[PPT] - Triplet-Quadruplet Fermionic Dark Matter Backups Conclusion PowerPoint Presentation

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Triplet-Quadruplet Fermionic Dark Matter

Zhao-Huan Yu (余钊焕)

ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, the University of Melbourne

Based on Tim Tait and ZHY, arXiv:1601.01354, JHEP CosPA 2016, Sydney 1 December, 2016

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 1 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Dark Matter in the Universe

dark matter halo stellar disk gas

M33

Bullet Cluster Bullet Cluster Spiral galaxy M33 Spiral galaxy M33 CMB CMB Planck 2015

[1502.01589]

Cold DM (25.8%) Ωch2 = 0.1186 ± 0.0020 Baryons (4.8%) Ωbh2 = 0.02226 ± 0.00023 Dark energy (69.3%) ΩΛ = 0.692 ± 0.012

Dark matter (DM) makes up most of the matter component in the Universe, as suggested by astrophysical and cosmological observations

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 2 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

DM Relic Abundance

[Feng, arXiv:1003.0904]

If DM particles (χ) were thermally produced in the early Universe, their relic abundance would be determined by the annihilation cross section 〈σannv〉: Ωχh2 ≃ 3 × 10−27 cm3 s−1 〈σannv〉 Observation value Ωχh2 ≃ 0.1 ⇒ 〈σannv〉 ≃ 3 × 10−26 cm3 s−1 Assuming the annihilation process consists of two weak interaction vertices with the gauge coupling , for we have A very attractive class of DM candidates: Weakly interacting massive particles (WIMPs)

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 3 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

DM Relic Abundance

[Feng, arXiv:1003.0904]

If DM particles (χ) were thermally produced in the early Universe, their relic abundance would be determined by the annihilation cross section 〈σannv〉: Ωχh2 ≃ 3 × 10−27 cm3 s−1 〈σannv〉 Observation value Ωχh2 ≃ 0.1 ⇒ 〈σannv〉 ≃ 3 × 10−26 cm3 s−1 Assuming the annihilation process consists of two weak interaction vertices with the SU(2)L gauge coupling g ≃ 0.64, for mχ ∼ O(TeV) we have 〈σannv〉 ∼ g4 16π2m2

χ

∼ O(10−26) cm3 s−1 ⇒ A very attractive class of DM candidates: Weakly interacting massive particles (WIMPs)

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 3 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

WIMP Models

WIMPs are typically introduced in the extensions of the Standard Model (SM) aiming at solving the gauge hierarchy problem Supersymmetry (SUSY): the lightest neutralino ( ˜ χ0

1)

Universal extra dimensions: the lightest KK particle (B(1), W 3(1), or ν(1)) For DM phenomenology, it is quite natural to construct WIMP models by extending the SM with a dark sector consisting of multiplets, whose neutral components could provide a viable DM candidate 1 multiplet in a high-dimensional representation: minimal DM model [Cirelli et al., hep-ph/0512090] (DM stability is explained by an accidental symmetry) 2 types of multiplets: an artifjcial symmetry is usually needed Singlet-doublet DM model [Mahbubani & Senatore, hep-ph/0510064;

D’Eramo, 0705.4493; Cohen et al., 1109.2604]

Doublet-triplet DM model [Dedes & Karamitros, 1403.7744]

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 4 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

WIMP Models

WIMPs are typically introduced in the extensions of the Standard Model (SM) aiming at solving the gauge hierarchy problem Supersymmetry (SUSY): the lightest neutralino ( ˜ χ0

1)

Universal extra dimensions: the lightest KK particle (B(1), W 3(1), or ν(1)) For DM phenomenology, it is quite natural to construct WIMP models by extending the SM with a dark sector consisting of SU(2)L multiplets, whose neutral components could provide a viable DM candidate 1 multiplet in a high-dimensional representation: minimal DM model [Cirelli et al., hep-ph/0512090] (DM stability is explained by an accidental symmetry) 2 types of multiplets: an artifjcial Z2 symmetry is usually needed Singlet-doublet DM model [Mahbubani & Senatore, hep-ph/0510064;

