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

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Perturbative Unitarity Constraints On (non-)SUSY Higgs Portals

and in collaboration with K. Betre and S. El Hedri (to appear) Devin Walker SLAC arXiv:1310.8286

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A Brief History of New Physics

2

• 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!

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• H. Murayama, LP2013

!

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4

• Today: Use perturbative unitarity constraints and the

thermal dark matter hypothesis to place bounds

• n 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.)

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Today’s Talk

5

• 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

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6

Basic Philosophy

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• 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.

Basic Philosophy

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8

• Now consider simple WW scattering amplitudes:

Mgauge = g2 4 m2

W

(s + t) ( MSM higgs = − g2 4 m2

W

(s + t) cos2 θ Mdark higgs = − g2 4 m2

W

(s + t) sin2 θ

Basic Philosophy

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9

Both higgses needed to unitarize WW scattering because of the mixing.

Mgauge = g2 4 m2

W

(s + t) ( MSM higgs = − g2 4 m2

W

(s + t) cos2 θ Mdark higgs = − g2 4 m2

W

(s + t) sin2 θ

• Now consider simple WW scattering amplitudes:

Basic Philosophy

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10

Mgauge = g2 4 m2

W

(s + t) ( MSM higgs = − g2 4 m2

W

(s + t) cos2 θ Mdark higgs = − g2 4 m2

W

(s + t) sin2 θ

• As the dark Higgs mass is raised, one is forced to set

the mixing angle to zero to satisfy unitarity.

• Now consider simple WW scattering amplitudes:

Basic Philosophy

Both higgses needed to unitarize WW scattering because of the mixing.

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• However, (in the decoupled dark Higgs limit) the relic

abundance prevents .

DM SM Higgs DM SM

⟨σ|v|⟩ ∼ sin4 θ m2

χ

⟨σ|v|⟩ ∼ sin2 θ cos2 θ m2

χ

.

SM Higgs

sin θ → 0 (

Basic Philosophy

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DM SM Higgs DM SM

⟨σ|v|⟩ ∼ sin4 θ m2

χ

⟨σ|v|⟩ ∼ sin2 θ cos2 θ m2

χ

.

SM Higgs

Basic Philosophy

• However, (in the decoupled dark Higgs limit) the relic

abundance prevents .

sin θ → 0 (

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13

DM SM Higgs DM SM

⟨σ|v|⟩ ∼ sin4 θ m2

χ

⟨σ|v|⟩ ∼ sin2 θ cos2 θ m2

χ

.

SM Higgs

• The dark Higgs mass cannot completely decoupling.

Basic Philosophy

• However, (in the decoupled dark Higgs limit) the relic

abundance prevents .

sin θ → 0 (

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• 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

Basic Philosophy

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A (non-SUSY) Higgs Portal

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A (non-SUSY) Higgs Portal

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• A Higgs portal:

L = χ

• λχV + i λχAγ5
• Φ χ.

V = λ1

• h†h − v2

2 2 + λ2

• φ2 − u2

2 2

• + λ3
• h†h − v2

2

• φ2 − u2

2

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A (non-SUSY) Higgs Portal

17

V = λ1

• h†h − v2

2 2 + λ2

• φ2 − u2

2 2

• + λ3
• h†h − v2

2

• φ2 − u2

2

• mixing term

dark matter L = χ

• λχV + i λχAγ5
• Φ χ.
• A Higgs portal:

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A (non-SUSY) Higgs Portal

18

V = λ1

• h†h − v2

2 2 + λ2

• φ2 − u2

2 2

• + λ3
• h†h − v2

2

• φ2 − u2

2

• mixing term

dark matter

• Two models:

Model 1: λχ A = 0, Model 2: λχ A and λχ V are non-zero,

Pseudo-scalar coupling for Model 2. Important for dark matter annihilation channels. L = χ

• λχV + i λχAγ5
• Φ χ.
• A Higgs portal:

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• Masses and mixings:

m2

h = 2 λ1v2

• 1 −

λ2

3

4 λ1λ2 + . . .

• m2

ρ = 2 λ2 u2

• 1 + λ2

3

4 λ2

2

v2 u2 + . . .

