Thermal, Non-thermal and their detection

Sarif Khan

Harish-Chandra Research Institute, Allahabad, India

Talk at: MPIK, Heidelberg

November 5, 2018

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 1 / 60 DM Evidences

Thermal DM

Non-thermal DM

Talk Plan

Motivation

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 2 / 60 Thermal DM

Non-thermal DM

Talk Plan

Motivation

DM Evidences

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 2 / 60 Non-thermal DM

Talk Plan

Motivation

DM Evidences

Thermal DM

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 2 / 60 Talk Plan

Motivation

DM Evidences

Thermal DM

Non-thermal DM

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 2 / 60 Almost 80% matter contents of the is unknown to us, namely Dark Matter (DM) [Many evidences which support the presence of DM].

Why there exist excess matter over antimatter in the universe.

Disagreement between the theoretical and experimental value of muon (g 2). −

Motivation

Discovery of oscillation implies the existence of neutrino mass.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 3 / 60 Why there exist excess matter over antimatter in the universe.

Disagreement between the theoretical and experimental value of muon (g 2). −

Motivation

Discovery of neutrino oscillation implies the existence of neutrino mass.

Almost 80% matter contents of the universe is unknown to us, namely Dark Matter (DM) [Many evidences which support the presence of DM].

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 3 / 60 Disagreement between the theoretical and experimental value of muon (g 2). −

Motivation

Discovery of neutrino oscillation implies the existence of neutrino mass.

Almost 80% matter contents of the universe is unknown to us, namely Dark Matter (DM) [Many evidences which support the presence of DM].

Why there exist excess matter over antimatter in the universe.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 3 / 60 Motivation

Discovery of neutrino oscillation implies the existence of neutrino mass.

Almost 80% matter contents of the universe is unknown to us, namely Dark Matter (DM) [Many evidences which support the presence of DM].

Why there exist excess matter over antimatter in the universe.

Disagreement between the theoretical and experimental value of muon (g 2). −

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 3 / 60 Using (which relates the KE and PE), he determined the Gravitational mass (GM). Compared GM with the bright, luminous mass, got discrepancy. Concluded that, extra matter is there and called it “Dark Matter”.

Evidences

1. Clusters:

Figure:

In 1933, Fritz Zwicky was studying the nearest Coma Cluster.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 4 / 60 Compared GM with the bright, luminous mass, got discrepancy. Concluded that, extra matter is there and called it “Dark Matter”.

Evidences

1. Galaxy Clusters:

Figure: Coma Cluster

In 1933, Fritz Zwicky was studying the nearest Coma Cluster. Using Virial theorem (which relates the KE and PE), he determined the Gravitational mass (GM).

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 4 / 60 Concluded that, extra matter is there and called it “Dark Matter”.

Evidences

1. Galaxy Clusters:

Figure: Coma Cluster

In 1933, Fritz Zwicky was studying the nearest Coma Cluster. Using Virial theorem (which relates the KE and PE), he determined the Gravitational mass (GM). Compared GM with the bright, luminous mass, got discrepancy.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 4 / 60 Evidences

1. Galaxy Clusters:

Figure: Coma Cluster

In 1933, Fritz Zwicky was studying the nearest Coma Cluster. Using Virial theorem (which relates the KE and PE), he determined the Gravitational mass (GM). Compared GM with the bright, luminous mass, got discrepancy. Concluded that, extra matter is there and called it “Dark Matter”.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 4 / 60 Velocity of the stars remained almost constant regardless of how far they are from GC. [Small: v(r) r, Large: v(r) √1 ] ∝ ∝ r Excess matter is present, namely DM. (Another way: MOND theory!)

Evidences

2. Galactic Rotation Curve:

Figure: GC rotation curve

Vera Rubin and Kent Ford were studying Andromeda galaxy in 1960, got similar things.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 5 / 60 Excess matter is present, namely DM. (Another way: MOND theory!)

Evidences

2. Galactic Rotation Curve:

Figure: GC rotation curve

Vera Rubin and Kent Ford were studying Andromeda galaxy in 1960, got similar things. Velocity of the stars remained almost constant regardless of how far they are from GC. [Small: v(r) r, Large: v(r) √1 ] ∝ ∝ r

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 5 / 60 Evidences

2. Galactic Rotation Curve:

Figure: GC rotation curve

Vera Rubin and Kent Ford were studying Andromeda galaxy in 1960, got similar things. Velocity of the stars remained almost constant regardless of how far they are from GC. [Small: v(r) r, Large: v(r) √1 ] ∝ ∝ r Excess matter is present, namely DM. (Another way: MOND theory!)

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 5 / 60 From spectrum we come to know: 2 Baryon density: Ωbh 0.02 2 ' DM density: ΩDM h 0.1203 ' −1 −1 Hubble Parameter: H0 67.11 MPc s (τU 13.819 Gy). ' ∼

3. CMB Spectrum:

Figure: CMB Spectrum

CMB Power Spectrum has been measured by the WMAP and Planck.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 6 / 60 3. CMB Spectrum:

Figure: CMB Spectrum

CMB Power Spectrum has been measured by the WMAP and Planck. From spectrum we come to know: 2 Baryon density: Ωbh 0.02 2 ' DM density: ΩDM h 0.1203 ' −1 −1 Hubble Parameter: H0 67.11 MPc s (τU 13.819 Gy). ' ∼

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 6 / 60 Red regions are obtained by the X-ray emission and the blue regions by the gravitational lensing. center of the total matter and the visible matter does not coincide, hence DM is present.

Evidences

4. Bullet Cluster:

Figure: Bullet Cluster

In Bullet-Cluster, X-ray emission and gravitational lensing are used.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 7 / 60 center of the total matter and the visible matter does not coincide, hence DM is present.