D’Eramo, 0705.4493; Cohen et al., 1109.2604]

Doublet-triplet DM model [Dedes & Karamitros, 1403.7744] ··· ···

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 4 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Connection to SUSY models

The above models with SU(2)L multiplets can be understood as simplifjcations

f more complete models, but the model parameters are much more free

Singlet-doublet fermionic DM model: Bino-higgsino sector in the MSSM Lmass ⊃ −1 2 M1 ˜ B˜ B − µ( ˜ H+

u ˜

H−

d − ˜

H0

u ˜

H0

d) + g′vd

2

˜ B ˜ H0

d − g′vu

2

H0

u ˜

H0

d) − gvd

2

˜ W 0 ˜ H0

d

+ gvu

2

˜ W 0 ˜ H0

u − gvu ˜

H+

u ˜

W − − gvd ˜ W + ˜ H−

d + h.c.

Triplet-quadruplet fermionic DM model: no analogue in usual SUSY models

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 5 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Triplet-Quadruplet Fermionic DM Model

Introduce left-handed Weyl fermions in the dark sector: T =   T + T 0 T −   ∈ (3,0), Q1 =     Q+

1

Q0

1

Q−

1

Q−−

1

    ∈

4,−1

2

,

Q2 =     Q++

2

Q+

2

Q0

2

Q−

2

    ∈

4,+1

2

Covariant kinetic and mass terms:

LT = iT † ¯ σµDµT − 1 2(mT T T + h.c.) LQ = iQ†

1 ¯

σµDµQ1 + iQ†

2 ¯

σµDµQ2 − (mQQ1Q2 + h.c.) Yukawa couplings: LHTQ = y1ϵjl(Q1)jk

i T i kHl − y2(Q2)jk i T i kH† j + h.c.

Z2 symmetry: odd for dark sector fermions, even for SM particles ⇒ forbids operators like T LH, TecH†H†, Q1L†HH†, Q2LHH†, ...

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 6 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

State Mixing

Lmass = −1 2(T 0,Q0

1,Q0 2)MN

  T 0 Q0

1

Q0

2

  − (T −,Q−

1,Q− 2)MC

  T + Q+

1

Q+

2

  − mQQ−−

1 Q++ 2

+ h.c. = −1 2

3

∑

i=1

mχ0

i χ0

i χ0 i − 3

∑

i=1

mχ±

i χ−

i χ+ i + h.c. − mQχ−−χ++

MN =    mT

1

3 y1v

− 1

3 y2v

1

3 y1v

mQ − 1

3 y2v

mQ   , MC =    mT

1

2 y1v

− 1

6 y2v

− 1

6 y1v

−mQ

1

2 y2v

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Introduction Model Details Mass corrections Constraints Conclusion Backups

y1 = y2: Custodial Symmetry

When the two Yukawa couplings are equal (y = y1 = y2), the Lagrangian has an SU(2)L × SU(2)R global symmetric form: LQ + LHTQ = i(Q†A)k

i j ¯

σµDµ(QA)i j

k − 1

2[mQϵABϵil(QA)i j

k (QB)lk j + h.c.]

+[yϵAB(QA)jk

i T i k(HB)j + h.c.]

SU(2)R doublets: (QA)i j

k =

(Q1)i j

k

(Q2)i j

k

, (HA)i =
H†

i

Hi

This is a custodial symmetry, explicitly broken by U(1)Y gauge interactions

This approximate symmetry leads to special mixing patterns: Identical magnitudes of Q1 and Q2 components in χ0

i and χ± i Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 8 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

y1 = y2: Custodial Symmetry

Mass (GeV) y

LO, mQ = 200 GeV, mT = 400 GeV, y = y1 = y2 150 200 250 300 350 400 450 500

1.0
0.5

0.0 0.5 1.0 mχ0

1 = mχ± 1 = mχ±±

mχ0

2 = mχ± 2

mχ0

3 = mχ± 3

Mass (GeV) y

LO, mQ = 400 GeV, mT = 200 GeV, y = y1 = y2 150 200 250 300 350 400 450 500

1.0
0.5

0.0 0.5 1.0 mχ0

1 = mχ± 1

mχ0

2 = mχ± 2 = mχ±±

mχ0

3 = mχ± 3

mQ < mT case mT < mQ case In the custodial symmetry limit, each of the dark sector neutral fermions is exactly degenerate in mass with a singly charged fermion at the LO. Mass corrections at the NLO are needed to check if mχ0