• h′

ρ′

• =

cos θ − sin θ sin θ cos θ h ρ

• sin θ ∼ λ3 v

2λ2 u.

A (non-SUSY) Higgs Portal

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m2

h = 2 λ1v2

• 1 −

λ2

3

4 λ1λ2 + . . .

• m2

ρ = 2 λ2 u2

• 1 + λ2

3

4 λ2

2

v2 u2 + . . .

• h′

ρ′

• =

cos θ − sin θ sin θ cos θ h ρ

• dark Higgs
• sin θ ∼ λ3 v

2λ2 u.

mixing angle

A (non-SUSY) Higgs Portal

• Masses and mixings:
• Interested in the limit where the dark Higgs is heavy

but the mixing angle is non-trivial.

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• t-channel annihilation:

(heavy dark Higgs limit)

Relic Abundance

⟨σ|v|⟩ = sin4 θ 4π

• 2 m2

χ − m2 h

2

• 1 − m2

h

m2

χ

• m2

χ

• λ4

χA + 6 λ2 χAλ2 χV + λ4 χV

• − m2

h

• λ2

χA + λ2 χV

2 + . . .

• s-channel annihilation:

(heavy dark Higgs limit)

⟨σ|v|⟩ ¯

ff = λ2 χA sin2 θ cos2 θ

4π

• f=u,d,c,s,t,b,e,µ,τ
• 1 −

m2

f

m2

χ

• g mf

mW 2 m2

χ − m2 f

• 4 m2

χ − m2 h

2

• + . . .

⟨σ|v|⟩V V = λ2

χA m2 W sin2 θ cos2 θ

8 π

• V =W,Z
• 1 − m2

V

m2

χ

• g2

V h

m4

V

• 4m2

χ − m2 h

2

• 3 m4

V − 4m2 V m2 χ + 4 m4 χ

• + . . .

⟨σ|v|⟩hh = λ2

h3 λ2 χA sin2 θ

2 π

• 1 − m2

h

m2

χ

9 u2

• 4 m2

χ − m2 h

2 + . . .

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• t-channel annihilation:

(heavy dark Higgs limit)

Relic Abundance

⟨σ|v|⟩ = sin4 θ 4π

• 2 m2

χ − m2 h

2

• 1 − m2

h

m2

χ

• m2

χ

• λ4

χA + 6 λ2 χAλ2 χV + λ4 χV

• − m2

h

• λ2

χA + λ2 χV

2 + . . .

• s-channel annihilation:

(heavy dark Higgs limit)

⟨σ|v|⟩ ¯

ff = λ2 χA sin2 θ cos2 θ

4π

• f=u,d,c,s,t,b,e,µ,τ
• 1 −

m2

f

m2

χ

• g mf

mW 2 m2

χ − m2 f

• 4 m2

χ − m2 h

2

• + . . .

⟨σ|v|⟩V V = λ2

χA m2 W sin2 θ cos2 θ

8 π

• V =W,Z
• 1 − m2

V

m2

χ

• g2

V h

m4

V

• 4m2

χ − m2 h

2

• 3 m4

V − 4m2 V m2 χ + 4 m4 χ

• + . . .

⟨σ|v|⟩hh = λ2

h3 λ2 χA sin2 θ

2 π

• 1 − m2

h

m2

χ

9 u2

• 4 m2

χ − m2 h

2 + . . .

*Lopez-Honorez, Schwetz and Zupan,

• Phys. Lett. B 716, 179

Proportional to pseudo-scalar coupling

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• Dark matter/dark matter scattering:

(Similar to unitarity bounds* on heavy 4th generation fermions)

Unitarity Considerations

DM DM DM DM Dark Higgs Dark Higgs

* Furman, Hinchliffe and Chanowitz, Nuclear Physics B153, 402; Physics Letters B78, 285

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Full Unitarity Considerations

(Goldstone Boson Limit)

− λ3 4π ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝

s2 √ 32 c2 √ 32 − sc 4 s2 8 c2 8 −sc √ 32 s2 √ 32 s2 8

κ δ ξ

c2 √ 32 c2 8

δ α β − sc

4

− sc

√ 32

ξ β η

s2 4

− sc

4

− sc

4 c2 4

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ M − λ1 4π ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1