Evidences

4. Bullet Cluster:

Figure: Bullet Cluster

In Bullet-Cluster, X-ray emission and gravitational lensing are used. Red regions are obtained by the X-ray emission and the blue regions by the gravitational lensing.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 7 / 60 Evidences

4. Bullet Cluster:

Figure: Bullet Cluster

In Bullet-Cluster, X-ray emission and gravitational lensing are used. Red regions are obtained by the X-ray emission and the blue regions by the gravitational lensing. center of the total matter and the visible matter does not coincide, hence DM is present.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 7 / 60 Since, DM only interacts via , hence we can tackle this by modifying gravity like MOND theory, but it can not explain all except flatness of rotation curve (Although gravity is well known to us by GR, e.g. GPS system). Another possibility was MACHO type objects (e.g. neutron stars, and brown and white dwarfs), possible to detect by the Gravitational lensing. But failed to explain the entire amount of DM. From BBN and CMB, we know the amount of baryonic matter present in the universe, hence DM will be non baryonic.

Evidences and Attempts

Large-Scale Structure Formation: SDSS telescope when maps to large scale, it sees some patterns which can not be explained just by the ordinary matter.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 8 / 60 Another possibility was MACHO type objects (e.g. neutron stars, and brown and white dwarfs), possible to detect by the Gravitational lensing. But failed to explain the entire amount of DM. From BBN and CMB, we know the amount of baryonic matter present in the universe, hence DM will be non baryonic.

Evidences and Attempts

Large-Scale Structure Formation: SDSS telescope when maps to large scale, it sees some patterns which can not be explained just by the ordinary matter. Since, DM only interacts via gravity, hence we can tackle this by modifying gravity like MOND theory, but it can not explain all except flatness of rotation curve (Although gravity is well known to us by GR, e.g. GPS system).

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 8 / 60 From BBN and CMB, we know the amount of baryonic matter present in the universe, hence DM will be non baryonic.

Evidences and Attempts

Large-Scale Structure Formation: SDSS telescope when maps to large scale, it sees some patterns which can not be explained just by the ordinary matter. Since, DM only interacts via gravity, hence we can tackle this by modifying gravity like MOND theory, but it can not explain all except flatness of rotation curve (Although gravity is well known to us by GR, e.g. GPS system). Another possibility was MACHO type objects (e.g. neutron stars, and brown and white dwarfs), possible to detect by the Gravitational lensing. But failed to explain the entire amount of DM.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 8 / 60 Evidences and Attempts

Large-Scale Structure Formation: SDSS telescope when maps to large scale, it sees some patterns which can not be explained just by the ordinary matter. Since, DM only interacts via gravity, hence we can tackle this by modifying gravity like MOND theory, but it can not explain all except flatness of rotation curve (Although gravity is well known to us by GR, e.g. GPS system). Another possibility was MACHO type objects (e.g. neutron stars, and brown and white dwarfs), possible to detect by the Gravitational lensing. But failed to explain the entire amount of DM. From BBN and CMB, we know the amount of baryonic matter present in the universe, hence DM will be non baryonic.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 8 / 60 Theoretically well motivated and also testable at the satelite and earth based experiments. Many theories are there: SUSY, Extra dimensions, heavy , MeV DM, Axion, Fermionic and Scalar DM... I will focus on the Fermionic DM, by conidering its thermal and non-thermal ways of production.

Particle Dark Matter

I will discuss DM from particle physics point of view, Easy to explain everything with the particle DM.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 9 / 60 Many theories are there: SUSY, Extra dimensions, heavy neutrinos, MeV DM, Axion, Fermionic and Scalar DM... I will focus on the Fermionic DM, by conidering its thermal and non-thermal ways of production.

Particle Dark Matter

I will discuss DM from particle physics point of view, Easy to explain everything with the particle DM. Theoretically well motivated and also testable at the satelite and earth based experiments.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 9 / 60 I will focus on the Fermionic DM, by conidering its thermal and non-thermal ways of production.

Particle Dark Matter

I will discuss DM from particle physics point of view, Easy to explain everything with the particle DM. Theoretically well motivated and also testable at the satelite and earth based experiments. Many theories are there: SUSY, Extra dimensions, heavy neutrinos, MeV DM, Axion, Fermionic and Scalar DM...

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 9 / 60 Particle Dark Matter

I will discuss DM from particle physics point of view, Easy to explain everything with the particle DM. Theoretically well motivated and also testable at the satelite and earth based experiments. Many theories are there: SUSY, Extra dimensions, heavy neutrinos, MeV DM, Axion, Fermionic and Scalar DM... I will focus on the Fermionic DM, by conidering its thermal and non-thermal ways of production.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 9 / 60 Thermal Dark Matter

“Singlet-Triplet Fermionic Dark Matter and LHC Phenomenology”, S. Choubey, S.K., M. Mitra and S. Mondal, Eur. Phys. J. C 78, no. 4, 302 (2018) [arXiv:1711.08888 [hep-ph]].

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 10 / 60 ; DM direct detection.

; DM indirect detection.

; DM collider signature.

Strategy in thermal DM Study

In discussing DM, I will be focusing on the following points

; Satisfying Relic Density bound.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 11 / 60 ; DM indirect detection.

; DM collider signature.

Strategy in thermal DM Study

In discussing DM, I will be focusing on the following points

; Satisfying Relic Density bound.

; DM direct detection.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 11 / 60 ; DM collider signature.

Strategy in thermal DM Study

In discussing DM, I will be focusing on the following points

; Satisfying Relic Density bound.

; DM direct detection.

; DM indirect detection.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 11 / 60 Strategy in thermal DM Study

In discussing DM, I will be focusing on the following points

; Satisfying Relic Density bound.

; DM direct detection.

; DM indirect detection.