1 < mχ± 1 , mχ±±.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 9 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

y1 = y2: Custodial Symmetry

ghχ0

1χ0 1

y2 / y1

y1 = 1

0.60
0.40
0.20

0.00 0.20 0.40 0.60 0.80 1.00

1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0 mQ = 200 GeV mT = 400 GeV mQ = 400 GeV mT = 200 GeV

gZχ0

1χ0 1

y2 / y1

y1 = 1

0.20
0.15
0.10
0.05

0.00 0.05 0.10

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0 mQ = 200 GeV mT = 400 GeV mQ = 400 GeV mT = 200 GeV

hχ0

1χ0 1 coupling

Zχ0

1χ0 1 coupling

In the custodial symmetry limit, when mQ < mT, we have χ0

1 = (Q0 1 + Q0 2)/

2,

which leads to vanishing χ0

1 couplings to h and Z at the tree level. As a result,

χ0

1 cannot interacts with nuclei at the LO and could easily escape from current

DM direct detection bounds.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 10 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

LO Mass Spectrum: Generally mχ0

i ≃ mχ± i Mass (GeV) y2

LO, mQ = 200 GeV, mT = 400 GeV, y1 = 1 100 200 300 400 500 600

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0 mχ±± mχ0

1

mχ±

1

mχ0

2

mχ±

2

mχ0

3

mχ±

3

Mass (GeV) y2

LO, mQ = 400 GeV, mT = 200 GeV, y1 = 1 100 200 300 400 500 600

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0 mχ±± mχ0

1

mχ±

1

mχ0

2

mχ±

2

mχ0

3

mχ±

3

mQ < mT case mT < mQ case

Mass difference (GeV) y2

LO, mQ = 200 GeV, mT = 400 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

12
10
8
6
4
2

2 4 6

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

Mass difference (GeV) y2

LO, mQ = 400 GeV, mT = 200 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

20
15
10
5

5 10 15

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 11 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Mass Corrections at the NLO

χ0

j /χ+ j /χ++

W +/γ(Z)/W − χ+

i

χ+

i

χ∓

j /χ0 j

W ±/Z χ0

i

χ0

i

⇒ mχ0

1 < mχ± 1

?

One-loop corrections to an SU(2)L multiplet from electroweak gauge boson loops drive a charged component heavier than the neutral component (by ∼ Q2 · 170 MeV for a multiplet much heavier than Z with Y = 0).

[Feng et al., hep-ph/9904250; Cirelli et al., hep-ph/0512090; Hill & Solon, 1111.0016]

There are mixings among , , and , and corrections from the Higgs sector due to the Yukawa couplings. The situation is more complicated.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 12 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Mass Corrections at the NLO

χ0

j /χ+ j /χ++

W +/γ(Z)/W − χ+

i

χ+

i

χ∓

j /χ0 j

W ±/Z χ0

i

χ0

i

⇒ mχ0

1 < mχ± 1

χ0

j /χ+ j /χ++

G+/h(G0)/G− χ+

i

χ+

i

χ∓

j /χ0 j

G±/h(G0) χ0

i

χ0

i

?

One-loop corrections to an SU(2)L multiplet from electroweak gauge boson loops drive a charged component heavier than the neutral component (by ∼ Q2 · 170 MeV for a multiplet much heavier than Z with Y = 0).

