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Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Scalar Dark Matter candidatein Multi-Higgs Models
Dorota Sokołowska
University of Warsaw, Faculty of Physics,Institute of Theoretical Physics
Moriond QCD, La Thuile, 26.03.2017
based onJHEP 1612 (2016) 014 and work in progress
with A. Cordero-Cid, J. Hernandez-Sanchez, V. Keus,S. F. King, S. Moretti, D. Rojas
1 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
The Standard Model
A rigorously tested Theory of Fundamental Interactions
From the LHC:
• a Higgs particle found in 2012
• no significant deviation from the SM
• no sign of New Physics
But no explanation for:
• Dark Matter
• neutrino masses
• baryon asymmetry and baryogenesis
• extra source of CP violation
• vacuum stability
• ...
Parameter value1− 0.5− 0 0.5 1 1.5 2 2.5 3 3.5 4
bbµ
ττµ
WWµ
ZZµ
γγµ
Run 1LHCCMS and ATLAS ATLAS+CMS
ATLAS
CMS
σ1±σ2±
JHEP 08 (2016) 045
2 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Dark MatterEvidence for Dark Matter at diverse scales:
• galaxy scales: rotational speeds 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 Interacting Massive Particle
• stable due to the discrete symmetry
DM DM→ SM SM︸ ︷︷ ︸pair annihilation
, DM 6→ SM, ...︸ ︷︷ ︸stable
• annihilation cross-section 〈σv〉 ∝ EW interaction
• thermal evolution of DM density – a fixed value after freeze-out
3 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Higgs-portal DM
Simplest realisation: the SM with ΦSM + Z2-odd scalar S:
S → −S, SM fields→ SM fields
L = LSM +1
2(∂S)2 − 1
2m2DMS
2 − λDMS4 − λSShΦ2SMS
2
SM sectorHiggs←→ DM sector
DM
DM
hSM
N N
DM DM
hSM
SM
SM
DM
DM
hSM
⟨σv⟩ σDM−N ΓinvhSM
given by the same coupling
Strong constraints from relic density + direct detection + Higgs decays
⇒ modified Higgs-portal-type DM candidates in multi-scalar models
in this talk: focus on DM phenomenology in the I(2+1)HDM i.e.
3HDM with Two Inert and One Higgs doublet
4 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
I(2+1)HDM
Z2-symmetry in I(2+1)HDM:
φ1 → −φ1, φ2 → −φ2, φ3 → φ3, SM fields→ SM fields
Z2-invariant potential:
V =3∑i
[−|µ2
i |(φ†iφi) + λii(φ†iφi)
2]
+3∑ij
[λij(φ
†iφi)(φ
†jφj) + λ′ij(φ
†iφj)(φ
†jφi)
]+(−µ2
12(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.)
• 21 parameters in V
• µ212, λ1, λ2, λ3 are complex
• Yukawa interaction: ”Model I”-type (only φ3 couples to fermions)
• explicit Z2-symmetry
5 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Parameters of V
• µ23 = v2λ33 = m2
h/2 fixed from extremum conditions
• ”dark democracy”: µ21 = µ2
2, λ13 = λ23, λ′13 = λ′23, λ3 = λ2, e.g.
λ2(φ†2φ3)2 + λ3(φ†3φ1)2 + h.c.→ λ2
((φ†2φ3)2 + (φ†3φ1)2 + h.c.
)•(λ4(φ†3φ1)(φ†2φ3) + λ5(φ†1φ2)(φ†3φ3) + ...
