Sterile Neutrino Dark Matter - Institut national de ...vietnam.in2p3.fr/2016/nufact/transparencies/Parallel2/WG5_Schmidt.… · Adhikari et al. 1602.04816 Hint for 3.5 keV X-ray line

JHEP 1512 (2015) 023 [1507.05694]

JHEP 1501 (2015) 006 [1409.4330]

A. Adulpravitchai, MS

based on

Sterile Neutrino Dark Matter

Production from Scalar Decay

Michael A. Schmidt

23 August 2016 @ NuFact

The University of Sydney

http://www.arxiv.org/abs/1507.05694http://www.arxiv.org/abs/1409.4330

Dark Matter

• Virial theorem(12

〈v2〉

= GMR)

applied to

COMA cluster (F.Zwicky 1933)

• Galactic rotation curves [O(10s)kpc]• Gravitational lensing [< O(200)kpc]• Bullet cluster (X-ray + grav. lensing)• Cosmic microwave background

Large scale structure

• . . .

1

Dark Matter

〈v2〉

= GMR)

applied to

• . . .

1

Dark Matter

〈v2〉

= GMR)

applied to

• . . .

1

Dark Matter

〈v2〉

= GMR)

applied to

• . . .

1

Dark Matter

〈v2〉

= GMR)

applied to

• . . .

1

Properties of Dark Matter

• Relic density Planck 1502.01589

Ωdmh2 = 0.1199± 0.0022

• Stable on cosmological timescales

• Neutral• Structure formation⇒ DM sufficiently cold

1407.0017

• Consistent with stellar evolution and BBN• Not excluded by direct or indirect searches• Compatible with constraints on self-interactions

2

Properties of Dark Matter

• Relic density Planck 1502.01589

Ωdmh2 = 0.1199± 0.0022

• Stable on cosmological timescales

• Neutral• Structure formation⇒ DM sufficiently cold

1407.0017

• Consistent with stellar evolution and BBN• Not excluded by direct or indirect searches• Compatible with constraints on self-interactions

2

keV Sterile Neutrinos

Planck 2015

• Dark matter about a quarter of the energy density• Interacts with SM particles weakly• Existence established across many scales• However problems at small scales

• DM momentum distribution crucial foraccretion and structure formation

• Characterised by free-streaming horizonrFS =

∫ t0ti

〈v(t)〉a(t) dt

Lovell et al. 1104.2929

Lα Lβ

HνHν

H H

Nk

• Could be linked to neutrino physics• Decaying DM like a keV sterile neutrino• Fermionic DM in radiative seesaw Ma hep-ph/0601225

produced via freeze-in Molinaro, Yaguna, Zapata 1405.1259 3

http://www.arxiv.org/abs/1104.2929http://www.arxiv.org/abs/hep-ph/0601225http://www.arxiv.org/abs/1405.1259

Planck 2015

∫ t0ti

〈v(t)〉a(t) dt

Lovell et al. 1104.2929

Lα Lβ

HνHν

H H

Nk

Planck 2015

∫ t0ti

〈v(t)〉a(t) dt

100 101 102

k [h/Mpc]

10-2

10-1

100

∆2

(k)

pure CDM

WDM: m=2.0keV

WDM: m=3.0keV

WDM: m=4.0keV

Schneider 1412.2133

Lα Lβ

HνHν

H H

Nk

Planck 2015

∫ t0ti

〈v(t)〉a(t) dt

100 101 102

k [h/Mpc]

10-2

10-1

100

∆2

(k)

pure CDM

WDM: m=2.0keV

WDM: m=3.0keV

WDM: m=4.0keV

Schneider 1412.2133

Lα Lβ

HνHν

H H

Nk

What do we know?

Constraints

• X -ray observations

• Coarse-grained phasespace density

Tremaine,Gunn 1979

• Ly-α forestViel et. al 1306.2314

mth ≥ 3.3keV(2σ)[mth ≥ 2keV(cons)]

Interaction strength Sin2(2θ)

Dark matter mass MDM [keV]

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Tremaine-Gunn / Lyman-α Excluded by X-ray observations

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

Adhikari et. al 1602.04816

DW production

N νν `

Wγ

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

Projected DM mass density, MSun/pc2

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

Adhikari et al. 1602.04816

Hint for 3.5 keV X-ray line

Bulbul et al. 1402.2301; Boyarsky et al. 1402.4119; . . .

⇒ Could be explained by7 keV sterile neutrino with∑α sin

2(2θα) ' 7× 10−11

4

http://www.arxiv.org/abs/1306.2314http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1402.2301http://www.arxiv.org/abs/1402.4119

What do we know?

Constraints

Tremaine,Gunn 1979

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

DW production

N νν `

Wγ

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

2(2θα) ' 7× 10−11

4

http://www.arxiv.org/abs/1306.2314http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1402.2301http://www.arxiv.org/abs/1402.4119

What do we know?

Constraints

Tremaine,Gunn 1979

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

2 5 50 1 10

DM overproduction

DW production

N νν `

Wγ

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

1

10

0.01 0.1

Lin

e f

lux,

10

-6 p

ho

ton

s c

m-2

s-1

GC

M31

Perseus

Blank-sky

Bulb

ul e

t al.

(201

4)

Stac

ked

dSph

bou

nd

τ DM =

15.

6 x 1

027 s

ec

2(2θα) ' 7× 10−11

but challenged e.g. Jeltema, Profumo 1408.1699

no excess in Perseus Hitomi 1607.074204

http://www.arxiv.org/abs/1306.2314http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1602.04816http://www.arxiv.org/abs/1402.2301http://www.arxiv.org/abs/1402.4119http://www.arxiv.org/abs/1408.1699http://www.arxiv.org/abs/1607.07420

Sterile Neutrino DM Production

Neutrino oscillations Barbieri, Dolgov 1991; Enqvist, Kainulainen, Maalampi 1991

• Non-resonant oscillations – Dodelson-Widrow mechanismDodeson, Widrow hep-ph/9303287

• Resonant oscillations – Shi-Fuller mechanism Shi, Fuller astro-ph/9810076

Thermal production• Hidden decoupled (mirror) sector

Berezhiani, Mohapatra hep-ph/9505385; Berezhiani, Dolgov, Mohapatra hep-ph/9511221

• New gauge interaction and entropy dilutionBezrukov, Hettmansperger, Lindner 0912.4415; Nemevsek, Senjanovic, Zhang 1205.0844

Scalar decays [if via same coupling as oscillations typically subdominant]• Inflaton decay Shaposhnikov, Tkachev hep-ph/0604236; Bezrukov, Gorbunov 0912.0390• In thermal equilibrium

Kusenko hep-ph/0609081; Kusenko, Petraki 0711.4646; Frigerio, Yaguna 1409.0659; Adulpravitchai, MS 1507.05694

• Out of thermal equilibrium Merle, Niro, Schmidt 1306.3996; Adulpravitchai, MS 1409.4330 5

http://www.arxiv.org/abs/hep-ph/9303287http://www.arxiv.org/abs/astro-ph/9810076http://www.arxiv.org/abs/hep-ph/9505385http://www.arxiv.org/abs/hep-ph/9511221http://www.arxiv.org/abs/0912.4415http://www.arxiv.org/abs/1205.0844http://www.arxiv.org/abs/hep-ph/0604236http://www.arxiv.org/abs/0912.0390http://www.arxiv.org/abs/hep-ph/0609081http://www.arxiv.org/abs/0711.4646http://www.arxiv.org/abs/1409.0659http://www.arxiv.org/abs/1507.05694http://www.arxiv.org/abs/1306.3996http://www.arxiv.org/abs/1409.4330

• Non-resonant oscillations – Dodelson-Widrow mechanismDodeson, Widrow hep-ph/9303287 excluded e.g. Horiuchi et al. 1311.0282

http://www.arxiv.org/abs/hep-ph/9303287http://www.arxiv.org/abs/1311.0282http://www.arxiv.org/abs/astro-ph/9810076http://www.arxiv.org/abs/hep-ph/9505385http://www.arxiv.org/abs/hep-ph/9511221http://www.arxiv.org/abs/0912.4415http://www.arxiv.org/abs/1205.0844http://www.arxiv.org/abs/hep-ph/0604236http://www.arxiv.org/abs/0912.0390http://www.arxiv.org/abs/hep-ph/0609081http://www.arxiv.org/abs/0711.4646http://www.arxiv.org/abs/1409.0659http://www.arxiv.org/abs/1507.05694http://www.arxiv.org/abs/1306.3996http://www.arxiv.org/abs/1409.4330

• Non-resonant oscillations – Dodelson-Widrow mechanismDodeson, Widrow hep-ph/9303287 excluded e.g. Horiuchi et al. 1311.0282

http://www.arxiv.org/abs/hep-ph/9303287http://www.arxiv.org/abs/1311.0282http://www.arxiv.org/abs/astro-ph/9810076http://www.arxiv.org/abs/hep-ph/9505385http://www.arxiv.org/abs/hep-ph/9511221http://www.arxiv.org/abs/0912.4415http://www.arxiv.org/abs/1205.0844http://www.arxiv.org/abs/hep-ph/0604236http://www.arxiv.org/abs/0912.0390http://www.arxiv.org/abs/hep-ph/0609081http://www.arxiv.org/abs/0711.4646http://www.arxiv.org/abs/1409.0659http://www.arxiv.org/abs/1507.05694http://www.arxiv.org/abs/1306.3996http://www.arxiv.org/abs/1409.4330

In thermal equilibrium decay

SM+N+Hν [1507.05694]

http://www.arxiv.org/abs/1507.05694

Neutrinophillic Two-Higgs Doublet Model

• New particles odd under Z2Sterile neutrino N → −NSecond Higgs doublet Hν → −Hν

• Lagrangian

−LN = yLNLHνN +1

2mNN N + h. c.

• Scalar potential

V = µ2νH†νHν +

λ22

(H†νHν)2

+ λ3H†H H†νHν + λ4|H†Hν |2 +

λ52

[(H†Hν)2 + h. c.]

• Scalar particle masses m2kk = µ2ν + (λ3 + λ4) v2

m2k,K0 = m2kk ± λ5v2 m2K± = m2kk − λ4v2

6

Neutrino Mass

Radiative seesaw Ma hep-ph/0601225; Molinaro, Yaguna, Zapata 1405.1259• Hν does not obtain VEV• Radiative neutrino mass generation

mν ' 10−2eV(λ5y

22,3

10−11

)×

(

1TeVM2,3

)mkk � M2,3(

1TeVmkk

)(M2,3mkk

)mkk � M2,3

• keV sterile neutrino does not (significantly) contribute• Sterile neutrino is stable

Lα Lβ

HνHν

H H

Nk

Naturally small seesaw Ma hep-ph/0011121; Haba, Ishida, Takahashi 1407.6827• Soft-breaking term Vsoft = µ212H†Hν + h. c.⇒ Induced VEV 〈Hν〉v =

Re(µ212)

m2k+ i

Im(µ212)

m2K0

• Active-sterile mixing θα ' yLN,α〈Hν〉mN⇒ Possible explanation of 3.5 keV X-ray line

Lα Lβ

Hν Hν

Nk

7

http://www.arxiv.org/abs/hep-ph/0601225http://www.arxiv.org/abs/1405.1259http://www.arxiv.org/abs/hep-ph/0011121http://www.arxiv.org/abs/1407.6827

Neutrino Mass

Radiative seesaw Ma hep-ph/0601225; Molinaro, Yaguna, Zapata 1405.1259• Hν does not obtain VEV• Radiative neutrino mass generation

mν ' 10−2eV(λ5y

22,3

10−11

)×

(

1TeVM2,3

)mkk � M2,3(

1TeVmkk

)(M2,3mkk

)mkk � M2,3

• keV sterile neutrino does not (significantly) contribute• Sterile neutrino is stable

Lα Lβ

HνHν

H H

Nk

Naturally small seesaw Ma hep-ph/0011121; Haba, Ishida, Takahashi 1407.6827• Soft-breaking term Vsoft = µ212H†Hν + h. c.⇒ Induced VEV 〈Hν〉v =

Re(µ212)

m2k+ i

Im(µ212)

m2K0

• Active-sterile mixing θα ' yLN,α〈Hν〉mN⇒ Possible explanation of 3.5 keV X-ray line

Lα Lβ

Hν Hν

Nk

7

http://www.arxiv.org/abs/hep-ph/0601225http://www.arxiv.org/abs/1405.1259http://www.arxiv.org/abs/hep-ph/0011121http://www.arxiv.org/abs/1407.6827

Scalar decay

k,K 0,K±

ν, ν, `±

N

• Dominating for T . mkk• One daughter has Fermi-Dirac distribution⇒ Pauli-blocking

Scattering

• Freeze-in IR dominated• Scattering suppressed for T . mkk• In agreement with Adulpravitchai, MS 1409.4330• Neglected in analytic study

k ,K 0,K±

`∓, `∓, ν W±

N

ν, ν, `±

Derived analytic solution to Boltzmann equationFinite temperature corrections neglected among other

approximations.

See Drewes, Kang 1510.05646 for finite temperature corrections 8

Scalar decay

k,K 0,K±

ν, ν, `±

N

• Dominating for T . mkk• One daughter has Fermi-Dirac distribution⇒ Pauli-blocking

Scattering

• Freeze-in IR dominated• Scattering suppressed for T . mkk• In agreement with Adulpravitchai, MS 1409.4330• Neglected in analytic study

k ,K 0,K±

`∓, `∓, ν W±

N

ν, ν, `±

Derived analytic solution to Boltzmann equationFinite temperature corrections neglected among other

approximations.

See Drewes, Kang 1510.05646 for finite temperature corrections 8

Dark Matter Abundance [Pauli blocking neglected]

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

M1 (GeV)

10-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102

ΩN

1h

2

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS=200 GeV

mS=400 GeV

mS=800 GeV

mS=1000 GeV

mS=2000 GeV

100 101 102 103 104 105

T (GeV)

10-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-2

YN

1(T

)

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS =400 GeV

mH± =400 GeV, mH0 =200 GeV

mH± =400 GeV, mH0 =600 GeV

mH± =200 GeV, mH0 =400 GeV

mH± =600 GeV, mH0 =400 GeV

study of fermionic FIMP DM in radiative seesaw model Molinaro, Yaguna, Zapata 1405.1259

9

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

M1 (GeV)

10-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102

ΩN

1h

2

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS=200 GeV

mS=400 GeV

mS=800 GeV

mS=1000 GeV

mS=2000 GeV

100 101 102 103 104 105

T (GeV)

10-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-2

YN

1(T

)

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS =400 GeV

mH± =400 GeV, mH0 =200 GeV

mH± =400 GeV, mH0 =600 GeV

mH± =200 GeV, mH0 =400 GeV

mH± =600 GeV, mH0 =400 GeV

9

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

M1 (GeV)

10-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102

ΩN

1h

2

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS=200 GeV

mS=400 GeV

mS=800 GeV

mS=1000 GeV

mS=2000 GeV

100 101 102 103 104 105

T (GeV)

10-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-2

YN

1(T

)

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS =400 GeV

mH± =400 GeV, mH0 =200 GeV

mH± =400 GeV, mH0 =600 GeV

mH± =200 GeV, mH0 =400 GeV

mH± =600 GeV, mH0 =400 GeV

9

10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

M1 (GeV)

10-1210-1110-1010-910-810-710-610-510-410-310-210-1100101102

ΩN

1h

2

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS=200 GeV

mS=400 GeV

mS=800 GeV

mS=1000 GeV

mS=2000 GeV

100 101 102 103 104 105

T (GeV)

10-1610-1510-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-2

YN

1(T

)

y1 =10−8

y1 =10−9

y1 =10−10

y1 =10−11

y1 =10−12

100 101 102 103 104

T (GeV)

10-11

10-10

10-9

10-8

10-7

YN

1(T

)

mS =400 GeV

mH± =400 GeV, mH0 =200 GeV

mH± =400 GeV, mH0 =600 GeV

mH± =200 GeV, mH0 =400 GeV

mH± =600 GeV, mH0 =400 GeV

9

Momentum Distribution Function

non-relativistic

relativistic

thermal

this work

0 2 4 6 8 10x=

p

T

x2f(x) • Distribution functions normalised to 1

• Assumption: common scalar mass

• Spectrum cooler than thermal decoupling

• Similar to decay of relativistic scalar

• Hotter than decay of non-relativistic scalar

10

Dark Matter Abundance

100 200 300 400 500 600 700 800 900 1000mkk [GeV]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

√∑

α|y L

Nα|2

×10−8

0.1

0.2

0.30.51.0

0.01

0.05

Contour plot of ΩNh2

∑α sin

2(2θα) ' 7× 10−11mN = 7.1 keV,

0.1199± 2σ

Contribution from non-resonant oscillations negligible11

Dark Matter Abundance II

10 20 30 40 50 60 70 80 90 100mN [keV]

0.0

0.2

0.4

0.6

0.8

1.0

√∑

α|y L

Nα|2

×10−8

100

300500

700 1000

2000

Contour plot of mkk [GeV]

10 20 30 40 50 60 70 80 90 100mN [keV]

100

200

400

600

800

1000

mkk

[GeV

]

3× 10−9

4× 10−9

6×10−9

7× 1

0−9

1×

10−8

2×

10−8

Contour plot of√∑

α |yLNα|2/10−8

DM abundance

ΩNh2 ' 3.5× 1015 mN

10keV

100GeV

mkk

∑

α

|yLN,α|2

⇒ Yukawa couplings ∼ 10−8 for scalars at TeV scale12

Suppression of Small Scale Structure

Free-streaming scale: rFS

Size of astrophysical object: L

time

ν

c

ψ

L� rFS

c ν c ν cνcνcψ

L� rFS

c

ν

νc

ψ

L� rFS

cψ

L� rFS

Potential stays the samePotential

weakens

CDM and ν’s cluster only

CDM

clusters

13

time

ν

c

ψ

L� rFS

c ν c ν cνcνcψ

L� rFS

c

ν

νc

ψ

L� rFS

cψ

L� rFS

weakens

CDM

clusters

13

time

ν

c

ψ

L� rFS

c ν c ν cνcνcψ

L� rFS

c

ν

νc

ψ

L� rFS

cψ

L� rFS

weakens

CDM

clusters

13

• Free streaming horizon e.g. Boyarsky, Lesgourges, Ruchayskiy, Viel 0812.0010

rFS '∫ t0td

〈v(t)〉a(t)

dt =

∫ tnrtd

1

a(t)dt+

∫ teqtnr

〈v(t)〉a(t)

dt+

∫ t0teq

〈v(t)〉a(t)

dt

td decay time; teq time of matter-radiation equality; t0 today

Hasenkamp, Kersten 1212.4160; Merle, Niro, Schmidt 1306.3996; Adulpravitchai, MS 1409.4330

• Average velocity

〈v(t)〉 =

1 for t < tnr〈p〉mN

for t > tnr

• Sterile neutrino become non-relativistic at time tnr with

mN = 〈p(Tnr )〉 ' 2.46Tnr ⇒ tnr ' 1500s(

10keV

mN

)2

14

http://www.arxiv.org/abs/0812.0010http://www.arxiv.org/abs/1212.4160http://www.arxiv.org/abs/1306.3996http://www.arxiv.org/abs/1409.4330

Free-Streaming Horizon

10 20 30 40 50 60 70 80 90 100mN [keV]

10−2

10−1

r FS

[Mpc

]

Ly-α

mth [keV]23.35

10

20

HDM

CDM

WDM

rFS =√teqtnraeq

(5 + ln

teqtnr

)' 0.047Mpc

(10keVmN

)

1keV < mth < 5keV ⇒ 2.5 keV . mN . 13 keV15

Free-Streaming Horizon

10 20 30 40 50 60 70 80 90 100mN [keV]

10−2

10−1

r FS

[Mpc

]

Ly-α

mth [keV]23.35

10

20

HDM

CDM

WDM

rFS =√teqtnraeq

(5 + ln

teqtnr

)' 0.047Mpc

(10keVmN

)

1keV < mth < 5keV ⇒ 2.5 keV . mN . 13 keV15

Out-of-equilibrium decay

SM+N+ϕ [1409.4330]

Model

• New particles and discrete lepton number Z4: L→ iLSterile neutrino N → −iNReal scalar φ→ −φ• Lagrangian

−∆L = −λHφ2

H†Hφ2 +[yLNLHN +

yN2φN2 + h.c.

]

• Small couplings: λHφ, yLN � 1• