Perturbative Unitarity Constraints On (non-)SUSY Higgs Portals - PowerPoint PPT Presentation

Perturbative Unitarity Constraints On (non-)SUSY Higgs Portals Devin Walker SLAC arXiv:1310.8286 and in collaboration with K. Betre and S. El Hedri (to appear)

A Brief History of New Physics • Historically perturbative unitarity arguments have reliably indicated when new, perturbative physics will appear: Fermi theory: Dimension six operators violate unitarity around 350 GeV. Rescued: W boson at 80 GeV. Light pion effective theory: Pion scattering violates unitarity around 1.2 GeV. Rescued: Axial and vector resonances at 800 MeV. Electroweak theory: WW scattering requires new physics around 1.2 TeV. Rescued: SM Higgs boson at 125.5 GeV. A primary motivation for 14 TeV LHC! 2

! H. Murayama, LP2013

• Today: Use perturbative unitarity constraints and the thermal dark matter hypothesis to place bounds on Higgs portal dark matter as well as the visible particles needed for annihilation. (Aside: Essentially, trying to replace naturalness arguments with more rigorous perturbative unitarity arguments to get a better understanding of when new physics will appear.) 4

Today’s Talk • Basic Philosophy • A (Non-SUSY) Higgs portal • Two models with fermionic dark matter • Perturbative unitarity arguments/relic abundance • Bounds/Signatures • NMSSM Higgs portal • NMSSM review • Perturbative unitarity arguments/relic abundance • Mass/bounds on SUSY Breaking scales • Some Signatures • Conclusions 5

Basic Philosophy 6

Basic Philosophy • For the basic philosophy, consider a generic Higgs portal: 1. A dark Higgs that couples directly to dark matter. 2. The dark and the SM Higgses mix to facilitate dark matter annihilations. 7

Basic Philosophy • Now consider simple WW scattering amplitudes: g 2 M gauge = ( s + t ) ( 4 m 2 W g 2 ( s + t ) cos 2 θ M SM higgs = − 4 m 2 W g 2 ( s + t ) sin 2 θ M dark higgs = − 4 m 2 W 8

Basic Philosophy • Now consider simple WW scattering amplitudes: g 2 M gauge = ( s + t ) ( 4 m 2 W g 2 ( s + t ) cos 2 θ M SM higgs = − 4 m 2 W g 2 ( s + t ) sin 2 θ M dark higgs = − 4 m 2 W Both higgses needed to unitarize WW scattering because of the mixing. 9

Basic Philosophy • Now consider simple WW scattering amplitudes: g 2 M gauge = ( s + t ) ( 4 m 2 W g 2 ( s + t ) cos 2 θ M SM higgs = − 4 m 2 W g 2 ( s + t ) sin 2 θ M dark higgs = − 4 m 2 W Both higgses needed to unitarize WW scattering because of the mixing. • As the dark Higgs mass is raised, one is forced to set the mixing angle to zero to satisfy unitarity. 10

Basic Philosophy • However, (in the decoupled dark Higgs limit) the relic abundance prevents . sin θ → 0 ( DM SM Higgs SM DM SM Higgs ⟨ σ | v | ⟩ ∼ sin 4 θ ⟨ σ | v | ⟩ ∼ sin 2 θ cos 2 θ . m 2 m 2 χ χ 11

Basic Philosophy • However, (in the decoupled dark Higgs limit) the relic abundance prevents . sin θ → 0 ( DM SM Higgs SM DM SM Higgs ⟨ σ | v | ⟩ ∼ sin 4 θ ⟨ σ | v | ⟩ ∼ sin 2 θ cos 2 θ . m 2 m 2 χ χ 12

Basic Philosophy • However, (in the decoupled dark Higgs limit) the relic abundance prevents . sin θ → 0 ( DM SM Higgs SM DM SM Higgs ⟨ σ | v | ⟩ ∼ sin 4 θ ⟨ σ | v | ⟩ ∼ sin 2 θ cos 2 θ . m 2 m 2 χ χ • The dark Higgs mass cannot completely decoupling. 13