): no new phenomenology
2M ⇒ λ4−8 = 0
• λ1, λ11,22,12, λ′12 – self-interactions of inert doublets
21 parameters → 7 important parameters
• µ22 – mass scale of inert particles
• µ212 = |µ2
12|eiθ12 , λ2 = |λ2|eiθ2 – mass splittings and CPv phase
• λ2, λ23, λ′23 – DM-Higgs coupling
6 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
DM in I(2+1)HDM
Z2-invariant vacuum state:
φ1 =
(H+
1
H01+iA0
1√2
), φ2 =
(H+
2
H02+iA0
2√2
), φ3 =
(G+
v+h+iG0√
2
)
• φ3 – SM-like doublet with SM-like Higgs h
• Z2-odd doublets φ1 and φ2 mix:
S1 =αH0
1 + αH02 −A0
1 +A02√
2α2 + 2, S2 =
−H01 −H0
2 − αA01 + αA0
2√2α2 + 2
S3 =βH0
1 − βH02 +A0
1 +A02√
2β2 + 2, S4 =
−H01 +H0
2 + βA01 + βA0
2√2β2 + 2
H±1 =e±iθ12/2√
2(S±1 − S
±2 ), H±2 =
e∓iθ12/2√2
(S±1 + S±2 )
• 4 neutral and 4 charged Z2-odd particles (double the IDM)
• S1 – DM candidate, other dark particles heavier
7 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Physical Parameters
Parameters of V : µ22, |λ2|, |µ2
12|, λ23, λ′23, θ12, θ2
Physical parameters:
DM mass:
mS1
Mass splittings:
δ12 = mS2 −mS1
δ1c = mS±1−mS1
δc = mS±2−m
S±1
Higgs-DM coupling:
gS1S1h
CPv phases:
θ12, θ2
8 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Benchmark scenarios
This talk: mS1 < mZ :
A1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 1.5
mS1 < mS2,3,4 ,mS±1,2
(no coannihilation)
B1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 0.82
mS1 ≈ mS3 < mS2,4 ,mS±1,2
C1 : δ12 = 12 GeV, δ1c = 100 GeV, δc = 1 GeV, θ2 = θ12 = 1.57
mS1 ≈ mS3 ≈ mS4 ≈ mS2 < mS±1,2
Checked against experimental and theoretical constraints:details in JHEP 1612 (2016) 014
9 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
DM Annihilation for light DM
S1
S1
h
f
f
Higgs-mediated annihilation
depends on mS1 and gS1S1h
S1
Sj
Z
f
f ′
Z-mediated coannihilation
depends on mSj −mS1 :
A1: no coannihilation
B1: S1S3 coannihilation only
C1: S1S3, S2S4, S1S4, S2S3 coann.
depends on ZSiSj couplings
10 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Z-inert couplings
χZS1S3 = χZS2S4 = α+β√α2+1√β2+1
, χZS1S4 = χZS2S3 = αβ−1√α2+1√β2+1
,
χ2ZS1S3
+ χ2ZS1S4
= 1, χ2ZS2S3
+ χ2ZS2S4
= 1
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
• mass order: mS1 < mS3 < mS4 < mS2
• CPc value χZS1S3 = −1, χZS1S4 = 0
• ZS1S3 – reduced; 20− 50% for A1, B1, ∼ 0 for C1• ZS1S4 – close to the CPc value → dominant channel for C1
11 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Low DM mass
45 50 55 60ms1
[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)
B1: + ZS1S3 coannihilation (reduced with respect to the CPc case)
C1: mainly ZS1S4 coannihilation (χZS1S4 ≈ −1)
C1: + Higgs annihilation
Tools used in calculation: LanHEP, arXiv:1412.5016 [physics.comp-ph]; CalcHEP 3.4, Comput. Phys.
Commun. 184 (2013) 1729;micrOMEGAs 4.2 arXiv:1407.6129 [hep-ph]
12 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Medium DM mass
Main annihilation channels into gauge bosons V = W±, Z:S1
S1
h
V
V
gS1S1h, ge
S1
S1
V
V
gV V S1S1 =g2e
2 sin2 θW
no dependence on the benchmarks
65 70 75 80 85 90ms1
[GeV]
-0.3
-0.2
-0.1
0.1
0.2
0.3
gS1 S1 h
A1
B1
C1
13 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
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
mS1 < mh/2: many new solutions:
mS1 < mh/2: different mass splittings + ZSiSj interaction strength
mS1 > mh/2: less freedom but still new solutions:
mS1 > mh/2: Higgs mediated coannihilation + sign of hS3S3 coupling
14 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Direct detection
σS1,N ∝g2S1S1h
(mS1+mN )2
10-39
10-38
10-37
40 50 60 70 80 90
mS1 [GeV]
10-1510-1410-1310-1210-1110-1010-910-810-710-6
σS1,N
[pb
]
A1B1C1
LUX (2016)XENON1T
ν scattering
Case A1: mostly excluded (large gS1S1h)
Cases B1 and C1: mostly within the limits
15 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Indirect detection
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〉
[cm
3/s
]
mS1 [GeV]
A1B1C1
Fermi-LAT (bb-)
Most of the parameters space in agreement with Fermi-LAT
16 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
LHC constraints
Higgs invisible decays
Γ(h→ S1S1) =g2S1S1hv
2
32πmh
(1−
4m2S1
m2h
)1/2
, Br(h→ inv) = Γ(h→S1S1)
ΓSMh
+Γ(h→S1S1)
Higgs total decay
µtot = BR(h→XX)BR(hSM→XX)
=ΓSMtot (h)
ΓSMtot (h)+Γinert(h)
LHC limits
µtot = 1.17± 0.17 and Br(h→ inv) < 0.2
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
17 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
LHC constraints
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
In general: scenarios of type C are the least constrained.
