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Dark matter in three Higgs doublet models Diana Rojas University of Southampton & NExT Institute January 15, 2019 Diana Rojas DM in the 3HDM N-Higgs Doublet Models (NHDM) N copies of the Higgs doublet with identical quantum numbers:

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Dark matter in three Higgs doublet models

Diana Rojas

University of Southampton & NExT Institute

January 15, 2019

Diana Rojas DM in the 3HDM

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N-Higgs Doublet Models (NHDM)

N copies of the Higgs doublet with identical quantum numbers: Φα =

  • φ+

α 1 √ 2(ρα + iηα)

  • ,

α = 1, 2, . . . , N The most general potential V = Yab(Φ†

aΦb) + Zabcd(Φ† aΦb)(Φ† cΦd)

contains N2(N2 + 3)/2 free parameters. All Abelian symmetries realisable in NHDM have been found. [Ivanov, et al., J.Phys.A 45,215201 (2012)]

Diana Rojas DM in the 3HDM

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SLIDE 3

IDM

* Amongst 2HDMs, the IDM has the advantage of including DM candidates * Characteristic: An unbroken Zn symmetry is imposed * Is an example of the Higgs-portal DM models1

Figure: Higgs-portal Feynman diagrams. LEFT: DM annihilation produce SM particles (astrophysical

  • bservation). MIDDLE: nucleon-DM scattering (direct detection). RIGHT: Higgs decaying to DM pair (collider

signature).

  • 1B. Patt and F. Wilczek, hep-ph/0605188.

Diana Rojas DM in the 3HDM

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3HDM · Motivations

richer symmetry groups than the 2HDMs richer particle spectrum possible update to 6HDM it resembles the 3 generation of fermions in this talk 3HDMs with

Two inert plus One Higgs doublet, I(2+1)HDM One inert plus Two Higgs doublets, I(1+2)HDM CPC and CPV versions

Previous work from: Adriana Cordero-Cid, Jaime Hernandez-Sanchez, Venus Keus, Steve King, Stefano Moretti, Dorota Sokolowska, Kei Yagyu

Diana Rojas DM in the 3HDM

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SLIDE 5

I(1+2)HDM

May be regarded as an extension to the 2HDM by the addition of an extra inert scalar doublet Symmetry: Z2 × ˜

  • Z2. We assign Z2 = +1 : active doublets,

Z2 = −1 : inert doublets. ˜ Z2 in the active sector to avoid FCNCs Theoretical restrictions similar to I(2 + 1)HDM However, one should be careful with unitarity, in fact we have stronger bounds than in 2HDM and I(2+1)HDM2

  • 2S. Moretti, K. Yagyu Phys.Rev. D91 (2015) 055022

Diana Rojas DM in the 3HDM

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Charge assignments under Z2 × ˜ Z2

(Z2, ˜ Z2) charge Φ1 Φ2 η QL LL uR dR eR Type-I (+, +) (+, −) (−, +) (+, +) (+, +) (+, −) (+, −) (+, −) Type-II (+, +) (+, −) (−, +) (+, +) (+, +) (+, −) (+, +) (+, +) Type-X (+, +) (+, −) (−, +) (+, +) (+, +) (+, −) (+, −) (+, +) Type-Y (+, +) (+, −) (−, +) (+, +) (+, +) (+, −) (+, +) (+, −) Φ1, Φ2 are the active doublets η is the inert doublet Symmetries: Z2(unbroken) guarantees stability of DM ˜ Z2 (soflty-broken) forbids FCNC at tree level

Diana Rojas DM in the 3HDM

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SLIDE 7

Scalar potential

The most general phase invariant part of a 3HDM potential is3 V0 = −µ2

i (Φ† i Φi) + λij(Φ† i Φi)(Φ† j Φj) + λ′ ij(Φ† i Φj)(Φ† j Φi)

and, considering an unbroken Z2 symmetry we add the terms: VZ2 = −µ2

12(Φ† 1Φ2) + λ1(Φ† 2Φ2)2 + λ2(Φ† 2Φ3)2 + λ3(Φ† 3Φ1)2 + h.c.

where gZ2 = (+, +, −) and Φα =

  • H±

α 1 √ 2(Hα + iAα)

  • ,

α = 1, 2, 3 1,2 are the actives and 3 is the inert

  • 3V. Keus, S. F. King and S. Moretti, Phys. Rev. D 90, no. 7, 075015 (2014)

doi:10.1103/PhysRevD.90.075015 [arXiv:1408.0796 [hep-ph]]. Diana Rojas DM in the 3HDM

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Why studying the H±W ∓Z/γ vertex?

To test the structure of the Higgs sector Not at tree-level in NHDMs An enhancement due to non-decoupling effects Measure of custodial symmetry violation → NP

Diana Rojas DM in the 3HDM

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The vertex HW ±Z/γ

Loop amplitude of H± → W ±V (V = Z, γ) iM(H± → W ±V ) = igmW V µν

V ǫW µ(pW )ǫV ν(pV )

with V µν

V

written in terms of dimensionless form factors: V µν

V

= gµνFV + pµ

V pν W

m2

W

GV + iǫµνρσ pV ρpW σ m2

W

HV with pµ

W and pµ V incoming momenta for W ± and V .

For the case of V = γ, Waard identity V µν

γ pγν = 0 implies

Fγ = Gγ 2

  • 1 − m2

H±

m2

W

  • where p2

W = m2 W and (pW + pγ)2 = m2 H±.

Diana Rojas DM in the 3HDM

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The vertex HW ±Z/γ

Loop amplitude of H± → W ±V (V = Z, γ) iM(H± → W ±V ) = igmW V µν

V ǫW µ(pW )ǫV ν(pV )

with V µν

V

written in terms of dimensionless form factors: V µν

V

= gµνFV + pµ

V pν W

m2

W

GV + iǫµνρσ pV ρpW σ m2

W

HV with pµ

W and pµ V incoming momenta for W ± and V .

The effective lagrangian:

Leff = fZH+W −

µ Z µ + gV H+F µν W FV µν + ihV ǫµνρσH+F µν W F ρσ V

+ h.c. where F µν

W and F µν V

are the field strength tensors. The coefficient fZ has mass dimension one whereas gV and hV have mass dimension minus one.

Diana Rojas DM in the 3HDM

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Figure: The 1PI diagrams for the HWZ and HW γ vertices. The diagrams which vanish in the limit sin(β − α) = 1 are not displayed.

Diana Rojas DM in the 3HDM

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Form Factors

Calculations are made in Type I and X where mH± can be light

mH = mH± , −4002 GeV2 < M2 < 4002 GeV2, 100 GeV< mA < 260 (350) GeV, mηA = 400 GeV Diana Rojas DM in the 3HDM

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The I(2+1)HDM

May be regarded as an extension to the IDM by the addition

  • f an extra inert scalar doublet

The work we did

Could the DM pheno distinguish CPC and CPV inert sectors? Which pheno is interesting to study at the LHC? Can it be differenciated from IDM in experiments?

Diana Rojas DM in the 3HDM

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SLIDE 14

Constructing the (Z2 symmetric) I(2+1)HDM

The most general phase invariant part of a 3HDM potential is4 V0 = −µ2

i (Φ† i Φi) + λij(Φ† i Φi)(Φ† j Φj) + λ′ ij(Φ† i Φj)(Φ† j Φi)

and, considering an unbroken Z2 symmetry we add the terms: VZ2 = −µ2

12(Φ† 1Φ2) + λ1(Φ† 1Φ2)2 + λ2(Φ† 2Φ3)2 + λ3(Φ† 3Φ1)2 + h.c.

where gZ2 = (−, −, +) and Φα =

  • H±

α 1 √ 2(Hα + iAα)

  • ,

α = 1, 2, 3 1,2 are the inerts and 3 is the active

  • 4V. Keus, S. F. King and S. Moretti, Phys. Rev. D 90, no. 7, 075015 (2014)

doi:10.1103/PhysRevD.90.075015 [arXiv:1408.0796 [hep-ph]]. Diana Rojas DM in the 3HDM

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Dark democracy limit

To obtain the mass spectrum → solve analytically or numerically. We simplify the model5 µ2

1 = µ2 2,

λ3 = λ2, λ31 = λ23, λ′

31 = λ′ 23

Note: if µ2

12 = 0 → doubled IDM!

Two DM candidates, difficult to satisfy both relic density and LHC (invisible channel) constraints Then only two complex parameters: µ2

12 = |µ2 12|eiθ12,

λ2 = |λ2|eiθ2

  • 5B. Grzadkowski, O. M. Ogreid, P. Osland, A. Pukhov and M. Purmohammadi, JHEP 1106, 003 (2011)

doi:10.1007/JHEP06(2011)003 [arXiv:1012.4680 [hep-ph]]. Diana Rojas DM in the 3HDM

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Neutral mass spectrum

m2

S1

= v 2 2 (λ′

23 + λ23) − Λ − µ2 2

m2

S2

= v 2 2 (λ′

23 + λ23) + Λ − µ2 2

m2

S3

= v 2 2 (λ′

23 + λ23) − Λ′ − µ2 2

m2

S4

= v 2 2 (λ′

23 + λ23) + Λ′ − µ2 2

where

Λ =

  • v 4|λ2|2 + |µ2

12|2 − 2v 2|λ2||µ2 12| cos(θ12 + θ2)

Λ′ =

  • v 4|λ2|2 + |µ2

12|2 + 2v 2|λ2||µ2 12| cos(θ12 + θ2)

For S1 to be DM, θ2 + θ12 in 2nd quadrant and λ2 < 0.

Diana Rojas DM in the 3HDM

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Potential parameters

|µ2

12| = 1

2(m2

S±

2 − m2

S±

1 ),

λ23 = 2µ2

2

v 2 + m2

S±

2 + m2

S±

1

v 2 , λ′

23 = 1

v 2 (m2

S2 + m2 S1 − m2 S±

2 − m2

S±

1 ),

µ2

2 = v 2

2 gS1S1h − v 2|λ2| 2(1 + α2)

  • 4α sin θ2 + 2(α2 − 1) cos θ2
  • − m2

S2 + m2 S1

2 , |λ2| = 1 v 2

  • |µ2

12| cos(θ2 + θ12)

+

  • |µ2

12|2 cos2(θ2 + θ12) +

  • m2

S2 − m2 S1

2 2 − |µ2

12|2 ].

where

α = −|µ2

12| cos θ12 + v 2|λ2| cos θ2 − Λ

|µ2

12| sin θ12 + v 2|λ2| sin θ2 Diana Rojas DM in the 3HDM

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Physical parameters

Parameters of V: µ2

2, |λ2|, |µ2 12|, λ23, λ′ 23, θ12, θ2

DM mass: mS1 mass splittings: δ12 = mS2 − mS1 δ1c = mS±

1 − mS1

δc = mS±

2 − mS± 1

Higgs-DM coupling: gS1S1h CPV phases: θ12, θ2 We recover CPC when θ2 + θ12 = π, where cos(θ2 + θ12) = −1 and Λ = v 2|λ2| + |µ2

12|, Λ = v 2|λ2| − |µ2 12| and α, β → ∞.

Diana Rojas DM in the 3HDM

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Benchmark scenarios

A1: δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 0.5 mS1< m2,3,4, mS±

1,2 (no co-annihilation)

B1: δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 0.82 mS1 ≈ mS3< m2,4, mS±

1,2

C1: δ12 = 12 GeV, δ1c = 100 GeV, δc = 1 GeV, θ2 = θ12 = 1.57 mS1 ≈ mS2 ≈ mS3 ≈ mS4< mS±

1,2

G1: δ12 = 2 GeV, δ1c = 1 GeV, δc = 1 GeV, θ2 = θ12 = 0.82 mS1 ≈ mS2 ≈ mS3 ≈ mS4 ≈ mS±

1 ≈ mS± 2

H1: δ12 = 50 GeV, δ1c = 1 GeV, δc = 50 GeV, θ2 = θ12 = 0.82 mS1 ≈ mS3 ≈ mS±

1 < mS4 ≈ mS2 ≈ mS± 2

  • A. Cordero-Cid, J. Hern´

andez-S´ anchez, V. Keus, S. F. King, S. Moretti, D. Rojas and D. Soko lowska, JHEP 1612, 014 (2016) Diana Rojas DM in the 3HDM

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Low DM mass

45 50 55 60

ms1 [GeV]

  • 0.2
  • 0.1

0.1 0.2

gS1 S1 h A1 B1 C1

A1: mainly Higgs annihilation, large gS1S1h B1: Higgs annihilation (smaller gS1S1h) + ZS1S3 coannihilation (reduced with respect to the CPC case) C1: mainly ZS1S4 coannihilation (χZS1S4 ≈ −1) + Higgs annihilation

Tools used in calculation: LanHEP, arXiv:1412.5016 [physics.comp-ph]; CalcHEP, Comput. Phys. Commun. 184 (2013) 1729; micrOMEGAs 4.2 arXiv:1407.6129 [hep-ph]

Diana Rojas DM in the 3HDM

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medium DM mass

S1 S1 h V V

gS1S1h, ge

S1 S1 V V

gVVS1S1 =

g2 e 2 sin2 θW

no dependence on the benchmarks

65 70 75 80 85 90 ms1 [GeV]

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

gS1 S1 h A1 B1 C1

Diana Rojas DM in the 3HDM

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Relic density

  • 0.2
  • 0.1

0.0 0.1 0.2 gS1 S1 h 0.05 0.10 0.15 0.20 0.25 0.30 ΩDMh2 B1:mS1 = 45 GeV A1:mS1 = 47 GeV B1:mS1 = 47 GeV B1:mS1 = 50 GeV A1:mS1 = 53 GeV

  • 0.2
  • 0.1

0.0 0.1 0.2 gS1 S1 h 0.05 0.10 0.15 0.20 0.25 0.30 ΩDMh2 A1:mS1 = 69 GeV A1:mS1 = 75 GeV

Diana Rojas DM in the 3HDM

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SLIDE 23

Filling the plot

50 60 70 80 90 ms1 [GeV]

  • 0.2
  • 0.1

0.1 0.2

gS1 S1 h CPC B2 B3 B4 Other

mS1 < mh/2: many new solutions: different mass splittings + ZSiSj interaction strength mS1 > mh/2: less freedom but still new solutions: Higgs mediated coannihilations + sign of hS3S3 coupling

Diana Rojas DM in the 3HDM

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LHC phenomenology

In the CPC-I(2+1)HDM the process contributing to the E Tf ¯ f signature is: gg → h → H1H2 → H1H1γ∗ → H1H1f ¯ f H2 H1 γ∗ e− e+ not possible in the IDM small mass difference: mAi − mH1 or mH2 − mH1 (≈ 2me):

  • nly e+e− signature → EM shower

charged inerts not to heavy otherwise loop suppression!

Diana Rojas DM in the 3HDM

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SLIDE 25

The one-loop diagrams

H2 H+

1,2

H1 W + H+

1,2

γ∗ H2 W + H1 H+

1,2

W + γ∗

Figure: Triangle diagrams

M = ie¯ v(k1)γνu(k2) igµν (p3 − p2)2

  • i

M(i)

µ

M(1)

µ (mH±

i , mW , m2

12, mHi) = g2e

4 A±

i m(1) µ (mH±

i , mW , m2

12, mHi)

m2

12 = (p3 − p2)2 = (k1 + k2)2 = 2k1 · k2

taking me = 0

Diana Rojas DM in the 3HDM

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SLIDE 26

One loop diagrams

H2 H1 γ∗ H+

1,2

W + H2 H1 γ∗ H+

1,2

H+

1,2

H2 γ∗ H1 H+

1,2

W +

Figure: Bubble diagrams

Diana Rojas DM in the 3HDM

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SLIDE 27

Effective vertex

Using the effective lagrangian approach one can deduce L(H2H1e+e−) = i c1v2 sin θh cos θh Λ2 (H1∂µH2 − H2∂µH1)¯ eγµe = iK(H1∂µH2 − H2∂µH1)¯ eγµe The amplitude can be written as: M = iK ¯ v(k1)γµ(p3 + p2)µu(k2) then K 2 = 16π3m3

H2Γ(H2 → H1e+e−)

I3 K depends on mH1,2, mH±

1,2, θc, θh Diana Rojas DM in the 3HDM

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SLIDE 28

Higgs production

g g h Si Sj

Figure: The ggF-induced production of the SM-like Higgs particle at the LHC

gluon fusion ggF gg → h → H1H2 → H1H1γ∗ → H1H1f ¯ f vector boson fusion VBF qiqj → qkqlH1H2 → H1H1γ∗ → H1H1f ¯ f

Also competitive, the tree-level channel q¯ q → Z ∗ → H1H1Z → H1H1f ¯ f

Diana Rojas DM in the 3HDM

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SLIDE 29

VBF channel

qiqj → qkqlH1H2 → H1H1γ∗ → H1H1f ¯ f qi Z, W + Z, W + qj h H1 H2 qk ql (A) qi Z, W + Z, W + qj qk ql H1 H2 (B) qi Z(W +) A1(H+

1 )

Z(W +) qj qk ql H1 H2 (C)

Figure: Diagrams leading to the E T + f ¯ f final state via VBF topologies.

loop calculation enters H2 → H1f ¯ f (A) depends on gH1H2h (B) depends on gH1H2ZZ - fixed gauge (C) depends on gH1A1Z

Diana Rojas DM in the 3HDM

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SLIDE 30

Tree-level channel

qiqj → qkqlH1H2 → H1H1γ∗ → H1H1f ¯ f qi ¯ qi Z ∗ h H1 H1 Z (A) q ¯ q Z ∗ H1 H1 Z (B) q ¯ q Z ∗ H1 A1,2 H1 Z (∗) (C) (A) depends on gH1H1h (B) depends on gH1H1ZZ - fixed gauge coupling (C) depends on gH1A1Z - possible differences w/r IDM we may learn something about Ai

Diana Rojas DM in the 3HDM

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SLIDE 31

Benchmark scenarios

Benchmark ∆12 ∆A1 ∆A2 ∆H±

1

∆H±

2

A50 50 75 125 75 125 I5 5 10 15 90 95 I10 10 20 30 90 100

Table: In here: ∆12 = mH2 − mH1, ∆A1 = mA1 − mH1, ∆A2 = mA2 − mH1, ∆H±

1 = mH± 1 − mH1, ∆H± 2 = mH± 2 − mH1

We calculated the VBF and the ggF process in the factorised form: σtotal = σH1H2 × BR(H2 → H1f ¯ f ).

Diana Rojas DM in the 3HDM

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SLIDE 32

Results · scenario A50

  • ■■■■■■■■

■■■■ ■■■■■■■■■■■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 10-9 10-6 10-3

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

  • ■■■■■■■■

■■■■ ■■■■■■■■■■■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 10-11 10-9 10-7 10-5 0.001 0.100

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

50 60 70 80

mDM [GeV]

0.05 0.10 0.15

Scenario A50 |gZH1A12| (tree level) |ghH1H2| (ggF) |gZH1A1*gZH2A1| (neutral VBF) |gW + H1- H1*gW - H1+ H2| (charged VBF) |ghDM*ghZZ| Diana Rojas DM in the 3HDM

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SLIDE 33

Results · scenario I5

  • ■

■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 90 10-11 10-8 10-5 10-2

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

  • ■■■■■■■■■■

■ ■■■■■■■■■■■■■■■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 90 10-9 10-7 10-5 10-3

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

50 60 70 80 90 mDM [GeV] 10-4 0.001 0.010 0.100 1

Scenario I5 |gZH1A12| (tree level) |ghH1H2| (ggF) |gZH1A1*gZH2A1| (neutral VBF) |gW + H1- H1*gW - H1+ H2| (charged VBF) |ghDM*ghZZ| Diana Rojas DM in the 3HDM

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SLIDE 34

Results · scenario I10

  • ■■■■■■■■■

■■■■■■■■■■■■■■■■■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 90 10-9 10-7 10-5 10-3

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

  • ■■■■■■■■■

■■■■■■■■■■■■■■■■■ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆

40 50 60 70 80 90 10-8 10-6 10-4 10-2

mDM(GeV) σ(pb)

  • tree - level

■

ggF

◆

VBF

50 60 70 80 90 mDM [GeV] 10-4 0.001 0.010 0.100 1

Scenario I10 |gZH1A12| (tree level) |ghH1H2| (ggF) |gZH1A1*gZH2A1| (neutral VBF) |gW + H1- H1*gW - H1+ H2| (charged VBF) |ghDM*ghZZ| Diana Rojas DM in the 3HDM

slide-35
SLIDE 35

Conclusions

We studied I(1+2)HDM: H±W ∓Z, H±W ∓γ vertices I(2+1)HDM: CPV phase in dark sector I(2+1)HDM: LHC phenomenology

Diana Rojas DM in the 3HDM

slide-36
SLIDE 36

Conclusions

We studied I(1+2)HDM: H±W ∓Z, H±W ∓γ vertices

|FZ|2 can be one order of magnitude greater than in the 2HDM For the vertex H±W ∓γ not great difference BR(H±

2 → W ±Z) = 4(0.2)%, 40(2)%, 0.4(0.3)% in the cases

  • f mH± = 150, 170, 200 GeV in Type-I (Type-X)

Diana Rojas DM in the 3HDM

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SLIDE 37

Conclusions

We studied I(2+1)HDM: CPV phase in dark sector

CPV is controlled by a single angle θ12 + θ2 CPC is recovered when θ12 + θ2 = π mass degeneration is θ12 + θ2 = π/2 With CPV it is possible to have smaller ghH1H1 for lower DM mass in the low mass region

Diana Rojas DM in the 3HDM

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SLIDE 38

Conclusions

We studied I(2+1)HDM: LHC phenomenology

Interesting signal: one-loop process that includes H2 → H1f ¯ f (not present in IDM) Two production channels: ggF and VBF This process could be distinguished at LHC Run2/Run3 if DM in the low mass region

Diana Rojas DM in the 3HDM

slide-39
SLIDE 39

Thank you for your attention!

Diana Rojas DM in the 3HDM

slide-40
SLIDE 40

BACKUP SLIDES

Diana Rojas DM in the 3HDM

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SLIDE 41

Dark matter

Evidence for Dark Matter at diverse scales: galaxy scales: rotational speed of galaxies cluster scales: gravitational lensing at galaxy clusters horizon scales: anisotropies in the CMB ⇒ around 25 % of the Universe is: cold non-baryonic neutral very weakly interacting ⇒ Weakly Interactive Massive Particle stable due to the discrete symmetry DM DM → SM SM

  • pair annihilation

, DM SM, . . .

  • stable

annihilation cross section σv ∝ EW interaction

thermal evolution of DM density - a fixed value after freeze-out

Diana Rojas DM in the 3HDM

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SLIDE 42

Invisible decays

If the only invisible channel is h → S1S1: Br(h → inv.) = Γ(h → S1S1) ΓSM

h

+ Γ(h → S1S1). (1) If particles S2,3,4 are long-lived enough (i.e with Γtot ≤ 6.58 × 10−18 GeV ⇔ τ ≥ 10−7 s), they will not decay inside the detector, therefore seen as Higgs decays h → SiSi, then Br(h → inv.) =

  • i Γ(h → SiSi)

ΓSM

h

+

i Γ(h → SiSi).

(2)

Diana Rojas DM in the 3HDM

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SLIDE 43

3HDM unitarity bounds

Diana Rojas DM in the 3HDM

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SLIDE 44

Branching Ratios for the H±W ∓Z process

If mH± < mt: t → H±b dominant If mH± > mt: H±-strahlung dominant

Diana Rojas DM in the 3HDM

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SLIDE 45

Cross sections for the H±W ∓Z process

For the signature pp → b¯ bH±W ∓ → b¯ bW ±W ∓V σtop

S,V = 2 × σt¯ t × [1 − BR(t → H±b)] × BR(t → H±b) × BR(H± → W ±V ),

(3) Also EW productions e.g. pp → H±A/H±H → W ±V + X 0 pp → H+H− → W ±V + X ± σEW

S,V = (σH±A + σH±H + 2σH+H− ) × BR(H± → W ±V ),

(4) Type-I Type-X σtop

S,Z [fb]

(390, 700, 29) (15, 28, 1.6) σtop

S,γ [fb]

(940, 420, 1.4) (35, 16, 0.075) σEW

S,Z [fb]

(2.3, 7.5, 46) (0.087, 0.30, 2.5) σEW

S,γ [fb]

(5.5, 4.5, 2.2) (0.20, 0.17, 0.12) here we are considering the three cases mH± = 130, 150 and 170 GeV6

  • 6S. Moretti, D. Rojas and K. Yagyu, JHEP 1508, 116 (2015) doi:10.1007/JHEP08(2015)116

[arXiv:1504.06432 [hep-ph]]. Diana Rojas DM in the 3HDM

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SLIDE 46

I(2+1)HDM (CPC) Higgs sector

Higgs physical states From active doublet: hSM and G 0(G ±) goldstones which gives massive Z(W ±) Two inert generations: (H1, A1, H±

1 ) chosen to be lighter than

(H2, A2, H±

2 ), the lightest is the DM candidate

1 The fields are rotated by

Rθi = cos θi sin θi − sin θi cos θi

  • ,

θi = θh, θc, θa θh(c)(a) rotation angle for the neutral (charged) (pseudo-scalar)

2 The mass matrix can be written in terms of

Σ = 4µ2

12 + (µ2 1 − ΛΦ1 − µ2 2 + ΛΦ2)2

Diana Rojas DM in the 3HDM

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SLIDE 47

Relic density

Dark matter could have been created thermally in early universe (Wimps), or non-thermally in a phase transition (axions). Thermal reaction

1 When the universe was at very high T, thermal equilibrium

  • btained, then

nDM = nγ.

2 When the universe cooled, the number of DM and γ

decreased together as long as T > mDM.

3 When T < mDM, creation of DM would require being on the

tail of the thermal distribution. In equilibrium nDM would drop as e−mDM/T.

4 Freeze-out. If equilibrium were maintained, nDM → 0.

But, at some point the probability of one DM finding another to annihilate would become small.

Diana Rojas DM in the 3HDM

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SLIDE 48

Relic density in I(2+1)HDM

The relic density of DM after freeze-out is given by the solution of the Boltzmann eq:

dnS dt = −3HnS − σeff v(n2

S − neq 2 S

), (5)

where the thermally averaged effective (co)annihilation cross-section contains all relevant annihilation processes of any SiSj pair into SM particles:

σeff v =

  • ij

σijvijneq

i

neq

S

neq

j

neq

S

, (6)

where neq

i

neq

S

∼ exp(−mi − mS T ). (7) Therefore, only processes for which the mass splitting between a state Si and the lightest Z2-odd particle S are comparable to the thermal bath temperature T provide a sizeable contribution to this sum.

Diana Rojas DM in the 3HDM

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SLIDE 49

Annihilation channels

Relevant diagrams contributing to the total cross section.

Important aspects: relation between mDM and its coupling to the Higgs particle. Is mDM > mW ? If not, diagrams with off-shell gauge bosons may be important and must be included.

Diana Rojas DM in the 3HDM

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SLIDE 50

Co-annihilation channels

Co-annihilation effects play an important role in scenarios with multiple particles that are close in mass. Particles up to 20% heavier than DM may influence relic density.

Figure: The co-annihilation channels we need to include. Figure: Diagrams we need to include if all inerts are close in mass.

Diana Rojas DM in the 3HDM

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SLIDE 51

Heavy Dark Matter in the I(2+1)HDM

400 500 600 700 800ms1 [GeV]

  • 0.6
  • 0.4
  • 0.2

0.2 0.4 0.6

gS1 S1 h H1 G1

gS1S1h in case G > gS1S1h in case H The same behaviour in both cases Lower mS1 for case G Not really different from the CPC case

Diana Rojas DM in the 3HDM

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SLIDE 52

Direct detection CPV model

10-39 10-38 10-37 40 50 60 70 80 90 mS1 [GeV] 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-7 10-6 σS1,N [pb] A1 B1 C1 LUX (2016) XENON1T ν scattering

σS1,N ∝ g2

S1S1h

(mS1 + mN)2

Case Case A1: mostly excluded (large gS1S1h) Cases B1 and C1: mostly within the limits7

7[?] A. Cordero-Cid, J. Hern´ andez-S´ anchez, V. Keus, S. F. King, S. Moretti, D. Rojas and D. Soko lowska, JHEP 1612, 014 (2016) doi:10.1007/JHEP12(2016)014 [arXiv:1608.01673 [hep-ph]]. Diana Rojas DM in the 3HDM

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SLIDE 53

Direct detection CPV model - heavy case

                 ◆ ◆ ◆ ◆ ◆ ◆ ◆◆◆◆◆                  ◆ ◆ ◆ ◆ ◆ ◆ ◆◆◆◆◆ 400 500 600 700 800 mS1 [GeV] 10-15 10-13 10-11 10-9 σ(DM,N} [pb] LUX XENON 1T ν scattering

case G1

◆

case H1

σDM,N ∝ g2

S1S1h

(MS1 + MN)2

In agreement with LUX Within the reach of XENON-1T case G (bigger couplings) easier to see/exclude than case H (smaller couplings)

Diana Rojas DM in the 3HDM

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SLIDE 54

Indirect detection CPV model

10-33 10-32 10-31 10-30 10-29 10-28 10-27 10-26 10-25 40 50 60 70 80 90 〈vσ〉 [cm3/s] mS1 [GeV] A1 B1 C1 Fermi-LAT (bb

  • )

Most of the parameter space in agreement with Planck

Diana Rojas DM in the 3HDM

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SLIDE 55

Planck vs LHC

45 50 55 60

ms1 [GeV]

  • 0.2
  • 0.1

0.0 0.1 0.2

gS1 S1 h case A1 μmintot(h)=0.66 Br(h→inv)=0.20

45 50 55 60

ms1 [GeV]

  • 0.2
  • 0.1

0.0 0.1 0.2

gS1 S1 h case B1 μmintot(h)=0.66 Br(h→inv)=0.20

Diana Rojas DM in the 3HDM

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SLIDE 56

CalcHEP batch

../bin/set_param thetah 0.0483 ../bin/set_param MH1 40 ../bin/set_param gDMh 0.02 ../bin/set_param thetaa 0.0215986 ../bin/set_param thetac 0.00436336 ../bin/set_param n 0.641179 ../bin/set_param Delta 10 ../bin/set_param K 1.2542e-08 ../bin/set_vegas 10 1000000 0 0 0 ../bin/subproc_cycle 0 >out40.txt

Diana Rojas DM in the 3HDM