cp violating dark matter - ulisboacftp.tecnico.ulisboa.pt/~2hdmwork/slides/2016/day1/venus...cp...

CP violating Dark Matter

Venus Keus

University of Helsinki & Helsinki Institute of Physics

In collaboration with

S. F. King & S. Moretti & D. Sokolowska & J. Hernandez & D. Rojas & A. Cordero

arXiv:1608.01673 & work in progress

September 2016

1 Introduction and motivation

2 Relic densityRelevant DM scenarios

3 LHC limitsHiggs invisible branching ratio and total decay widthThe signal strength of Higgs decay into two photons

4 LHC SignalsInert cascade decays at the LHC

5 Summary

Introduction Relic density LHC limits LHC Signals Summary

Shortcomings of SM and the need for BSM

No sign of New Physics at the LHC

No viable DM candidate

Insufficient amount of CP violation

An unstable vacuum

No explanation for the fermion mass hierarchy

...

Scalar extensions aiming to provide a solution:

Higgs portal models: φ, S

2HDM: φ1, φ2

IDM - I(1+1)HDM: φ1, φ2

3HDM - I(1+2)HDM: φ1, φ2, φ3, I(2+1)HDM: φ1, φ2, φ3

Venus Keus (Helsinki) CPV DM September 2016 3/23


The scalar potential with explicit CPV

V3HDM = V0 + VZ2

V0 =3∑i

[−µ2i (φ†i φi ) + λii (φ

†i φi )

2

]

+3∑i ,j

[λij(φ

†i φi )(φ†j φj) + λ′ij(φ

†i φj)(φ†j φi )

]VZ2 = −µ212(φ†1φ2) + λ1(φ†1φ2)2 + λ2(φ†2φ3)2 + λ3(φ†3φ1)2 + h.c .

+λ4(φ†3φ1)(φ†2φ3) + λ5(φ†1φ2)(φ†3φ3) + λ6(φ†1φ2)(φ†1φ1)

+λ7(φ†1φ2)(φ†2φ2) + λ8(φ†3φ1)(φ†3φ2) + h.c.

The Z2 symmetry

φ1 → −φ1, φ2 → −φ2, φ3 → φ3, SM fields→ SM fields



Parameters of the model

no new phenomenology from λ4, · · · , λ8 terms → λ4−8 = 0

“dark” parameters λ1, λ11, λ22, λ12, λ′12

“dark democracy” limitµ21 = µ22, λ3 = λ2, λ31 = λ23, λ′31 = λ′23fixed by the Higgs mass µ23 = v2λ33 = m2

h/2

7 important parameters

CPV and mass splittings µ212 = |µ212|e iθ12 , λ2 = |λ2|e iθ2

Higgs-DM coupling λ2, λ23, λ′23

Mass scale of inert particles µ22



The CP-mixed mass eigenstates

The doublet compositions

φ1 =

(H+1

H01+iA0

1√2

), φ2 =

(H+2

H02+iA0

2√2

), φ3 =

(G+

v+h+iG0√2

)

The mass eigenstates

S1 =αH0

1+αH02−A0

1+A02√

2α2+2, S2 =

−H01−H0

2−αA01+αA

02√

2α2+2

S3 =βH0

1−βH02+A0

1+A02√

2β2+2, S4 =

−H01+H0

2+βA01+βA

02√

2β2+2

S±1 = e∓iθ12/2√2

(H±2 + H±1 ), S±2 = e∓iθ12/2√2

(H±2 − H±1 )

S1 is assumed to be the DM candidate



Input parameters and constraints

DM mass mS1 , Mass splittings δS2−S1 , δS±1 −S1

, δS±2 −S±

1,

Higgs-DM coupling gS1S1h, CPV phases θ2, θ12

Constraints taken into account include:

Limits from gauge bosons width:mSi + mS±

j≥ mW , mSi + mSj ≥ mZ , 2mS±

1,2≥ mZ

Limits on charged scalar mass and lifetime:mS±

i≥ 70 GeV, τ ≤ 10−7 s → Γtot ≥ 10−18 GeV

Null DM collider searches excluding simultaneously:mSi ≤ 100 GeV, mS1 ≤ 80 GeV, ∆m(S1,Si ) ≥ 8 GeV



Relevant DM scenarios and sum of the CPV phases

In the low mass region (mS1 < mZ ):

Scenario A: mS1 � mS2 ,mS3 ,mS4 ,mS±1,mS±

2

Scenario B: mS1 ∼ mS3 � mS2 ,mS4 ,mS±1,mS±

2

Scenario C: mS1 ∼ mS3 ∼ mS2 ∼ mS4 � mS±1,mS±

2

In the heavy mass region (mS1 > 400 GeV):

Scenario G: mS1 ∼ mS3 ∼ mS±1� mS2 ∼ mS4 ∼ mS±

2

Scenario H: mS1 ∼ mS3 ∼ mS2 ∼ mS4 ∼ mS±1∼ mS±

2

Details in Dorota’s talk on Friday



Relevant DM scenarios in the low mass region

50 60 70 80ms1 [GeV]