[Feng et al., hep-ph/9904250; Cirelli et al., hep-ph/0512090; Hill & Solon, 1111.0016]

There are mixings among T, Q1, and Q2, and corrections from the Higgs sector due to the HTQ Yukawa couplings. The situation is more complicated.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 12 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Mass Corrections at the NLO

Mass difference (GeV) y

NLO, mQ = 200 GeV, mT = 400 GeV, y = y1 = y2 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

mχ±± − mχ0

1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1.0
0.5

0.0 0.5 1.0

Mass difference (GeV) y

NLO, mQ = 400 GeV, mT = 200 GeV, y = y1 = y2 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

mχ±± − mχ0

2

1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

1.0
0.5

0.0 0.5 1.0

mQ < mT case mT < mQ case In the custodial symmetry limit, we always have mχ0

1 < mχ± 1 at the NLO and

hence χ0

1 is stable as required for a DM candidate. Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 13 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Mass Corrections at the NLO

Mass difference (GeV) y2

NLO, mQ = 200 GeV, mT = 400 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

mχ±± − mχ0

1

12
10
8
6
4
2

2 4 6

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

Mass difference (GeV) y2

NLO, mQ = 400 GeV, mT = 200 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

20
15
10
5

5 10 15

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

mQ < mT case mT < mQ case Beyond the custodial symmetry limit: When and have opposite signs, we may have at the NLO and is unstable and no longer a viable DM candidate.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 14 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Mass Corrections at the NLO

Mass difference (GeV) y2

NLO, mQ = 200 GeV, mT = 400 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

mχ±± − mχ0

1

12
10
8
6
4
2

2 4 6

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

Mass difference (GeV) y2

NLO, mQ = 400 GeV, mT = 200 GeV, y1 = 1 mχ±

1 − mχ0 1

mχ±

2 − mχ0 2

mχ±

3 − mχ0 3

20
15
10
5

5 10 15

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

mQ < mT case mT < mQ case Beyond the custodial symmetry limit: When y1 and y2 have opposite signs, we may have mχ±

1 < mχ0 1 at the NLO and

χ0

1 is unstable and no longer a viable DM candidate. Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 14 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Relic Abundance

In this model, we always have the mass degeneracy mχ±

1 ≃ mχ0 1 . Besides,

mQ < mT ⇒ maybe mχ±± ≃ mχ0

1

|y1,2v| ≪ mQ < mT ⇒ mχ0

2 ≃ mχ± 2 ≃ mχ0 1

These dark sector fermions, with close masses and comparable interaction strengths, basically decoupled at the same time in the early Universe. Coannihilation processes among them signifjcantly afgected their abundances. After freeze-out, χ±

1 , χ±±, χ0 2, and χ± 2 decayed into χ0 1 and contributed to the

DM relic abundance. FeynRules → MadGraph → MadDM: includes all annihilation and coannihilation channels Observed DM abundance Ωh2 = 0.1186 ⇔ mχ0

1 ∼ 2.4 TeV

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 15 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Electroweak Oblique Parameters

χ+

i /χ++

χ−

i /χ−−

γ γ(Z) χ0

i /χ+ i /χ++

χ0

j /χ− j /χ−−

Z Z χ0

i /χ− i

χ+

j /χ++

W + W +

Gauge interactions of the triplet and quadruplets afgect these parameters Electroweak oblique parameters S, T, and U describe new physics contributions through gauge boson propagator corrections [Peskin & Takeuchi, ’90, ’92]

S = 16πc2

Ws2 W

e2

Π′

ZZ(0) −

c2

W − s2 W

cWsW Π′

ZA(0) − Π′ AA(0)

T = 4π

e2

ΠWW(0)

m2

W

− ΠZZ(0) m2

Z

U =

16πs2

W

e2

Π′

WW(0) − c2 WΠ′ ZZ(0) − 2cWsWΠ′ ZA(0) − s2 WΠ′ AA(0)

Zhao-Huan Yu (Melbourne)

Triplet-Quadruplet Fermionic Dark Matter December 2016 16 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Prediction for Electroweak Oblique Parameters