18 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Conclusions and Outlook
• 3HDM with Z2 symmetry: I(2+1)HDM
• viable DM candidate
• large dark sector: important coannhilation effects in ΩDMh2
ala → varying strength of gauge-inert couplings
ala → new regions in agreement with Planck
• agreement with direct and indirect detection limits:
45 GeV . mS1 . 62.5 GeV, 64 GeV . mS1 . 74 GeV, mS1 & 400 GeV
→ as long as DM is practically invisible
→ other detections prospects?
19 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Inert cascade decays at the LHC
work in progress
pp→ Z → S2,3,4S1 → S1S1Z∗ → S1S1e
+e−
S2,3,4
Z∗e−
e+
S1
• signature: missing ET and dilepton pair
• dominant if there is a large mass splitting between DM and otherinert particles
• process present in the IDM (through HAZ vertex)
• note: possible differences with respect to the IDM due to varyingstrength of S1SjZ vertex
20 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Inert cascade decays at the LHC
work in progress
pp→ h→ S2,3,4S1 → S1S1γ∗ → S1S1e
+e−
S2,3,4
S+
S1
W+
S+
γ∗
S2,3,4
S1
γ∗
S+
W+
• signature: missing ET and dilepton pair
• important if there is a small mass splitting between DM and otherinert particles → scenario C is preferred anyway
• process absent in the IDM (no A→ Hγ∗ loop)
• promising preliminary results σ ∼ 10−5 pb
21 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
DM self-couplings
Dark self-couplings – no impact on standard DM and LHC phenomenology
• In the I(1+1)HDM – λ2
• In the I(2+1)HDM – λ1, λ11,22,12, λ′12
• Possible relevant corrections to loop processes, e.g.:
D
D γD+
γ
D
D D+
h
f
f
D – DM matter, D± – charged dark scalar
• Astrophysical DM detection experiments:
DM very weakly coupled to the visible sector
⇒ loop corrections can be important!
22 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
Final Summary
Scalar DM models:
• interesting phenomenology
• strong constraints on gDMh from DM experiments
• need to move away from Higgs-portal
• solution: rich particle spectrum & coannihilation effects
• interesting LHC signatures – a tool for testing DM models?
• loop processes & role of self-couplings – can be important
• Further work needed!