1 √ 8 c2 √ 8 s2 √ 8 sc 2 1 √ 8 3 4 c2 4 s2 4 sc √ 8 c2 √ 8 c2 4 3c4 4 3s2c2 4 3 sc3 √ 8 s2 √ 8 s2 4 3 s2c2 4 3s4 4 3 cs3 √ 8 sc 2 sc √ 8 3 sc3 √ 8 3 cs3 √ 8 3 c2s2 2 c2 2 sc 2 sc 2 s2 2

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

M(0)

I

=

• W +

L W − L , ZLZL

√ 2 , hh √ 2, ρρ √ 2, hρ, hZL, ρZL

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Full Unitarity Considerations

(Goldstone Boson Limit)

− λ3 4π ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝

s2 √ 32 c2 √ 32 − sc 4 s2 8 c2 8 −sc √ 32 s2 √ 32 s2 8

κ δ ξ

c2 √ 32 c2 8

δ α β − sc

4

− sc

√ 32

ξ β η

s2 4

− sc

4

− sc

4 c2 4

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ M − λ1 4π ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 1

1 √ 8 c2 √ 8 s2 √ 8 sc 2 1 √ 8 3 4 c2 4 s2 4 sc √ 8 c2 √ 8 c2 4 3c4 4 3s2c2 4 3 sc3 √ 8 s2 √ 8 s2 4 3 s2c2 4 3s4 4 3 cs3 √ 8 sc 2 sc √ 8 3 sc3 √ 8 3 cs3 √ 8 3 c2s2 2 c2 2 sc 2 sc 2 s2 2

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

M(0)

I

=

• W +

L W − L , ZLZL

√ 2 , hh √ 2, ρρ √ 2, hρ, hZL, ρZL

• dark higgs

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Perturbative Corrections

• Tree-level unitarity constraints are not enough to

get an accurate scale of new physics.*

*See Aydemir, Anber and Donoghue, arXiv:1203.5153, for a similar conclusion using chiral perturbation theory.

• In addition require the next order correction not to

generate a 30% correction larger than the tree-level correction**. (no Landau poles)

**See Barbieri, Hall and Rychkov, arXiv:0603188.

• More (fuller explanation) on this in the next

section.

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(Walker, arXiv:1310.1083)

A (non-SUSY) Higgs Portal

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(Walker, arXiv:1310.1083)

• Points which satisfy (or give smaller) relic abundance.

A (non-SUSY) Higgs Portal

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(Walker, arXiv:1310.1083)

• 1T direct detection searches are sensitive to all of the

above points.

A (non-SUSY) Higgs Portal

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(Walker, arXiv:1310.1083)

• Points which satisfy (or give smaller) half of measured

relic abundance.

A (non-SUSY) Higgs Portal

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(Walker, arXiv:1310.1083)

• Precisely measuring deviation from the SM Higgs

decays to WW and ZZ can severely constrain the parameter space.

Philosophy from (non-SUSY) Higgs Portals

Χh2 0.1199 0.0081 Xenon100 Constraints

a

10000 20000 30000 40000 50000 0.80 0.85 0.90 0.95 1.00

Dark Matter Mass GeV

cos Θ

Perturbative Model 2 Parameter Space mΡ mh, mΧ

0.05995 Constraints

b

000 000 000 000 000 0.80 0.85 0.90 0.95 1.00

ILC500/ILCTeV ILC500/ILCTeV

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NMSSM Higgs Portal

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• Focus on the NMSSM Higgs sector

(only higgsino/singlino dark matter)

NMSSM Higgs Sector

• Superpotential/soft-breaking terms:

WNMSSM =

c − λ ˆ

S ˆ H1 · ˆ H2 + 1 3κ ˆ S3, Vsoft = m2

H1H† 1H1 + m2 H2H† 2H2 + m2 SS†S −

• λAλSH1 · H2 − 1

3κAκS3 + h.c.

• (scale invariant NMSSM)

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34

• Focus on the NMSSM Higgs sector

(only higgsino/singlino dark matter)

NMSSM Higgs Sector

• Six free parameters:

(after requiring the correct electroweak vacuum)

, , tan , µ, Aλ, Aκ

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• Focus on the NMSSM Higgs sector

(only higgsino/singlino dark matter)

NMSSM Higgs Sector

• Six free parameters:

(after requiring the correct electroweak vacuum)

, , tan , µ, Aλ, Aκ

dimensionless couplings/parameters dimension-full masses/couplings

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36

NMSSM Higgs Sector

Want to generate tension by decoupling the NMSSM SUSY breaking scales.