; DM collider signature.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 11 / 60 Standard Model Particles

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 12 / 60 p One of the Simplest extension is to introduce a triplet fermion,

where

+ ρ0 √ρ ! 2 2 ρ = − . √ρ ρ0 2 − 2

p Need to extend the SM.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 13 / 60 p Need to extend the SM. p One of the Simplest extension is to introduce a triplet fermion,

where

+ ρ0 √ρ ! 2 2 ρ = − . √ρ ρ0 2 − 2

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 13 / 60 m This simplest model has few drawbacks which are as follows.

Relic Density

1

2 0.1 h

Ω Region Satisfying DM Relic Density

Ω h2 = 0.1199 ± 0.0027

0.01

0 1000 2000 3000 4000 5000

Mρ0 [GeV]

m Relic density satisfies around 2.3 TeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 14 / 60 Relic Density

1

2 0.1 h

Ω Region Satisfying DM Relic Density

Ω h2 = 0.1199 ± 0.0027

0.01

0 1000 2000 3000 4000 5000

Mρ0 [GeV]

m Relic density satisfies around 2.3 TeV. m This simplest model has few drawbacks which are as follows.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 14 / 60 § No tree level DD processes exist and only possible via one loop, hence SIDD is suppressed.

Drawbacks

§ Relic density satisfies around 2.3 TeV. Difficult to produce and detect such High mass DM at the current energy range of LHC.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 15 / 60 Drawbacks

§ Relic density satisfies around 2.3 TeV. Difficult to produce and detect such High mass DM at the current energy range of LHC.

§ No tree level DD processes exist and only possible via one loop, hence SIDD is suppressed.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 15 / 60 § Pure triplet DM is ruled out by the HESE and Fermi-LAT data which give bound on the γγ channel.

Cont...

J. Hisano et. al. [PRD 05]

§ Annihilation gets Sommerfeld enhancement after mass greater than 1 TeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 16 / 60 Cont...

J. Hisano et. al. [PRD 05]

§ Annihilation gets Sommerfeld enhancement after mass greater than 1 TeV. § Pure triplet DM is ruled out by the HESE and Fermi-LAT data which give bound on the γγ channel.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 16 / 60 Complete particles list are as follows,

Will see, after adding two particles all the above drawbacks are solved.

Way Out

One way out is to introduce a Singlet fermion and triplet scalar.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 17 / 60 Will see, after adding two particles all the above drawbacks are solved.

Way Out

One way out is to introduce a Singlet fermion and triplet scalar.

Complete particles list are as follows,

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 17 / 60 Way Out

One way out is to introduce a Singlet fermion and triplet scalar.

Complete particles list are as follows,

Will see, after adding two particles all the above drawbacks are solved.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 17 / 60 The complete form of the potential V (φh, Ω) takes the following form,

2 † λh † 2 2 † † 2 † † V (φh, ∆) = −µ φ φh + (φ φh) + µ Tr[∆ ∆] + λ∆(∆ ∆) + λ1 (φ φh) Tr [∆ ∆] h h 4 h ∆ h  † 2 † 2 † † † +λ2 Tr[∆ ∆] + λ3 Tr[(∆ ∆) ] + λ4 φh ∆∆ φh + (µφh ∆φh + h.c.) .

Lagrangian

Lagrangian for the present model is given by,

 µ  ¯0 µ 0 † µ L = LSM + Tr ρ¯ i γ Dµρ + N i γ DµN + Tr[(Dµ∆) (D ∆)] − V (φh, ∆) 0 ¯c ¯0c 0 −Yρ∆ (Tr[ρ ¯ ∆] N + h.c.) − Mρ Tr[ρ ρ] − MN0 N N

where the triplet fermion takes the following form,

 ρ +  0 ρ√ ρ =  2 2  .  − ρ  ρ√ − 0 2 2

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 18 / 60 Lagrangian

Lagrangian for the present model is given by,

 µ  ¯0 µ 0 † µ L = LSM + Tr ρ¯ i γ Dµρ + N i γ DµN + Tr[(Dµ∆) (D ∆)] − V (φh, ∆) 0 ¯c ¯0c 0 −Yρ∆ (Tr[ρ ¯ ∆] N + h.c.) − Mρ Tr[ρ ρ] − MN0 N N

where the triplet fermion takes the following form,

 ρ +  0 ρ√ ρ =  2 2  .  − ρ  ρ√ − 0 2 2

The complete form of the potential V (φh, Ω) takes the following form,

2 † λh † 2 2 † † 2 † † V (φh, ∆) = −µ φ φh + (φ φh) + µ Tr[∆ ∆] + λ∆(∆ ∆) + λ1 (φ φh) Tr [∆ ∆] h h 4 h ∆ h  † 2 † 2 † † † +λ2 Tr[∆ ∆] + λ3 Tr[(∆ ∆) ] + λ4 φh ∆∆ φh + (µφh ∆φh + h.c.) .

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 18 / 60 After symmetry breaking, there will be mixing between the two neutral scalars, two charged scalars, and two neutral fermions. Therefore, we need to introduce mass basis in the following way,

Neutral Higgs:

h1 = cos α H + sin α ∆0

h2 = − sin α H + cos α ∆0

Charged Higgs:

G ± = cos δ φ± + sin δ ∆± H± = − sin δ φ± + cos δ ∆±

Fermions:

0 0c ρ2 = cos β ρ0 + sin β N 0 0c ρ1 = − sin β ρ0 + cos β N

Mass Eigenstates

φh will take vev spontaneously, and simultaneously the triplet scalar ∆ will get induced vev,

2 2 µh > 0, µ∆ > 0, λh > 0 and λ∆ > 0 .

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 19 / 60 Therefore, we need to introduce mass basis in the following way,

Neutral Higgs:

h1 = cos α H + sin α ∆0

h2 = − sin α H + cos α ∆0

Charged Higgs:

G ± = cos δ φ± + sin δ ∆± H± = − sin δ φ± + cos δ ∆±

Fermions:

0 0c ρ2 = cos β ρ0 + sin β N 0 0c ρ1 = − sin β ρ0 + cos β N

Mass Eigenstates

φh will take vev spontaneously, and simultaneously the triplet scalar ∆ will get induced vev,

2 2 µh > 0, µ∆ > 0, λh > 0 and λ∆ > 0 .