23 / 24
Motivation I(2+1)HDM mS1< mZ LHC Conclusion
References
• Higgs-portal DM models[B. Patt and F. Wilczek, hep-ph/0605188, X. Chu, T. Hambye, and M. H. Tytgat, JCAP 1205
(2012) 034, A. Djouadi, O. Lebedev, Y. Mambrini, and J. Quevillon, Phys.Lett. B709 (2012)
65–69]
• 3HDM[V. Keus, S. King, S. Moretti JHEP 1401 (2014) 052, arXiv:1408.0796; V. Keus, S. F. King,
S. Moretti and D. Sokolowska, JHEP 1411 (2014) 016, JHEP 1511, 003 (2015)]
• Experimental constraints[ATLAS and CMS collaborations, JHEP 08 (2016) 045; http://lux.brown.edu/LUX_dark_matter/Talks_
files/LUX_NewDarkMatterSearchResult_332LiveDays_IDM2016_160721.pdf(“Dark-matter results from 332 new
live days of LUX data, Identification of Dark Matter, The University of Sheffield, Sheffield, UK,
21 July, 2016”), M. Ackermann et al. [Fermi-LAT Collaboration], Phys. Rev. Lett. 115 (2015)
23, 231301, XENON1T Collaboration, Springer Proc. Phys. 148 (2013) 93 ]
• Numerical Tools[LanHEP, arXiv:1412.5016 [physics.comp-ph]; CalcHEP 3.4, Comput. Phys. Commun. 184
(2013) 1729; micrOMEGAs 4.2 arXiv:1407.6129 [hep-ph]]
24 / 24
BACKUP SLIDES
25 / 24
Heavy DM
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 Case H
• The same behaviour in both cases
• Lower mS1 for Case G
• Not really different from the CPc case
26 / 24
Direct Detection
σDM,N ∝g2S1S1h
(MS1+MN )2
400 500 600 700 800mS1 [GeV]
10-15
10-13
10-11
10-9
σ(DM,N [pb]
LUX
XENON 1T
ν scattering
case G1
case H1
• in agreement with LUX
• within the reach of XENON-1T
• case G (bigger couplings) easier to see/exclude than case H (smallercouplings)
27 / 24
Mass formulas
m2
S±1
= (−µ22 − |µ2
12|) +1
2λ23v
2, m2
S±2
= (−µ22 + |µ2
12|) +1
2λ23v
2.
m2S1
=v2
2(λ′23 + λ23)− Λ− µ2
2,
m2S2
=v2
2(λ′23 + λ23) + Λ− µ2
2,
m2S3
=v2
2(λ′23 + λ23)− Λ′ − µ2
2,
m2S4
=v2
2(λ′23 + λ23) + Λ′ − µ2
2,
Λ =√v4|λ2|2 + |µ2
12|2 − 2v2|λ2||µ212| cos(θ12 + θ2),
Λ′ =√v4|λ2|2 + |µ2
12|2 + 2v2|λ2||µ212| cos(θ12 + θ2).
α =−|µ2
12| cos θ12 + v2|λ2| cos θ2 − Λ
|µ212| sin θ12 + v2|λ2| sin θ2
, β =|µ2
12| cos θ12 + v2|λ2| cos θ2 − Λ′
|µ212| sin θ12 − v2|λ2| sin θ2
.
28 / 24
Physical Basis
|µ212| =
1
2(m2
S±2−m2
S±1
),
λ23 =2µ2
2
v2+m2
S±2
+m2
S±1
v2,
λ′23 =1
v2(m2
S2+m2
S1−m2
S±2−m2
S±1
),
µ22 =
v2
2gS1S1h −
v2|λ2|2(1 + α2)
(4α sin θ2 + 2(α2 − 1) cos θ2
)−m2S2
+m2S1
2,
|λ2| =1
v2
[|µ2
12| cos(θ2 + θ12)+√|µ2
12|2 cos2(θ2 + θ12) +
(m2S2−m2
S1
2
)2
− |µ212|2
.
29 / 24
DM annihilation diagrams
Light DM annihilation:
S
S
h
f
f(a)
S
S′
V
f
f ′
(b)Virtual gauge bosons:
S
S′
h
V, V ∗
V, V ∗
(a)
S
S
V, V ∗
V, V ∗
(b)
30 / 24
DM annihilation diagrams - gauge limit
Heavy DM (co)annihilation diagrams with pure gauge boson final states:
S
S′
V
V ′
V ′′
(a)
S
S′
V
V ′
(b)
S
S′′
S′
V
V ′
+ crossed
(c)
31 / 24
DM annihilation diagrams
Heavy DM (co)annhilation channels involving the SM-like Higgs boson:
S
S′
h
V
V ′
(a)
S
S′
h
V
V ′
(b)
S
S′′
S′
V
h
+ crossed
(c)
S
S′
h
h
h(d)
S
S′
h
h(e)
S
S′′
S′
h
h
+ crossed
(f)
32 / 24
Relic density
-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
-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
33 / 24
Higgs-inert couplings
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
34 / 24