Basic Philosophy • General Philosophy: Generate tension between unitarity and low- energy observables (e.g. relic abundance) to produce upper bounds on new particles. • Basic claim: Relic abundance constraints (WIMP dark matter) + SM Higgs mass constraints + Unitarity constraints = New (tighter) Physics Bounds 14

A (non-SUSY) Higgs Portal 15

A (non-SUSY) Higgs Portal • A Higgs portal: � � � � 2 � 2 h † h − v 2 φ 2 − u 2 � �� � h † h − v 2 φ 2 − u 2 � � + λ 3 V = λ 1 + λ 2 2 2 2 2 � � L = χ λ χ V + i λ χ A γ 5 Φ χ . 16

A (non-SUSY) Higgs Portal • A Higgs portal: � � � � 2 � 2 h † h − v 2 φ 2 − u 2 � �� � h † h − v 2 φ 2 − u 2 � � + λ 3 V = λ 1 + λ 2 2 2 2 2 mixing term � � L = χ λ χ V + i λ χ A γ 5 Φ χ . dark matter 17

A (non-SUSY) Higgs Portal • A Higgs portal: � � � � 2 � 2 h † h − v 2 φ 2 − u 2 � �� � h † h − v 2 φ 2 − u 2 � � + λ 3 V = λ 1 + λ 2 2 2 2 2 mixing term � � L = χ λ χ V + i λ χ A γ 5 Φ χ . Pseudo-scalar coupling for Model 2. dark matter Important for dark matter annihilation channels. • Two models: Model 1: λ χ A = 0, Model 2: λ χ A and λ χ V are non-zero, 18

A (non-SUSY) Higgs Portal • Masses and mixings: λ 2 � � � h ′ � � cos θ − sin θ � � h � m 2 h = 2 λ 1 v 2 3 1 − + . . . = 4 λ 1 λ 2 ρ ′ sin θ cos θ ρ � 1 + λ 2 v 2 � � m 2 ρ = 2 λ 2 u 2 3 u 2 + . . . 4 λ 2 sin θ ∼ λ 3 v 2 2 λ 2 u. 19

A (non-SUSY) Higgs Portal • Masses and mixings: λ 2 � � � h ′ � � cos θ − sin θ � � h � m 2 h = 2 λ 1 v 2 3 1 − + . . . = 4 λ 1 λ 2 ρ ′ sin θ cos θ ρ � 1 + λ 2 v 2 � � m 2 ρ = 2 λ 2 u 2 3 u 2 + . . . 4 λ 2 sin θ ∼ λ 3 v 2 2 λ 2 u. dark Higgs mixing angle • Interested in the limit where the dark Higgs is heavy but the mixing angle is non-trivial. 20

Relic Abundance • t-channel annihilation: (heavy dark Higgs limit) sin 4 θ � 1 − m 2 � � 2 � h m 2 λ 4 χ A + 6 λ 2 χ A λ 2 χ V + λ 4 − m 2 λ 2 χ A + λ 2 � � � ⟨ σ | v | ⟩ = + . . . h � 2 m 2 χ χ V χ V � χ − m 2 4 π 2 m 2 χ h • s-channel annihilation: (heavy dark Higgs limit) � 2 � χ A sin 2 θ cos 2 θ � � � ff = λ 2 m 2 m 2 χ − m 2 g m f � f f ⟨ σ | v | ⟩ ¯ 1 − + . . . m 2 � 2 4 π m W � χ − m 2 4 m 2 χ f = u,d,c,s,t,b,e,µ, τ h W sin 2 θ cos 2 θ � � �� � = λ 2 χ A m 2 g 2 1 − m 2 � V V h 3 m 4 V − 4 m 2 V m 2 χ + 4 m 4 ⟨ σ | v | ⟩ V V + . . . � 2 m 2 χ 8 π � m 4 χ − m 2 4 m 2 χ V = W,Z V h χ A sin 2 θ � ⟨ σ | v | ⟩ hh = λ 2 h 3 λ 2 1 − m 2 9 u 2 h � 2 + . . . 2 π m 2 � χ − m 2 4 m 2 χ h 21

Relic Abundance • t-channel annihilation: (heavy dark Higgs limit) sin 4 θ � 1 − m 2 � � 2 � h m 2 λ 4 χ A + 6 λ 2 χ A λ 2 χ V + λ 4 − m 2 λ 2 χ A + λ 2 � � � ⟨ σ | v | ⟩ = + . . . h � 2 m 2 χ χ V χ V � χ − m 2 4 π 2 m 2 χ h • s-channel annihilation: (heavy dark Higgs limit) � 2 � χ A sin 2 θ cos 2 θ � � � ff = λ 2 m 2 m 2 χ − m 2 g m f � f f ⟨ σ | v | ⟩ ¯ 1 − + . . . m 2 � 2 4 π m W � χ − m 2 4 m 2 χ f = u,d,c,s,t,b,e,µ, τ h W sin 2 θ cos 2 θ � � �� � = λ 2 χ A m 2 g 2 1 − m 2 � V V h 3 m 4 V − 4 m 2 V m 2 χ + 4 m 4 ⟨ σ | v | ⟩ V V + . . . � 2 m 2 χ 8 π � m 4 χ − m 2 4 m 2 χ V = W,Z V h Proportional to χ A sin 2 θ � ⟨ σ | v | ⟩ hh = λ 2 h 3 λ 2 1 − m 2 9 u 2 h � 2 + . . . pseudo-scalar 2 π m 2 � χ − m 2 4 m 2 χ h coupling *Lopez-Honorez, Schwetz and Zupan, Phys. Lett. B 716, 179 22

Unitarity Considerations • Dark matter/dark matter scattering: (Similar to unitarity bounds* on heavy 4th generation fermions) DM DM Dark Higgs DM Dark Higgs DM * Furman, Hinchliffe and Chanowitz, Nuclear Physics B153, 402; Physics Letters B78, 285 23

Full Unitarity Considerations (Goldstone Boson Limit) � � L , Z L Z L 2 , hh 2 , ρρ W + L W − √ √ √ 2 , h ρ , hZ L , ρ Z L M c 2 s 2 1 sc ⎛ ⎞ 1 0 0 s 2 c 2 ⎛ ⎞ √ √ √ 32 − sc 0 0 0 0 2 8 8 8 √ √ 4 32 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ c 2 s 2 1 3 ⎜ ⎟ sc 0 0 ⎜ ⎟ s 2 c 2 − sc √ √ ⎜ 0 0 0 0 ⎟ 4 4 4 ⎜ 8 8 ⎟ √ ⎜ 8 8 ⎟ 32 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ c 2 c 2 3 c 4 3 s 2 c 2 3 sc 3 ⎜ ⎟ 0 0 ⎜ ⎟ s 2 s 2 √ √ ⎜ ⎟ 0 0 κ δ ξ 4 4 4 ⎜ ⎟ 8 8 √ ⎜ ⎟ 8 32 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ − λ 1 M (0) ⎜ ⎟ − λ 3 ⎜ ⎟ = s 2 s 2 3 s 2 c 2 3 s 4 3 cs 3 ⎜ 0 0 ⎟ c 2 c 2 ⎜ ⎟ √ √ 0 0 I δ α β 4 π ⎜ 4 4 4 ⎟ 8 8 4 π √ ⎜ ⎟ 8 32 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 3 sc 3 3 cs 3 3 c 2 s 2 ⎜ ⎟ sc sc − sc − sc 0 0 ξ β η 0 0 ⎜ ⎟ √ √ √ ⎜ ⎟ 2 2 √ 8 8 8 4 ⎜ ⎟ 32 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ c 2 s 2 ⎜ sc ⎟ − sc 0 0 0 0 0 ⎜ ⎟ 0 0 0 0 0 ⎜ ⎟ 2 2 ⎜ ⎟ 4 4 ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ s 2 c 2 sc − sc 0 0 0 0 0 0 0 0 0 0 2 2 4 4 24