After symmetry breaking, there will be mixing between the two neutral scalars, two charged scalars, and two neutral fermions.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 19 / 60 Mass Eigenstates

φh will take vev spontaneously, and simultaneously the triplet scalar ∆ will get induced vev,

2 2 µh > 0, µ∆ > 0, λh > 0 and λ∆ > 0 .

After symmetry breaking, there will be mixing between the two neutral scalars, two charged scalars, and two neutral fermions. Therefore, we need to introduce mass basis in the following way,

Neutral Higgs:

h1 = cos α H + sin α ∆0

h2 = − sin α H + cos α ∆0

Charged Higgs:

G ± = cos δ φ± + sin δ ∆± H± = − sin δ φ± + cos δ ∆±

Fermions:

0 0c ρ2 = cos β ρ0 + sin β N 0 0c ρ1 = − sin β ρ0 + cos β N

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 19 / 60 Constraints Used in DM Study

SI direct detection cross section

0 0 0 0 ρ1 ρ1 ρ1 ρ1

h1 h2

N N N N Direct detection cross section for the Higgses mediated diagrams is,

2 2 " 2 !# µred MN fN ∆M21 sin 2β sin 2α 1 1 σSI = π v 4v M2 − M2 ∆ h2 h1

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 20 / 60 Contd...

Invisible decay width of Higgs [ATLAS + CMS: JHEP 16] : Higgs can decay to DM, if Mh > 2M 0 and the constraint is, 1 ρ1

Γh →ρ0ρ0 1 1 1 34% at 95% C.L. ΓTotal ≤ h1 Planck Limit [Planck 15] : Relic density bound on the DM is,

0.1172 Ωh2 0.1226 at 68% C.L., ≤ ≤ ± 0 We consider the bounds on the masses of ρ , ρ2 which can come from the search of Wino like neutralinos and Chargino in the context of SUSY.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 21 / 60 DM Results

Feynman diagrams which take part in DM phenomenology

0 0 ρ1 ρ1 + + W , Z h1, h2, h1,H

h1, h2 h1, h2

h1, h2, h2,H− W −, Z 0 0 ρ1 ρ1

0 0 ρ1 f ρ1 u, c, t

h1, h2 W ±

d,s,b 0 ¯ ρ1 f ρ±

0 ρ1 H∓ (h2)

0 0 ρ∓ (ρ1, ρ2) 0 ρ1 (ρ±) W ±

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 22 / 60 Useful Vertices

0 0 ρ1ρ1h1,2 vertices look like as follows, 2 ∆M21 sin 2β sin α gρ0ρ0h = , 1 1 1 2v tan δ 2 ∆M21 sin 2β cos α gρ0ρ0h = 1 1 2 2v tan δ

where ∆M21 = Mρ0 Mρ0 . 2 − 1 Two important observations: Vertices are proportional to square of the fermionic mixing angle:

2 gρ0ρ0h sin β 1 1 1 ∝ 2 gρ0ρ0h sin β 1 1 2 ∝ when sin α = sin δ, then

gρ0ρ0h cos α 1 1 1 ∝ gρ0ρ0h 1/ sin α 1 1 2 ∝

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 23 / 60 DM Results

Line Plots :

106

sinα = 0.03 1000 sinβ = 0.10 Ω h2 = 0.12 Ω h2 = 0.12 sinβ = 0.05 sinα = sinδ = 0.01 1000 sinβ = 0.10 sinα = sinδ = 0.03 sinβ = 0.20 sinα = sinδ = 0.06 2 2 h h

Ω Ω 1 1

10−3 10−3

100 1000 100 1000

0 0 Mρ1 [GeV] Mρ1 [GeV]

Figure: BSM Higgs mass, Mh2 = 300 GeV, sin δ = sin α and ∆M12 = 50 GeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 24 / 60 DM Results

Line Plots :

sinβ = 0.1

0 0 Mρ2 - Mρ1 = 40 GeV

0 0 sinβ = 0.1 Mρ2 - Mρ1 = 50 GeV 2 1000 0 0 1000 Mρ2 - Mρ1 = 60 GeV Ω h = 0.12 2 Ω h = 0.12 Mh2 = 200 GeV

Mh2 = 300 GeV

Mh2 = 400 GeV 2 2 h h

Ω Ω

1 1

−3 10−3 10 100 1000 100 1000

0 0 Mρ1 [GeV] Mρ1 [GeV]

Figure: sin δ = sin α = 0.03 and ∆M12 = 50 GeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 25 / 60 DM Results

Scatter Plots :

Figure: M 0 , Mh and sin β three parameters have been varied for scatter plots. ρ1 2

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 26 / 60 Indirect Detection

Feynman diagrams contributing in γγ final state

0 γ 0 γ ρ1 ρ1

ρ± ρ± W ± + W ± = A γ Wρ 0 ρ0 ρ1 1 γ

γ 0 γ 0 ρ1 ρ1

ρ + ρ± ± H± H± = A γ Hρ 0 0 ρ1 ρ1 γ

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 27 / 60 Indirect Detection

Previous diagrams expression for the CS times velocity is, [L. Bergstrom et. al., NPB 97; Z. Bern et. al, PLB 97] 2 2 αEM M 0 ρ1 2 σv γγ = AW ρ + AHρ . h i 16π3 | |

10−24

10−25 Fermi-LAT Data

10−26 Fermi-LAT Collaboration (γγ)-2013 ]

1 −27 -

c 10 e s

3

m −28 c 10 [

γ γ >

v Fermi-LAT Collaboration (γγ)-2015 −29 σ 10 <

10−30

−31 γγ from Present Model 10

10−32 100 200 500

MDM [GeV]

Figure: Fermi-LAT bounds and the prediction from the present model

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 28 / 60 Collider Part

Signal Production :

p p XY → p p X Y j → p p X Y j j → Signal-I: XY = ρ0 ρ+ , ρ0 ρ− { } { 2 } { 2 } Signal-II: XY = ρ+ ρ− { } { } After showering the by Pythia, we have looked for the following signal,

ET + n j, where n 2 ≥

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 29 / 60 Collider Part

Production cross section at 13 TeV LHC :

10

+ 0 - 0 p p → ρ ρ2, ρ ρ2 p p → ρ+ ρ- 1 ] b p [

y x

0.1 → p p σ

0.01

10−3

200 400 600 800 1000

0 Mρ2 [GeV]

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 30 / 60 Collider Part

Benchmark points:

All the points satisfy relic density, direct and indirect detection bounds.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 31 / 60 Collider Part

Histograms for Signal and BKG :

1 W+jets W+jets Z+jets Z+jets QCD dN/N dN/N QCD −1 − tt+jets 10 10 1 tt+jets BP1 BP4 BP4 BP1 BP3 −2 10 BP3

− 10 2 − 10 3

−3 − 10 10 4

− 10 5 − 10 4 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 M [GeV] Eff ET [GeV]

where ET is the missing energy and MEff is defined as, X j X `  MEff = ~p + ~pT + ET | Ti | | i | i i

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 32 / 60 Selection Cuts

Basic Cuts (A0) : l Leptons are selected with pT > 10 GeV and the pseudo η` < 2.5, where ` = e, µ. | | γ γ We used pT > 10 GeV and rapidity η < 2.5 as the basic cuts for photon. | | We have chosen the jets which satisfy pj > 40 GeV and ηj < 2.5. T | | We have considered the azimuthal separation between all reconstructed jets and missing energy must be greater than 0.2 i.e.

∆φ(jet,E~T ) > 0.2.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 33 / 60 j1 A2: pT requirements on the hardest and second hardest jets: pT > 130 j2 GeV and pT > 80 GeV.

A3: In order to minimize QCD multi-jet, we have ensured that the E~T and the jets are well separated, i.e., ∆φ(ji ,E~T ) > 0.4 where i = 1, 2. For all the other jets, ∆φ(j,E~T ) > 0.2.

A4: We demand a hard cut on the effective mass variable, MEff > 800 GeV.

A5: We put the bound on the missing energy E T > 160 GeV.

Selection Cuts

A1: We have imposed a lepton and photon veto in the final state.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 34 / 60 A3: In order to minimize QCD multi-jet, we have ensured that the E~T and the jets are well separated, i.e., ∆φ(ji ,E~T ) > 0.4 where i = 1, 2. For all the other jets, ∆φ(j,E~T ) > 0.2.

A4: We demand a hard cut on the effective mass variable, MEff > 800 GeV.

A5: We put the bound on the missing energy E T > 160 GeV.

Selection Cuts

A1: We have imposed a lepton and photon veto in the final state. j1 A2: pT requirements on the hardest and second hardest jets: pT > 130 j2 GeV and pT > 80 GeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 34 / 60 A4: We demand a hard cut on the effective mass variable, MEff > 800 GeV.

A5: We put the bound on the missing energy E T > 160 GeV.

Selection Cuts

A1: We have imposed a lepton and photon veto in the final state. j1 A2: pT requirements on the hardest and second hardest jets: pT > 130 j2 GeV and pT > 80 GeV.

A3: In order to minimize QCD multi-jet, we have ensured that the E~T and the jets are well separated, i.e., ∆φ(ji ,E~T ) > 0.4 where i = 1, 2. For all the other jets, ∆φ(j,E~T ) > 0.2.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 34 / 60 A5: We put the bound on the missing energy E T > 160 GeV.

Selection Cuts

A1: We have imposed a lepton and photon veto in the final state. j1 A2: pT requirements on the hardest and second hardest jets: pT > 130 j2 GeV and pT > 80 GeV.

A3: In order to minimize QCD multi-jet, we have ensured that the E~T and the jets are well separated, i.e., ∆φ(ji ,E~T ) > 0.4 where i = 1, 2. For all the other jets, ∆φ(j,E~T ) > 0.2.

A4: We demand a hard cut on the effective mass variable, MEff > 800 GeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 34 / 60 Selection Cuts

A1: We have imposed a lepton and photon veto in the final state. j1 A2: pT requirements on the hardest and second hardest jets: pT > 130 j2 GeV and pT > 80 GeV.

A3: In order to minimize QCD multi-jet, we have ensured that the E~T and the jets are well separated, i.e., ∆φ(ji ,E~T ) > 0.4 where i = 1, 2. For all the other jets, ∆φ(j,E~T ) > 0.2.

A4: We demand a hard cut on the effective mass variable, MEff > 800 GeV.

A5: We put the bound on the missing energy E T > 160 GeV.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 34 / 60 Cut-flow table for BKG

BKG Contribution after applying cuts :

QCD BKG is huge, but after MEff cut it goes to zero.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 35 / 60 Cut-flow table for Signal-I

Signal-I Contribution after applying cuts :

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 36 / 60 Cut-flow table for Signal-II

Signal-II Contribution after applying cuts :

For each BPs, signal (s) = Signal-I + Signal-II .

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 37 / 60 Statistical Significance ( ) S

We have used following formula in determining , S r h  s  i = 2 (s + b) ln 1 + s S × b − for different BPs : S

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 38 / 60 © The lightest among the two neutral fermions becomes a viable DM candidate. © DM can be tested in different on going DD experiments like Xenon-1T, LUX. © Fermi-LAT and HESE can detect the DM indirectly by detecting gamma-rays signal in future.

© This model can also be tested at collider by searching multi-jet + ET signal.

Conclusion - First Part

© By introducing singlet fermion, we have overcome the drawbacks of pure triplet fermions.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 39 / 60 © DM can be tested in different on going DD experiments like Xenon-1T, LUX. © Fermi-LAT and HESE can detect the DM indirectly by detecting gamma-rays signal in future.

© This model can also be tested at collider by searching multi-jet + ET signal.

Conclusion - First Part

© By introducing singlet fermion, we have overcome the drawbacks of pure triplet fermions. © The lightest among the two neutral fermions becomes a viable DM candidate.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 39 / 60 © Fermi-LAT and HESE can detect the DM indirectly by detecting gamma-rays signal in future.

© This model can also be tested at collider by searching multi-jet + ET signal.

Conclusion - First Part

© By introducing singlet fermion, we have overcome the drawbacks of pure triplet fermions. © The lightest among the two neutral fermions becomes a viable DM candidate. © DM can be tested in different on going DD experiments like Xenon-1T, LUX.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 39 / 60 © This model can also be tested at collider by searching multi-jet + ET signal.

Conclusion - First Part

© By introducing singlet fermion, we have overcome the drawbacks of pure triplet fermions. © The lightest among the two neutral fermions becomes a viable DM candidate. © DM can be tested in different on going DD experiments like Xenon-1T, LUX. © Fermi-LAT and HESE can detect the DM indirectly by detecting gamma-rays signal in future.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 39 / 60 Conclusion - First Part

© By introducing singlet fermion, we have overcome the drawbacks of pure triplet fermions. © The lightest among the two neutral fermions becomes a viable DM candidate. © DM can be tested in different on going DD experiments like Xenon-1T, LUX. © Fermi-LAT and HESE can detect the DM indirectly by detecting gamma-rays signal in future.

© This model can also be tested at collider by searching multi-jet + ET signal.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 39 / 60 Non-thermal Dark Matter

“Explaining the 3.5 keV X-ray Line in a Lµ Lτ Extension of the Inert Doublet Model”, A. Biswas, S. Choubey,− L. Covi and S.K., JCAP 1802, no. 02, 002 (2018) [arXiv:1711.00553 [hep-ph]].

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 40 / 60 Direct Detection Cross section

DM mass vs SI DD cross section

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 41 / 60 In near future, SIDD cross section is going to touch neutrino floor.

We need to develop our detector to distinguish the DM and neutrino signal.

To tackle this, we can think of DM production mechanism where SIDD cross section is suppressed by model construction.

DM production via Freeze-in mechanism falls in this category. This type of DM never achieve thermal equilibrium hence non-thermal DM.

Few words on DD

So far no DD signal has been observed.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 42 / 60 We need to develop our detector to distinguish the DM and neutrino signal.

To tackle this, we can think of DM production mechanism where SIDD cross section is suppressed by model construction.

DM production via Freeze-in mechanism falls in this category. This type of DM never achieve thermal equilibrium hence non-thermal DM.

Few words on DD

So far no DD signal has been observed.

In near future, SIDD cross section is going to touch neutrino floor.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 42 / 60 To tackle this, we can think of DM production mechanism where SIDD cross section is suppressed by model construction.

DM production via Freeze-in mechanism falls in this category. This type of DM never achieve thermal equilibrium hence non-thermal DM.

Few words on DD

So far no DD signal has been observed.

In near future, SIDD cross section is going to touch neutrino floor.

We need to develop our detector to distinguish the DM and neutrino signal.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 42 / 60 DM production via Freeze-in mechanism falls in this category. This type of DM never achieve thermal equilibrium hence non-thermal DM.

Few words on DD

So far no DD signal has been observed.

In near future, SIDD cross section is going to touch neutrino floor.

We need to develop our detector to distinguish the DM and neutrino signal.

To tackle this, we can think of DM production mechanism where SIDD cross section is suppressed by model construction.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 42 / 60 Few words on DD

So far no DD signal has been observed.

In near future, SIDD cross section is going to touch neutrino floor.

We need to develop our detector to distinguish the DM and neutrino signal.

To tackle this, we can think of DM production mechanism where SIDD cross section is suppressed by model construction.

DM production via Freeze-in mechanism falls in this category. This type of DM never achieve thermal equilibrium hence non-thermal DM.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 42 / 60 DM relic density is proportional to the coupling strength.

Freeze-in mechanism [Hall et. al, 09]

Figure: DM production via freeze-in mechanism.

DM initial abundance is zero.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 43 / 60 Freeze-in mechanism [Hall et. al, 09]

Figure: DM production via freeze-in mechanism.

DM initial abundance is zero. DM relic density is proportional to the coupling strength.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 43 / 60 Due to such low coupling DM never achieve thermal equilibrium hΓi ( H < 1), hence it is also called non-thermal DM. Also for such low coupling, FIMP DM is safe from all the existing bounds.

Freeze-in coupling strength [Hall et. al, 09]

Figure: Freeze-in coupling strength.

Coupling strength is very feeble, hence feebly interacting massive particle (FIMP).

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 44 / 60 Also for such low coupling, FIMP DM is safe from all the existing bounds.

Freeze-in coupling strength [Hall et. al, 09]

Figure: Freeze-in coupling strength.

Coupling strength is very feeble, hence feebly interacting massive particle (FIMP). Due to such low coupling DM never achieve thermal equilibrium hΓi ( H < 1), hence it is also called non-thermal DM.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 44 / 60 Freeze-in coupling strength [Hall et. al, 09]

Figure: Freeze-in coupling strength.

Coupling strength is very feeble, hence feebly interacting massive particle (FIMP). Due to such low coupling DM never achieve thermal equilibrium hΓi ( H < 1), hence it is also called non-thermal DM. Also for such low coupling, FIMP DM is safe from all the existing bounds.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 44 / 60 Produce DM from the decay of extra gauge boson.

DM decay which gives 3.55 keV line.

In discussing above things, we assume U(1)Lµ−Lτ extension with additional particles.

Strategy in Non-thermal DM study

Briefly, we obey the following steps: Produce the extra gauge boson from the decay of the BSM Higgs.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 45 / 60 DM decay which gives 3.55 keV line.

In discussing above things, we assume U(1)Lµ−Lτ extension with additional particles.

Strategy in Non-thermal DM study

Briefly, we obey the following steps: Produce the extra gauge boson from the decay of the BSM Higgs.

Produce DM from the decay of extra gauge boson.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 45 / 60 In discussing above things, we assume U(1)Lµ−Lτ extension with additional particles.

Strategy in Non-thermal DM study

Briefly, we obey the following steps: Produce the extra gauge boson from the decay of the BSM Higgs.

Produce DM from the decay of extra gauge boson.

DM decay which gives 3.55 keV line.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 45 / 60 Strategy in Non-thermal DM study

Briefly, we obey the following steps: Produce the extra gauge boson from the decay of the BSM Higgs.

Produce DM from the decay of extra gauge boson.

DM decay which gives 3.55 keV line.

In discussing above things, we assume U(1)Lµ−Lτ extension with additional particles.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 45 / 60 Particle Spectrum

Particles and their charges under SM and Z2 gauge groups :

Particles and their charges under ( ) gauge group : U 1 Lµ−Lτ

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 46 / 60 Lagrangian

Complete Lagrangian:

Lagrangian for RH neutrinos:

Complete potential:

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 47 / 60 Symmetry break and mass

Scalars take the following from

   +  0   η vµτ + Hµτ 0 0 φh = v + H  , φH = , η = η + i η  . √2 R I √2 √2 Above vevs, break the symmetry: SU(2)L U(1)Y U(1) U(1)em × × Lµ−Lτ → Mass of the Higgses:

α is the mixing angle between neutral Higgses.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 48 / 60 Stability of Vacuum from below

Quartic Couplings need to follow the following criterion:

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 49 / 60 Neutrino mass

0 0 φh φh

η0 η0

νi Nk νj

Figure: Neutrino mass generate by the one loop diagram.

Neutrino mass generated by the one-loop diagram takes the following form,

" M2 M2 M2 M2 # X yik yjk Mk η0 η0 η0 η0 Mν = R ln R I ln I ij 16 2 M2 M2 M2 M2 M2 M2 π η0 k k − η0 k k k R − I − P where yji = hj Uji and Nα = Uαi Ni .

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 50 / 60 For FRW metric, the Lioville’s operator takes the following form, ∂ ∂ Lˆ = Hp ∂t − ∂p Depends on two variables (T(t),p) and if we define two new variables (ξp, r) [J. K¨oniget. al., JCAP16], where  0 −1 Msc p dT Tgs (T ) r = , ξp = (r) , and = HT 1 + r B T dt − 3gs (T ) Liouville’s Operator takes the following form ,  Tg 0 −1 ∂ Lˆ = r H 1 + s Dependent on one variable 3gs ∂ r →

BE for Gauge boson Production

Boltzmann Equation:

X hi →Zµτ Zµτ Zµτ → all Lfˆ Z = + µτ C C i=1,2

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 51 / 60 Depends on two variables (T(t),p) and if we define two new variables (ξp, r) [J. K¨oniget. al., JCAP16], where  0 −1 Msc p dT Tgs (T ) r = , ξp = (r) , and = HT 1 + r B T dt − 3gs (T ) Liouville’s Operator takes the following form ,  Tg 0 −1 ∂ Lˆ = r H 1 + s Dependent on one variable 3gs ∂ r →

BE for Gauge boson Production

Boltzmann Equation:

X hi →Zµτ Zµτ Zµτ → all Lfˆ Z = + µτ C C i=1,2 For FRW metric, the Lioville’s operator takes the following form, ∂ ∂ Lˆ = Hp ∂t − ∂p

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 51 / 60 Liouville’s Operator takes the following form ,  Tg 0 −1 ∂ Lˆ = r H 1 + s Dependent on one variable 3gs ∂ r →

BE for Gauge boson Production

Boltzmann Equation:

X hi →Zµτ Zµτ Zµτ → all Lfˆ Z = + µτ C C i=1,2 For FRW metric, the Lioville’s operator takes the following form, ∂ ∂ Lˆ = Hp ∂t − ∂p Depends on two variables (T(t),p) and if we define two new variables (ξp, r) [J. K¨oniget. al., JCAP16], where  0 −1 Msc p dT Tgs (T ) r = , ξp = (r) , and = HT 1 + r B T dt − 3gs (T )

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 51 / 60 BE for Gauge boson Production

Boltzmann Equation:

X hi →Zµτ Zµτ Zµτ → all Lfˆ Z = + µτ C C i=1,2 For FRW metric, the Lioville’s operator takes the following form, ∂ ∂ Lˆ = Hp ∂t − ∂p Depends on two variables (T(t),p) and if we define two new variables (ξp, r) [J. K¨oniget. al., JCAP16], where  0 −1 Msc p dT Tgs (T ) r = , ξp = (r) , and = HT 1 + r B T dt − 3gs (T ) Liouville’s Operator takes the following form ,  Tg 0 −1 ∂ Lˆ = r H 1 + s Dependent on one variable 3gs ∂ r →

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 51 / 60 Number density is given by 3 Z g T 3 2 nZ (r) = (r) dξp ξ fZ (ξp, r) , µτ 2π2 B p µτ where  1/3  1/3 gs (T0) gs (Msc /r) (r) = = . B gs (T ) gs (Msc /r0)

BE for Non-thermal Dark Matter

BE for the DM, p   dYNj Vij Mpl r g?(r) X X = Γ (Y Y Y ) 2  hk →Nj Ni hk Nj Ni  dr 1.66 M gs (r) h i − sc k=1,2 i=1,2,3 p Vij Mpl r g?(r) X + 2 ΓZµτ →Nj Ni NTH (YZµτ YNj YNi ) , 1.66 M gs (r) h i − sc i=1,2,3 2 n 2π where Y = Zµτ and s = g (T ) T 3 Zµτ s 45 s

