DM models with two mediators. How to save the WIMP Michael Duerr MU Programmtag 2016 Mainz, 12 December 2016 based on: arXiv:1304.0576 , arXiv:1309.3970 , arXiv:1409.8165 , arXiv:1508.01425 , and arXiv:1606.07609 in collaboration with: P . Fileviez Pérez, F . Kahlhoefer, K. Schmidt-Hoberg, ➞ NASA Th. Schwetz, J. Smirnov, S. Vogl, M. B. Wise
DM–Standard Model interaction. thermal freeze-out (early Univ.) indirect detection (now) DM SM direct detection DM SM production at colliders Michael Duerr | DM models with two mediators | 12 December 2016 | page 2
Connecting different DM experiments. > T op-down approach: thermal freeze-out (early Univ.) Study well-motivated candidates for indirect detection (now) DM, obtained in complete models that DM SM solve theoretical issues of the SM (e.g., the hierarchy problem). direct detection Most signatures/constraints not related to DM. DM SM > Bottom-up approach: production at colliders Add the minimal amount of structure to the SM that is necessary to explain DM. How simple can these setups be? Michael Duerr | DM models with two mediators | 12 December 2016 | page 3
Dark matter theory space. Less complete Dipole Interactions “Sketches of models” More complete Dark Matter Dark Effective Field Theories Photon Minimal Supersymmetric Z ′ boson Standard Model Simplified Dark Matter Models Contact Interactions Complete Higgs Dark Matter Portal “Squarks” Models Universal Extra Dimensions Little Higgs [Worm et al. , arXiv:1506.03116 ] Michael Duerr | DM models with two mediators | 12 December 2016 | page 4
Effective theories and simplified models. > DM simplified model: > DM EFT: keep DM and one mediator only keep DM particle, (the lightest) integrate out the rest Z 2 Z 3 Z 2 Z 3 Z 1 10 TeV 10 TeV ≀ ≀ ≀ ≀ Z 1 1 TeV 1 TeV t, h, Z, W t, h, Z, W χ χ 100 GeV 100 GeV [Worm et al. , arXiv:1506.03116 ] Michael Duerr | DM models with two mediators | 12 December 2016 | page 5
Spin-0 simplified DM model. > Interaction of the scalar S with SM quarks q and DM χ : g q y q g q y q � � � � L ⊃ y χ ¯ qqS = y χ ¯ χχS + � χχS + � q L q R + q R q L S 2 2 q q Problems > gauge invariance: left- and right-handed SM fermions have different SU ( 2 ) L ⊗ U ( 1 ) Y charges > S is a SM singlet: why are terms like S | H | 2 , S 2 | H | 2 , S 3 , S 4 not included although allowed by EW symmetry. Solution χχS + μS | H | 2 to SM Lagrangian > Add terms L ⊃ y χ ¯ > There is mixing between the SM Higgs and the singlet, resulting in two mass eigenstates h 1 and h 2 > Interaction with the SM quarks through mixing. Michael Duerr | DM models with two mediators | 12 December 2016 | page 6
Spin-1 simplified DM model. > Fermionic DM χ interacts with SM fermions ƒ via a Z ′ gauge boson � � � DM γ μ + g A � � ƒ γ μ + g A L ⊃− Z ′ g V DM γ μ γ 5 Z ′ μ ¯ g V ƒ γ μ γ 5 μ ¯ χ χ − ƒ ƒ ƒ Questions > Where does this model come from? > What’s the origin of the masses? > Are there relations between the couplings? > Are the results obtained reliable? > Is SM gauge invariance guaranteed? > How to find interesting regions of parameter space? > . . . Michael Duerr | DM models with two mediators | 12 December 2016 | page 7
Spin-1 simplified model. > Fermionic DM χ interacts with SM fermions ƒ via a Z ′ gauge boson � � � DM γ μ + g A � � ƒ γ μ + g A L ⊃− Z ′ g V DM γ μ γ 5 Z ′ μ ¯ g V ƒ γ μ γ 5 μ ¯ χ χ − ƒ ƒ ƒ Perturbative unitarity in χχ → Z ′ L Z ′ L for axial coupling � 2 � sm χ � g A DM > Matrix element grows with energy: M ∝ m 2 Z ′ πm 2 � Z ′ > theory only valid up to s < � 2 m χ g A � DM > New physics below that scale to restore perturbative unitarity > Use the Higgs mechanism to generate mass of the mediator, break the new U ( 1 ) ′ with the vev of a SM singlet scalar. Michael Duerr | DM models with two mediators | 12 December 2016 | page 8
Part I: A consistent simplified DM model – two-mediator DM [MD, Kahlhoefer, Schmidt-Hoberg, Schwetz, Vogl, arXiv:1606.07609 ]
Dark matter model with two mediators. > Majorana DM particle χ and two mediators: > massive vector boson Z ′ and real scalar s > Natural framework: SM gauge group extended by spontaneously broken U ( 1 ) ′ → generation of mass for χ and Z ′ > Interactions of DM and the SM quarks with the mediators: g χ y χ χγ μ γ 5 χZ ′ L χ ⊃ − ¯ μ − ¯ � χχs 2 2 2 m q � � � qγ μ qZ ′ L q ⊃ − g q ¯ μ + sin θ ¯ qqs q Michael Duerr | DM models with two mediators | 12 December 2016 | page 10
Dark matter model with two mediators. > Majorana DM particle χ and two mediators: > massive vector boson Z ′ and real scalar s > Natural framework: SM gauge group extended by spontaneously broken U ( 1 ) ′ → generation of mass for χ and Z ′ > Interactions of DM and the SM quarks with the mediators: g χ y χ χγ μ γ 5 χZ ′ L χ ⊃ − ¯ μ − ¯ � χχs 2 2 2 m q � � � qγ μ qZ ′ L q ⊃ − g q ¯ μ + sin θ ¯ qqs q > couplings are connected: > 6 independent parameters: particle masses coupling constants y χ g χ � DM mass m χ dark-sector coupling g χ or y χ = 2 2 Z ′ mass quark– Z ′ coupling m Z ′ g q m χ m Z ′ dark Higgs mass m s Higgs mixing angle θ Michael Duerr | DM models with two mediators | 12 December 2016 | page 10
Dark matter model with two mediators. > Majorana DM particle χ and two mediators: > massive vector boson Z ′ and real scalar s > Natural framework: SM gauge group extended by spontaneously broken U ( 1 ) ′ → generation of mass for χ and Z ′ > Interactions of DM and the SM quarks with the mediators: g χ y χ χγ μ γ 5 χZ ′ L χ ⊃ − ¯ μ − ¯ � χχs 2 flavor-universal vector 2 2 couplings to quarks m q � = baryon number � � qγ μ qZ ′ L q ⊃ − g q ¯ μ + sin θ ¯ qqs → see model building later q > couplings are connected: > 6 independent parameters: particle masses coupling constants y χ g χ � DM mass m χ dark-sector coupling g χ or y χ = 2 2 Z ′ mass quark– Z ′ coupling m Z ′ g q m χ m Z ′ dark Higgs mass m s Higgs mixing angle θ Michael Duerr | DM models with two mediators | 12 December 2016 | page 10
The connection to simplified models. > A combination of different simplified models: g q ≫ sin θ g q ∼ sin θ sin θ ≫ g q Spin-1 mediator Spin-0 mediator with m s ≫ m Z ′ simplified model spin-1 terminator m Z ′ ∼ m s T wo-mediator model Spin-1 mediator with Spin-0 mediator m Z ′ ≫ m s spin-0 terminator simplified model Michael Duerr | DM models with two mediators | 12 December 2016 | page 11
The connection to simplified models. > A combination of different simplified models: g q ≫ sin θ g q ∼ sin θ sin θ ≫ g q Spin-1 mediator Spin-0 mediator with m s ≫ m Z ′ simplified model spin-1 terminator m Z ′ ∼ m s T wo-mediator model Spin-1 mediator with Spin-0 mediator m Z ′ ≫ m s spin-0 terminator simplified model DM Dark terminator Dark terminator new final state for DM annihilation DM Dark terminator Michael Duerr | DM models with two mediators | 12 December 2016 | page 11
The connection to simplified models. > A combination of different simplified models: g q ≫ sin θ g q ∼ sin θ sin θ ≫ g q Spin-1 mediator Spin-0 mediator with m s ≫ m Z ′ simplified model spin-1 terminator m Z ′ ∼ m s T wo-mediator model Spin-1 mediator with Spin-0 mediator m Z ′ ≫ m s spin-0 terminator simplified model > Additional effects not present in usual simplified models: > The two mediators can interact with each other: leading to processes like χχ → Z ′ ∗ → Z ′ s or χχ → s ∗ → Z ′ Z ′ > Mixing between the dark Higgs and the SM Higgs: gauge-invariant realisation of simplified model with spin-0 s -channel mediator > DM stability is a consequence of the gauge symmetry > Kinetic mixing at loop level from SM quarks Michael Duerr | DM models with two mediators | 12 December 2016 | page 11
Spin-1 mediation ( θ ≈ 0). m χ = 100 GeV Partial wave perturbative unitarity: Monojets Perturbative unitarity violation g q = 0.1 > conditions on couplings and masses 10 0 > from χχ → χχ : � � 4 π , 8 π g χ < y χ < g χ Direct detection > equations can be rewritten in terms of 10 - 1 the couplings, e.g., � g χ m χ /m Z ′ < π Dileptons EWPT > from ss → ss and hh → hh : Dijets � 10 - 2 9 ( λ h − λ s ) 2 + λ 2 3 ( λ h + λ s ) ± hs < 16 π 10 1 10 2 10 3 10 4 m Z ' [ GeV ] > for λ hs = 0 (no Higgs mixing): > Relic density curve � m s < 4 π/ 3 m Z ′ /g χ > solid: m s = 3 m χ > dashed: m s = 0 . 1 m χ Michael Duerr | DM models with two mediators | 12 December 2016 | page 12
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