-0.2

-0.1

0.1

0.2

gS1 S1 h

Low and medium DM mass region

A1

B1

C1




Relevant DM scenarios in the heavy mass region

400 500 600 700 800ms1

[GeV]

-0.6

-0.4

-0.2

0.2

0.4

0.6

gS1 S1 h

H1

G1




Higgs invisible branching ratio and total decay

From ATLAS and CMS

Br(h→ inv) < 0.23− 0.36

for mi ,j < mh/2 if long lived

BR(h→ inv) =

∑i ,j Γ(h→ SiSj)

ΓSMh +

∑i Γ(h→ SiSj)

The total decay signal strength

µtot =BR(h→ XX )

BR(hSM → XX )=

ΓSMtot (h)

ΓSMtot (h) + Γinert(h)

We use µtot = 1.17± 0.17 at 3σ level.



Higgs-inert couplings in different scenarios

50 60 70 80 90

MS1 [GeV]

0.05

0.10

0.15

0.20

gSi Sj h

gS1 S1 h=0.1

hS1S1

B1:hS3S3

C1:hS1S2

C1:hS2S2

C1:hS3S3

C1:hS3S4

C1:hS4S4

50 60 70 80 90

mS1 [GeV]

0.02

0.04

0.06

0.08

0.10

0.12

gSi Sj h

gS1 S1 h=0.001

hS1S1

B1:hS3S3

C1:hS1S2

C1:hS2S2

C1:hS3S3

C1:hS3S4

C1:hS4S4



Higgs inert decays and Higgs total decay

-0.10 -0.05 0.05 0.10

gS1 S1 h

0.2

0.4

0.6

0.8

1.0

Br(h→SiSj)

mS1= 50 [GeV]

A1

B1

C1

LHC μhtot



Relic density vs. Higgs decay bounds

45 50 55 60ms1

[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 60ms1

[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




45 50 55 60ms1

[GeV]-0.2

-0.1

0.0

0.1

0.2

gS1 S1 h

case C1

μmintot(h)=0.66

Br(h→inv)=0.20



h→ γγ signal strength bounds

From ATLAS and CMS: µγγ = 1.16+0.20−0.18

µγγ =Γ(h→ γγ)3HDM Γ(h)SM

Γ(h→ γγ)SM Γ(h)3HDM

Modified by

charged scalars contribution to Γ(h→ γγ)3HDM

light neutral scalars contribution to Γ(h)3HDM



Relic density vs. h→ γγ signal strength - scenario A

40 45 50 55 60

-0.2

-0.1

0.0

0.1

0.2

MS1 [GeV]

gS1S1h

0.2

0.4

0.6

0.8

65 70 75 80 85 90

-0.3

-0.2

-0.1

0.0

0.1

MS1 [GeV]

gS1S1h

0.88

0.92

0.96

1.00



Relic density vs. h→ γγ signal strength - scenario B

40 45 50 55 60

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

MS1 [GeV]

gS1S1h

0.2

0.4

0.6

0.8

65 70 75 80 85 90

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

MS1 [GeV]

gS1S1h

0.75

0.80

0.85

0.90

0.95



Relic density vs. h→ γγ signal strength - scenario C

40 45 50 55 60

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

MS1 [GeV]

gS1S1h

0.2

0.4

0.6

0.8

65 70 75 80 85 90

-0.3

-0.2

-0.1

0.0

0.1

MS1 [GeV]

gS1S1h

0.81

0.83

0.85

0.87

0.89



Relic density vs. h→ γγ signal strength - scenarios G & H

400 500 600 700 800

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

MS1 [GeV]

gS1S1h

0.98

0.99

1.00

1.01

1.02

400 500 600 700 800

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

MS1 [GeV]

gS1S1h

0.98

0.99

1.00

1.01

1.02



Inert cascade decays at the LHC

Cross section for ETmiss + e+e− at the LHC13

At tree level pp → h→ S1S2,3,4 → S1S1Z∗ → S1S1e

+e− with σ ∼ 10−3

At loop level pp → h→ S1S2,3,4 → S1S1γ∗ → S1S1e

+e− with σ ∼ 10−63 Cascade decays

S2,3,4

Z⇤

S1

Figure 1: Tree-level cascade decays

S2,3,4

S+

S1W+

S+

�⇤

S2,3,4

W+

S1S+

W+

�⇤

Figure 2: Triangle cascade decays

S2,3,4

S1

�⇤

S+

W+

S2,3,4

�⇤

S1

S+

W+

S2,3,4

S1

�⇤

S+

S+

Figure 3: Bubble cascade decaysIn the studied model there is one absolutely stable particle, H1. Its decays into SM

particles are forbidden by the conservation of Z2 symmetry. By construction, all otherinert particles, which are also Z2-odd, are heavier and hence unstable. Their decaysmay provide striking signals for the studied I(2+1)HDM.

Access to the inert sector can be obtained through the Higgs particle. In this modelh can decay into various pairs of inert particles, leading to di↵erent signatures. Inthe following study we consider the Higgs production at the LHC mainly through the

6

3 Cascade decays

S2,3,4

S+

S1W+

S+

�⇤

S2,3,4

W+

S1S+

W+

�⇤


S2,3,4

S1

�⇤

S+

W+

S2,3,4

�⇤

S1

S+

W+

S2,3,4

S1

�⇤

S+

S+



Access to the inert sector can be obtained through the Higgs particle. In this modelh can decay into various pairs of inert particles, leading to di↵erent signatures. Inthe following study we consider the Higgs production at the LHC mainly through thegluon fusion, then its decay into pair of inert particles, with the heavy inert particlesubsequently decaying into H1 and o↵-shell W/Z/�. In the end, such decay chains couldresult in highly energetic Electro-Magnetic (EM) showers, alongside significant missingtransverse energy, ��ET , induced by the DM pair, which would generally be captured bythe detectors.

6

3 Cascade decays

S2,3,4

S+

S1W+

S+

�⇤

S2,3,4

W+

S1S+

W+

�⇤


S2,3,4

S1

�⇤

S+

W+

S2,3,4

�⇤

S1

S+

W+

S2,3,4

S1

�⇤

S+

S+



Access to the inert sector can be obtained through the Higgs particle. In this modelh can decay into various pairs of inert particles, leading to di↵erent signatures. Inthe following study we consider the Higgs production at the LHC mainly through thegluon fusion, then its decay into pair of inert particles, with the heavy inert particlesubsequently decaying into H1 and o↵-shell W/Z/�. In the end, such decay chains couldresult in highly energetic Electro-Magnetic (EM) showers, alongside significant missingtransverse energy, ��ET , induced by the DM pair, which would generally be captured bythe detectors.

6

Details in Diana’s talk on Tuesday



Summary

I(2+1)HDM: A minimal model for CP violating Dark Matter

Opens up new regions of parameter space regarding relic density

Observable at the LHC13


BACKUP SLIDES


The masses of the neutral inerts

m2S1 =

v2

2(λ′23 + λ23)− Λ− µ22,

m2S2 =

v2

2(λ′23 + λ23) + Λ− µ22,

m2S3 =

v2

2(λ′23 + λ23)− Λ′ − µ22,

m2S4 =

v2

2(λ′23 + λ23) + Λ′ − µ22,


In the CPC limit

α =−|µ212| cos θ12 + v2|λ2| cos θ2 − Λ

|µ212| sin θ12 + v2|λ2| sin θ2→∞

β =|µ212| cos θ12 + v2|λ2| cos θ2 − Λ′

|µ212| sin θ12 − v2|λ2| sin θ2→∞

where

Λ =√

v4|λ2|2 + |µ212|2 − 2v2|λ2||µ212| cos(θ12 + θ2),

Λ′ =√

v4|λ2|2 + |µ212|2 + 2v2|λ2||µ212| cos(θ12 + θ2).


Relevant DM scenarios and sum of the CPV phases



Benchmark scenarios

A1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 1.5

B1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 0.82

C1 : δ12 = 12 GeV, δ1c = 100 GeV, δc = 1 GeV, θ2 = θ12 = 1.57

G1 : δ12 = 2 GeV, δ1c = 1 GeV, δc = 1 GeV, θ2 = θ12 = 0.82

H1 : δ12 = 50 GeV, δ1c = 1 GeV, δc = 50 GeV, θ2 = θ12 = 0.82


Inert-Z couplings

50 60 70 80 90

mS1 [GeV]

-1.0

-0.8

-0.6

-0.4

-0.2

gSi Sj Z

CPC

A1:ZS1S3

A1:ZS1S4

B1:ZS1S3

B1:ZS1S4

C1:ZS1S3

C1:ZS1S4


Relic density for low DM mass region

-0.2 -0.1 0.0 0.1 0.2gS1 S1 h0.05

0.10

0.15

0.20

0.25

0.30ΩDMh

2

B1:mS1 = 45 GeV

A1:mS1 = 47 GeV

B1:mS1 = 47 GeV

B1:mS1 = 50 GeV

A1:mS1 = 53 GeV


Relic density for medium DM mass region

-0.2 -0.1 0.0 0.1 0.2gS1 S1 h0.05

0.10

0.15

0.20

0.25

0.30ΩDMh

2

A1:mS1 = 69 GeV

A1:mS1 = 75 GeV


Filling the plot

50 60 70 80 90ms1

[GeV]

-0.2

-0.1

0.1

0.2

gS1 S1 h

CPC

B2

B3

B4

Other


cp violating dark matter - ulisboacftp.tecnico.ulisboa.pt/~2hdmwork/slides/2016/day1/venus...cp...

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