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 52 / 60 BE for Non-thermal Dark Matter

BE for the DM, p   dYNj Vij Mpl r g?(r) X X = Γ (Y Y Y ) 2  hk →Nj Ni hk Nj Ni  dr 1.66 M gs (r) h i − sc k=1,2 i=1,2,3 p Vij Mpl r g?(r) X + 2 ΓZµτ →Nj Ni NTH (YZµτ YNj YNi ) , 1.66 M gs (r) h i − sc i=1,2,3 2 n 2π where Y = Zµτ and s = g (T ) T 3 Zµτ s 45 s Number density is given by 3 Z g T 3 2 nZ (r) = (r) dξp ξ fZ (ξp, r) , µτ 2π2 B p µτ where  1/3  1/3 gs (T0) gs (Msc /r) (r) = = . B gs (T ) gs (Msc /r0)

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 52 / 60 Non-thermal average of decay width Zµτ Nj Ni is, → f (p) R Zµτ d3p q 2 2 p +MZ Γ = M Γ µτ Zµτ →Nj Ni NTH Zµτ Zµτ →Nj Ni R 3 , h i fZµτ (p)d p

fZµτ is the non-thermal distribution of Zµτ .

Contd...

Thermal average of decay width is defined as,

 M  hk K1 r M Γ = Γ sc hk →Nj Ni hk →Nj Ni  M  , h i K r hk 2 Msc

th Ki is the modified Bessel function of i kind.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 53 / 60 Contd...

Thermal average of decay width is defined as,

 M  hk K1 r M Γ = Γ sc hk →Nj Ni hk →Nj Ni  M  , h i K r hk 2 Msc

th Ki is the modified Bessel function of i kind.

Non-thermal average of decay width Zµτ Nj Ni is, → f (p) R Zµτ d3p q 2 2 p +MZ Γ = M Γ µτ Zµτ →Nj Ni NTH Zµτ Zµτ →Nj Ni R 3 , h i fZµτ (p)d p

fZµτ is the non-thermal distribution of Zµτ .

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 53 / 60 Gauge boson distribution function

1 r=0.02

10−6 ) p ξ ( τ μ −12 Z

f 10

2 p ξ

10−18 Non-thermal Thermal

10−24 10−4 10−3 0.01 0.1 1 10 100 1000

ξp

Figure: Thermal and Non-thermal distribution function of Zµτ gauge boson.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 54 / 60 Line Plots

1

1 10−3 2 ΩDM h = 0.12 10−3

−6 2 10 ΩDM h = 0.12 10−6 Zμτ Dominant 2 2 10−9 h h −9 M 10 M D D Tini = 10 TeV Ω T = 7 TeV Ω ini 10−12 10−12 Tini = 3 TeV Tini = 0.5 TeV h2 Decay −15 h2 Dominant 10 Zμτ Decay 10−15 (h2 + Zμτ) Decay

−18 10−18 10

10−3 1 1000 106 10−3 1 1000 106

Mh1 Mh1 r (= T ) r (= T )

Figure: Variation of relic density with r where other parameters are fixed at −11 gµτ = 1.01 10 , α = 0.01, MZ = 1 TeV, MDM = 100 GeV, Mh = 5 TeV × µτ 2 and MN = 150 GeV and MDM = MN MN = 100 GeV. 1 2 ' 3

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 55 / 60 Contd..

10−9 1

10−6 10−12

Y −12 Zμτ 10 10−15 3 YN2 + N3 N

+

2 2 h N

2 Y N

, τ μ Ω Z Y

10−24

MZ = 2 TeV −21 μτ Zμτ → N1 N2 10 MZ = 1 TeV μτ Zμτ → N2 N2 M = 0.5 TeV Zμτ −30 Z → N N 10 μτ 2 3 Zμτ, h2 → N1 N2 + N2 N2 + N2 N3

10−24 10−36 10−3 1 1000 106 10−3 1 1000 106

Mh1 Mh1 r (= T ) r (= T )

Figure: Variation of relic density with r where other parameters are fixed at −11 gµτ = 1.01 10 , α = 0.01, MZ = 1 TeV, MDM = 100 GeV, Mh = 5 TeV × µτ 2 and MN = 150 GeV and MDM = MN MN = 100 GeV. 1 2 ' 3

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 56 / 60 3.55 keV γ-ray line

γ η η

N2 N3 N2 N3

γ l l

Figure: Diagrams for 3.55 keV γ-ray line.

Flux expression takes the following form, 1 Z Φ = ρN2 (~r)d~r 4πMN2 τN2 l.o.s.

where τN2 : DM decay life, ρN2 : DM halo density. Constraint on decay width to explain 3.55 keV line is,   −44 MN2 Γ(N2 N3γ) = (0.2 1.9) 10 GeV . → − × 100 GeV

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 57 / 60 Contd..

If N2 and N3 have opposite parity then, N2 N3γ happen by the magnetic moment term generated at the one→ loop level [Pal et. al, PRD 82]. Decay rate is:

2  2 µ23 3 MN3 Γ(N2 N3γ) = δ 1 P → 4π − MN2 where ! M2 X e 1 MN2 MN2 N3 µ23 = (yi2yi3) , δ = 1 , P = 1 2 (4π)2 M2 2 − M2 ± i η N2

6 2 −1 For Mη = 10 GeV, MN2 = 100 GeV, (yij ) = 10 , we get −44 ΓN 10 GeV, which can explain 3.55 keV line. 2 ∼

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 58 / 60 Conclusion

Present model generate the neutrino mass via one loop diagram.

Dark matter can be produced by the freeze-in mechanism in the right ball-park value put by Planck.

3.55 keV line can also be explained by the DM decay.

Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 59 / 60 Sarif Khan (HRI) DM and LHC Pheno November 5, 2018 60 / 60