒ � σ v � = 4 c where γ = � φ † φ † φφ � T M 2 γ n 2 eq D. Bodeker and M. Laine 1205.4987; S. Kim and M. Laine 1602.08105; S. Kim and M. Laine 1609.00474 thermal expectation value of the operators that annihilate/create a DM-DM pair γ = 1 � e − E m / T � m | φ † φ † | n �� n | φφ | m � Z m , n any correlator in equilibrium can be expressed in terms of a spectral function � ∞ � e i ω t − i k · r � 1 � � ( φφ )( t , r ) , ( φ † φ † )(0 , 0 ) ρ ( ω, k ) = dt � T 2 −∞ r � ∞ d ω � π e − ω ρ ( ω, k ) + O ( e − 4 M / T ) , α 2 M ≪ Λ ∼ M γ = T 2 M − Λ k S. Biondini (AEC) SEWM 2018, Barcelona 8 / 46

Non-relativistic WIMPs in a thermal bath From ρ to a Schr¨ odinger equation ρ is extracted from the imaginary part of a Green’s function Y. Burnier, M. Laine and M. Vepsalainen, (2007) E m ≡ ω = E ′ + 2 M + k 2 H = − ∇ 2 4 M , M + V ( r ) H − i Γ − E ′ � G ( E ′ ; r , r ′ ) = N δ 3 ( r − r ′ ) , r , r ′ → 0 Im G ( E ′ ; r , r ′ ) = ρ ( E ′ ) � lim S. Biondini (AEC) SEWM 2018, Barcelona 9 / 46

Non-relativistic WIMPs in a thermal bath From ρ to a Schr¨ odinger equation ρ is extracted from the imaginary part of a Green’s function Y. Burnier, M. Laine and M. Vepsalainen, (2007) E m ≡ ω = E ′ + 2 M + k 2 H = − ∇ 2 4 M , M + V ( r ) H − i Γ − E ′ � G ( E ′ ; r , r ′ ) = N δ 3 ( r − r ′ ) , r , r ′ → 0 Im G ( E ′ ; r , r ′ ) = ρ ( E ′ ) � lim � 3 � ∞ dE ′ T ρ ( E ′ ) → γ free = n 2 � MT π e − E ′ c 2 e − 2 M eq γ ≈ ⇒ � σ v � = T M 2 2 π 4 − Λ ρ ω 2 M S. Biondini (AEC) SEWM 2018, Barcelona 9 / 46

Non-relativistic WIMPs in a thermal bath From ρ to a Schr¨ odinger equation ρ is extracted from the imaginary part of a Green’s function Y. Burnier, M. Laine and M. Vepsalainen, (2007) E m ≡ ω = E ′ + 2 M + k 2 H = − ∇ 2 4 M , M + V ( r ) H − i Γ − E ′ � G ( E ′ ; r , r ′ ) = N δ 3 ( r − r ′ ) , r , r ′ → 0 Im G ( E ′ ; r , r ′ ) = ρ ( E ′ ) � lim � 3 � ∞ dE ′ � MT π e − E ′ 2 e − 2 M T ρ ( E ′ ) γ ≈ T 2 π − Λ ρ ∼ 2 M − α 2 M ω 2 M S. Biondini (AEC) SEWM 2018, Barcelona 10 / 46

Non-relativistic WIMPs in a thermal bath From ρ to a Schr¨ odinger equation ρ is extracted from the imaginary part of a Green’s function Y. Burnier, M. Laine and M. Vepsalainen, (2007) E m ≡ ω = E ′ + 2 M + k 2 H = − ∇ 2 4 M , M + V ( r ) H − i Γ − E ′ � G ( E ′ ; r , r ′ ) = N δ 3 ( r − r ′ ) , r , r ′ → 0 Im G ( E ′ ; r , r ′ ) = ρ ( E ′ ) � lim � 3 � ∞ dE ′ � MT π e − E ′ 2 e − 2 M T ρ ( E ′ ) γ ≈ T 2 π − Λ ρ ∼ 2 M − α 2 M ω 2 M S. Biondini (AEC) SEWM 2018, Barcelona 11 / 46

Non-relativistic WIMPs in a thermal bath Summary of the theoretical framework relic density can be computed in some steps M. Laine and S.‘Kim 1609.00474 Calculate the matching coefficients from the hard annihilation process, E ∼ 2 M Compute the static potentials and thermal widths induced by the particle exchanged by the heavy ones Extract the spectral function ⇒ annihilation rate Solve the Boltzmann equation with the thermal cross section Thermal Bound state SM dynamics potentials formation at T � = 0 � σv � T ann Boltzmann equation Overclosure bounds S. Biondini (AEC) SEWM 2018, Barcelona 12 / 46

Majorana DM with strongly interacting mediators Majorana DM and QCD colored scalar To link effectively a BSM theory and dark matter example: SUSY has a rather large parameter space Constraints are set on a simple model that captures the most relevant physics A. De Simone and T. Jacques 1603.08002 Majorana fermion DM + Coloured mediator L = L SM + L χ + L η + L int χ = 1 ∂χ − M � 2 L η = ( D µ η ) † ( D µ η ) − M 2 � L M η η † η − λ 2 η † η χ i / 2 ¯ 2 ¯ χχ , L int = − y η † ¯ χ P R q − y ∗ ¯ qP L χη − λ 3 η † η H † H M. Garny, A. Ibarra and S. Vogl 1503.01500 the annihilation of χχ pairs is p-wave suppressed J. Edsj¨ o and P. Gondolo hep/ph-9704361 ⇒ the role of the (co)annihilating η is important and driven by QCD � σ v � ≈ � σ v � χχ + e − ∆ M M � σ v � ηχ + e − 2 ∆ M M � σ v � ηη S. Biondini (AEC) SEWM 2018, Barcelona 13 / 46

Majorana DM with strongly interacting mediators Non-relativistic fields � φ e − iMt + ϕ † e iMt � and χ = ( ψ e − iMt , − i σ 2 ψ ∗ e iMt ) 1 Again η = √ 2 M � � � c 1 ψ † p ψ † ψ † p φ † α ψ p φ α + ψ † p ϕ † L abs = i q ψ q ψ p + c 2 α ψ p ϕ α �� � c 3 φ † α ϕ † α ϕ β φ β + c 4 φ † α ϕ † β ϕ γ φ δ T a αβ T a φ † α φ † β φ β φ α + ϕ † α ϕ † + γδ + c 5 β ϕ β ϕ α Simplification in the Majorana fermion sector: ψ † p ψ † r ψ s ψ q σ k pq σ k rs = − 3 ψ † p ψ † q ψ q ψ p a possible spin-dependent operator is reduced to a spin-independent one matching the c i with standard T = 0 techniques S. Biondini (AEC) SEWM 2018, Barcelona 14 / 46