S, T, U y

mQ = 100 GeV, mT = 200 GeV, y = y1 = y2 S T = U = 0

0.05

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

0.8
0.6
0.4
0.2

0.0 0.2 0.4 0.6 0.8

S, T, U y

mQ = 200 GeV, mT = 100 GeV, y = y1 = y2 S T = U = 0

0.05

0.00 0.05 0.10 0.15 0.20 0.25

0.8
0.6
0.4
0.2

0.0 0.2 0.4 0.6 0.8

Custodial symmetry limit Custodial symmetry limit

mQ < mT case mT < mQ case

S, T, U y2 / y1

mQ = 100 GeV, mT = 200 GeV, y1v = 150 GeV S T U

0.80
0.60
0.40
0.20

0.00 0.20 0.40 0.60

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

S, T, U y2 / y1

mQ = 200 GeV, mT = 100 GeV, y1v = 150 GeV S T U

0.40
0.30
0.20
0.10

0.00 0.10 0.20 0.30 0.40

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 2.0

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 17 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Current Constraints on Electroweak Oblique Parameters

meas

σ ) /

meas

O

fit

(O

3
2
1

1 2 3 )

2 Z

(M

(5) had

α ∆ )

2 Z

(M

s

α

t

m

b

R

c

R

0,b FB

A

0,c FB

A

b

A

c

A )

FB

(Q

lept eff

Θ

2

sin (SLD)

l

A (LEP)

l

A

0,l FB

A

lep

R

had

σ

Z

Γ

Z

M

W

Γ

W

M

H

M 0.0 (0.0)

1.4 (-1.3)

0.2 (0.1) 0.2 (0.2) 0.0 (0.1)

1.5 (-1.6)
1.0 (-1.1)
0.8 (-0.8)

0.2 (0.2)

2.0 (-2.0)
0.7 (-0.7)

0.0 (0.0) 0.6 (0.6) 0.9 (0.9) 2.5 (2.5) 0.0 (0.0)

0.8 (-0.7)

0.5 (0.4) 1.7 (0.9)

0.2 (-0.2)

Full EW 2-loop Z-partial widths at 1-loop

Global fjt based on the measurements of electroweak precision observables:

[Gfjtter Group, 1407.3792]

Fixed U = 0 → S = 0.06 ± 0.09, T = 0.10 ± 0.07, ρST = +0.91 Free U → S = 0.05 ± 0.11, T = 0.09 ± 0.13, U = 0.01 ± 0.11 ρST = +0.90, ρSU = −0.59, ρTU = −0.83

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 18 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Direct Detection

h χ0

1

χ0

1 A ZN A ZN

Spin independent (SI)

Z χ0

1

χ0

1 A ZN A ZN

Spin dependent (SD) L ⊃ 1 2 ghχ0

1 χ0 1 h ¯

χ0

1χ0 1 + 1

2 gZχ0

1 χ0 1 Zµ ¯

χ0

1γµγ5χ0 1

ghχ0

1 χ0 1 = − 2

3

(y1N21 − y2N31)N11 gZχ0

1 χ0 1 =

g 2cW (|N31|2 − |N21|2) For mQ < mT in the custodial symmetry limit, we have N11 = 0 and |N31| = |N21|, and both ghχ0

1 χ0 1 and gZχ0 1 χ0 1 vanish

Current direct detection experiments are much more sensitive to the SI DM-nucleus scatterings than the SD scatterings The exclusion limit on the SI cross section from the LUX experiment [1310.8214] is used to constrain the model

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 19 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Indirect Detection

χ+

i

χ0

1

χ0

1

W − W +

Dominant channel Indirect detection searches for products from nonrelativistic DM annihilations Suppressions on χ0

1χ0 1 annihilations into SM particles

χ0

1χ0 1 → Z∗ → f ¯

f : helicity suppression in s wave (〈σv〉 ∝ m2

f /m2 χ0

1 )

χ0

1χ0 1 → h∗ → f ¯

f : p-wave suppression (〈σv〉 ∝ v2) χ0

1χ0 1 → hh: p-wave suppression (〈σv〉 ∝ v2)

The cross section of χ0

1χ0 1 → W +W − is typically

larger than those of χ0

1χ0 1 → ZZ, Zh, t¯

t by at least 1 to 2 orders of magnitude The upper limit on the annihilation cross section into W +W − given by Fermi-LAT 6-year γ-ray

bservations of dwarf galaxies [1503.02641] is

used to constrain the model

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 20 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

mT (TeV) mQ (TeV)

y1 = y2 = 0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

mχ0

1 = 1 TeV

2 TeV 3 TeV

Fermi LUX EW oblique Ωh2 = 0.1186 Overproduction

mT (TeV) mQ (TeV)

y1 = 0.5, y2 = 1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

mχ0

1 = 1 TeV

2 TeV 3 TeV

Fermi LUX EW oblique Ωh2 = 0.1186 Overproduction

mT (TeV) mQ (TeV)

y1 = 0.5, y2 = -0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

mχ0

1 = 1 TeV

2 TeV 3 TeV

mχ±

1 < mχ0 1

Fermi LUX Ωh2 = 0.1186 Overproduction

mT (TeV) mQ (TeV)

y1 = 0.5, y2 = -1.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

mχ0

1 = 1 TeV

2 TeV 3 TeV

mχ±

1 < mχ0 1

Fermi LUX Ωh2 = 0.1186 Overproduction

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 21 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

y2 y1

mQ = 2.4 TeV, mT = 3 TeV

1.5
1.0
0.5

0.0 0.5 1.0 1.5

1.5
1.0
0.5

0.0 0.5 1.0 1.5

2.4 TeV m

χ

1 = 2.38 TeV

2.38 TeV 2.34 TeV 2.34 TeV

m

χ

± 1 < m

χ

1

m

χ

± 1 < m

χ

1

LUX LUX Ωh

2

= 0.1186 Overproduction

y2 y1

mQ = 3 TeV, mT = 2.4 TeV

1.5
1.0
0.5

0.0 0.5 1.0 1.5

1.5
1.0
0.5

0.0 0.5 1.0 1.5

2.41 TeV 2.41 TeV 2.4 TeV 2 . 4 T e V mχ0

1 = 2.38 TeV

2.38 TeV 2.34 TeV 2.34 TeV

L U X L U X Ω h

2

= . 1 1 8 6 Overp.

y2 y1

mQ = 1 TeV, mT = 1.7 TeV

1.5
1.0
0.5

0.0 0.5 1.0 1.5

1.5
1.0
0.5

0.0 0.5 1.0 1.5

1 TeV m

χ

1 = 0.99 TeV

0.99 TeV 0.94 TeV 0.94 TeV

m

χ

± 1 < m

χ

1

m

χ

± 1 < m

χ

1

LUX LUX Fermi Fermi

y2 y1

mQ = 1.5 TeV, mT = 0.7 TeV

1.5
1.0
0.5

0.0 0.5 1.0 1.5

1.5
1.0
0.5

0.0 0.5 1.0 1.5

710 GeV 710 GeV mχ0

1 = 700 GeV

7 G e V 670 GeV 670 GeV 630 GeV 630 GeV

LUX LUX LUX LUX Fermi Fermi

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 22 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Conclusion

1

We investigate a triplet-quadruplet WIMP model, whose dark sector involves 3 Majorana fermions, 3 singly charged fermions, and 1 doubly charged fermion.

2

The triplet and quadruplets can interact with the SM Higgs doublet through two Yukawa couplings, whose equality leads to an approximate custodial symmetry that would make the DM candidate χ0

1 easily escaping from

direct searches.

3

There are mass degeneracies among dark sector fermions. One-loop mass corrections are calculated to check if χ0

1 can be stable.

4

The observed relic abundance suggests mχ0

1 ∼ 2.4 TeV. Phenomenological

constraints from EW oblique parameters and direct and indirect detection experiments are also considered.

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 23 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Thanks for your attention!

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 24 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Outlook: Collider Signatures

h → γγ measurement: contribution from χ±

i loops

Monojet + / ET fjnal state: pp → χ0

1χ0 1 + j

Disappearing tracks: pp → χ±

1 χ∓ 1 → π+π− (soft) + χ0 1χ0 1

2ℓ + / ET fjnal state: pp → χ±

2,3χ∓ 2,3 → ℓ+ℓ− + ννχ0 1χ0 1

3ℓ + / ET fjnal state with same-sign dilepton: pp → χ±±χ∓

2,3 → ℓ±ℓ+ℓ− + νννχ0 1χ0 1

pp → χ±

2,3χ0 2,3 → ℓ±ℓ+ℓ− + νχ0 1χ0 1

4ℓ + / ET fjnal state: pp → χ±±χ∓∓ → ℓ+ℓ+ℓ−ℓ− + ννννχ0

1χ0 1

pp → χ0

2,3χ0 2,3 → ℓ+ℓ−ℓ+ℓ− + χ0 1χ0 1

··· ···

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 25 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Outlook: CEPC Precision for Electroweak Oblique Parameters

0.2
0.1

0.0 0.1 0.2

0.2
0.1

0.0 0.1 0.2

T S 95% CL contours for U = 0

Current CEPC-B CEPC-I

0.2
0.1

0.0 0.1 0.2

0.2
0.1

0.0 0.1 0.2

Assuming U = 0

[Cai, ZHY & Zhang, 1611.02186]

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

95% CL contours T Current CEPC-B CEPC-I

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

95% CL contours U S

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

95% CL contours T

0.3
0.2
0.1

0.0 0.1 0.2 0.3

0.3
0.2
0.1

0.0 0.1 0.2 0.3

Assuming free U

Current: current precision for EW oblique parameters [Gfjtter Group, 1407.3792] CEPC-B: CEPC baseline precision for EW oblique parameters CEPC-I: CEPC precision with improvements of mZ, ΓZ, and mt measurements

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 26 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

Outlook: CEPC Precision for Electroweak Oblique Parameters

101 102 103 104 101 102 103 104

mT (GeV) mQ (GeV) TQFDM, y1 = y2 = 1

101 102 103 104 101 102 103 104 mχ0

1 = 1000 GeV

200 50 50 20 20 DD-SI Current CEPC-B CEPC-I 101 102 103 104 101 102 103 104

mT (GeV) mQ (GeV) TQFDM, y1 = 1, y2 = 1.5

101 102 103 104 101 102 103 104 mχ0

1 = 1000 GeV

200 50 50 20 20 DD-SI DD-SD Current CEPC-B CEPC-I

Current: current precision for EW oblique parameters [Gfjtter Group, 1407.3792] CEPC-B: CEPC baseline precision for EW oblique parameters CEPC-I: CEPC precision with improvements of mZ, ΓZ, and mt measurements Solid lines: 95% CL constraints from the fjtting results assuming U = 0 Dot-dashed lines: 95% CL constraints from the fjtting results for free U SI direct detection constraints: PandaX-II [1607.07400] and LUX [1608.07648] SD direct detection constraints: LUX [1602.03489] and PICO [1503.00008, 1510.07754]

Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 27 / 28

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Introduction Model Details Mass corrections Constraints Conclusion Backups

State Mixing in the Custodial Symmetry Limit

Mass spectrum for y = y1 = y2 and mQ < mT: mLO

χ0

1 = mLO

χ±

1 = mLO

χ±± = mQ

mLO

χ0

2 = mLO

χ±

2 = 1

2

8y2v2/3 + (mQ + mT)2 + mQ − mT
mLO

χ0

3 = mLO

χ±

3 = 1

2

8y2v2/3 + (mQ + mT)2 − mQ + mT
N =

       ai b −

2

b 1

2

− i b − a

2b

1

2

i b a

2b

       , CL =         a b −

2i

b i 2 −

6

2b −

3ai

2b

3i

2

2

2b ai 2b         , CR =         − a b

2i

b

3i

2 −

2

2b − ai 2b i 2

6

2b

3ai

2b        

Identical magnitudes of Q0

1 and Q0 2 components in χ0 i

Identical magnitudes of Q+

1 (Q+ 2) and Q− 2 (Q− 1) components in χ± i Zhao-Huan Yu (Melbourne) Triplet-Quadruplet Fermionic Dark Matter December 2016 28 / 28