(analogous to decoupling the dark Higgs in the non-SUSY Higgs portal)

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, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

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, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

m2

SM = m2 H1 < m2 Z

✓ cos2(2) + 2||2 sin2(2) g2

1 + g2 2

◆

λ,

• NMSSM Higgs Sector
• SM Higgs mass constrains modulo :

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39

, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

*See, e.g., Kanehata, Kobayaski, Konishi, Seto and Shimomura, arXiv:1103.5109

NMSSM Higgs Sector

• 1. Forbid D-flat directions in the MSSM potential.
• 2. Forbid directions where only one MSSM Higgs
• r singlet gets a vev.
• Vacuum constrains*:

: , , tan , µ, Aλ, Aκ

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, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

• Mass spectrum (in the decoupling limit):

m ˜

H+/−

= µ + O(v) (

m ˜

H1

= µ + O(v) ( m ˜

H2

= µ + O(v) ( m ˜

S

= √ 2 κ µ/λ + O(v) (

mH0

1

= mh mH0

2

∼ f(µ, Aλ) ( mS ∼ g(µ, Aκ) ( mA1 ⇠ h(µ, Aλ) ( mA2 ⇠ h0(µ, Aκ) (

mH+/− ⇠ h(µ, Aλ) (

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41

, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

• Mass spectrum (in the decoupling limit):

m ˜

H+/−

= µ + O(v) (

m ˜

H1

= µ + O(v) ( m ˜

H2

= µ + O(v) ( m ˜

S

= √ 2 κ µ/λ + O(v) (

mH0

1

= mh mH0

2

∼ f(µ, Aλ) ( mS ∼ g(µ, Aκ) ( mA1 ⇠ h(µ, Aλ) ( mA2 ⇠ h0(µ, Aκ) (

mH+/− ⇠ h(µ, Aλ) (

All non-SM masses increase with decoupling.

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Perturbative Unitarity Arguments

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43

Perturbative Unitarity Arguments

• Use perturbative unitarity on both the dimensionless

and dimension-full parameters to estimate when perturbativity will break down.

: λ, κ, µ, Aλ, Aκ

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44

Perturbative Unitarity Arguments

• Use perturbative unitarity on both the dimensionless

and dimension-full parameters to estimate when perturbativity will break down.

: λ, κ, µ, Aλ, Aκ

• SUSY is a perturbative theory. Trilinear and

dimensionless couplings cannot be too large.

• Performed the standard analysis to bound the

scalar quartic couplings when . s ! 1

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45

Perturbative Unitarity Arguments

• Use perturbative unitarity on both the dimensionless

and dimension-full parameters to estimate when perturbativity will break down.

: λ, κ, µ, Aλ, Aκ

• Claim: Perturbative unitarity also has sensitivity to

ratios of the dimension-full parameters.

• SUSY is a perturbative theory. Trilinear and

dimensionless couplings cannot be too large.

• Performed the standard analysis to bound the

scalar quartic couplings when . s ! 1

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46

• Sensitivity to ratios:

Perturbative Unitarity Arguments

S S h Code scans over s. Selects a optimized value of s, where the amplitude can be maximized. h H

M ⇠ A2

λ

s m2

H

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47

Perturbative Unitarity Arguments

T J

fi = 1

2 λ1/4

f

λ1/4

i

16π s 1

−1

dcos θ ˆ Tfi(√s, cos θ) PJ(cos θ)

1 2i

• T J

fi − T J∗ if

∼ =

• h

T J∗

hf T J hi

Unitarity of the S-matrix requires where

• Review:

− i

• T − T †

= T †T ,

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48

• Our approach:

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

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49

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Exact computation of a scattering process to all orders

• f perturbation theory lie on

the Argand circle

• Our approach:

However, we almost always compute in perturbation theory to the lowest order possible (off the circle).

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50

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Unitarity computations in the tree-level, Born approximation appear on the x-axis.

• Our approach:

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51

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Higher-order corrections move “toward” to the Argand circle. However, a circuitous route is possible* depending on the size of the correction.

• Our approach:

*See Aydemir, Anber and Donoghue, arXiv:1203.5153, for a similar analysis

• f chiral perturbation theory.

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52

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

To conservatively estimate the perturbative corrections, take the tree-level computation and draw a straight line to the nearest point* on the circle.

• Our approach:

*Methodology from Schuessler and Zeppenfeld, arXiv:0710.5175. Schuessler thesis (2005, in German).

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53

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

This distance corresponds to the minimum perturbative correction needed to correct the tree-level amplitude*.

• Our approach:

}

⌘ |ttreelevel texact|2 |ttreelevel|2

*Methodology from Schuessler and Zeppenfeld, arXiv:0710.5175. Schuessler thesis (2005, in German).

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54

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

We scan over to give the maximum value of tree-level amplitude. We only allow points in the parameter space that correspond to less than a 20% correction* to the amplitude.

• Our approach:

}

⌘ |ttreelevel texact|2 |ttreelevel|2

ps

*Methodology from Schuessler and Zeppenfeld, arXiv:0710.5175. Schuessler thesis (2005, in German).

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Relic Abundance

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56

NMSSM Relic Abundance

• Relic abundance “anchors” the NMSSM spectrum.

Same for the non-SUSY Higgs portal.

• Roughly, raising the dark matter mass means larger

couplings to get the right relic abundance*.

*A moral of Griest and Kamionkowski, Phys. Rev. Lett. 64, 615.

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57

NMSSM Relic Abundance

h2Ωc  0.1199

• Require relic abundance to be less than or equal

to the Planck central value.

• Used MicrOmegas and NMSSMTools*.

*MicroOmegas authors: Bélanger, Boudjema, Pukhov and Semenov NMSSM Tools authors: Das, Ellwanger, Gunion, Hugonie, Jean-Louis and Teixeria

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58

NMSSM SUSY Mass Spectrum

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59

NMSSM SUSY Mass Spectrum

• Analysis: Scan over the NMSSM parameters:
• 1. SUSY mass parameters:
• 2. Dimensionless parameters:
• Apply constraints:

a) Perturbative unitarity constraints b) Relic abundance c) Vacuum and other NMSSM consistency constraints.

• Result is a bounded NMSSM spectra
• Ai
• ,
• µ
• ≤ 40 TeV
• λ
• ,
• κ
• ≤ 4

(

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60

NMSSM SUSY Mass Spectrum

Resonant annihilation fine-tuning parameter: Red - Xenon 1T projected exclusion

R = mini

• 2 mDM mHi
• /mHi
• Dark matter and Heaviest CP Even, Neutral Higgs Mass vs.

Resonant Fine-Tuning Parameter:

Dark Matter Mass Chargino Mass

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61

NMSSM SUSY Mass Spectrum

Resonant annihilation fine-tuning parameter: Red - Xenon 1T projected exclusion

R = mini

• 2 mDM mHi
• /mHi
• Dark matter and Heaviest CP Even, Neutral Higgs Mass vs.

Resonant Fine-Tuning Parameter:

Dark Matter Mass Chargino Mass

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62

NMSSM SUSY Mass Spectrum

Resonant annihilation fine-tuning parameter:

Heaviest CP Even, Neutral Higgs Mass

Red - Xenon 1T projected exclusion

R = mini

• 2 mDM mHi
• /mHi
• Heaviest CP Even, Neutral and Charged Higgs Mass vs.

Resonant Fine-Tuning Parameter:

Charged Higgs Mass

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63

NMSSM SUSY Mass Spectrum

Resonant annihilation fine-tuning parameter:

Heaviest CP Even, Neutral Higgs Mass

Red - Xenon 1T projected exclusion

R = mini

• 2 mDM mHi
• /mHi
• Heaviest CP Even, Neutral and Charged Higgs Mass vs.

Resonant Fine-Tuning Parameter:

Charged Higgs Mass

SLIDE 64

64

NMSSM SUSY Mass Spectrum

• Heaviest CP Even, Neutral Higgs Mass vs.

Relic Abundance:

Heaviest CP Even, Neutral Higgs Mass

Red - Xenon 1T projected exclusion Fine-tuning cutoff resonant annihilation fine-tuning parameter at 10%:

R = mini

• 2 mDM mHi
• /mHi

SLIDE 65

65

NMSSM SUSY Mass Spectrum

• μ parameter vs. Aλ

μ parameter

Red - Xenon 1T projected exclusion Fine-tuning cutoff resonant annihilation fine-tuning parameter at 10%:

R = mini

• 2 mDM mHi
• /mHi

SLIDE 66

66

Some Signatures

• Phenomenology is just starting:

Much that needs to be done to be sensitive to the full range of parameter space.

SLIDE 67

67

Some Signatures

• That said...
• Proposed indirect search experiments like

CTA (Cherenkov Telescope Array) uses very high energy gamma-rays to search for heavy LSPs.

T h e C h e r e n k

• v

T e l e s c

• p

e A r r a y ( C T A )

• Like the LHC, production of heavy colored

particles that decay to the Higgses/dark matter is compelling.

SLIDE 68

68

Some Signatures

*Low and Wang, arXiv: 1404.0682

[GeV]

χ ∼

m 500 1000 1500 2000 B δ S/ 1 2 3 4 5 6

• 1

MadGraph5 + Pythia6 + Delphes3, L = 3000 fb

Higgsino

1-2% syst.

Monojet 95% σ 5 100 TeV 14 TeV

Significance = S δB = S p B + λ2B2 + γ2S2 ,

λ and γ parameterize the systematic uncertainty on the background and signal, respectively Our work: NMSSM couplings likely will be stronger at larger scales.

• Work on searching for pure Higgsinos with mono-

jet searches in the MSSM* @ 100 TeV:

SLIDE 69

69

Conclusions

SLIDE 70

70

Conclusions

We used a combination of perturbative unitarity constraints and the relic abundance to generate upper bounds on two different Higgs portals.

SLIDE 71

71

Thank you ACFI!

SLIDE 72

72

Backup Slides

SLIDE 73

SLIDE 74

SLIDE 75

75

NMSSM Bounds

• How do dimensional unitarity constraints compare

to vacuum constraints? A2 < 3

• m2

φ1 + m2 φ2 + m2 φ3

• Generic Constraint from

Superpotential with three superfields

m2

S . 1

9A2

κ

From limit where:

VS(S) = 2S4 + 2 3AκS3 + m2

SS2 + ...

• The ratios are better at constraining the SUSY

breaking masses.

SLIDE 76

76

, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

M˜

χ0 =

B B B B @ M1 −cβsW mZ sβsW mZ M2 cβcW mZ −sβcW mZ −cβsW mZ cβcW mZ −λvs/ √ 2 −λvu/ √ 2 sβsW mZ −sβcW mZ −λvs/ √ 2 −λvd/ √ 2 −λvu/ √ 2 −λvd/ √ 2 √ 2κvs 1 C C C C A

Relatively small. Effectively no neutralino mixing Decoupled

• Neutralino mass spectrum (in the decoupling limit):

SLIDE 77

77

, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

• M

C

= XT X

• X

=

• M2

√ 2sβ mW √ 2cβ mW µ

• Chargino mass spectrum (in the decoupling limit):

SLIDE 78

78

, µ, Aλ, Aκ , µ, Aλ, Aκ

⇢

⇢

electroweak scale electroweak scale

NMSSM Higgs Sector

• M

C

= XT X

• X

=

• M2

√ 2sβ mW √ 2cβ mW µ

• Decoupled

Scales with SUSY breaking scales.

• Chargino mass spectrum (in the decoupling limit):

SLIDE 79

79

(Walker, arXiv:1310.1083)

Philosophy from (non-SUSY) Higgs Portals

Generalized Lee, Quigg, Thacker unitarity bound for dark Higgses. (For v ~ 246, )

mh bound ∼ 1.2 TeV

SLIDE 80

80

Perturbative Unitarity Arguments

Argand diagram

cle (called A r x =Re ˜ T J

ii

• r the Born ap

d y =Im ˜ T J

ii

1/2 (

Note: Lee, Quigg and Thacker works because . This x is close to the Argand circle.

• Our approach:

g2

i ⌧ 1

(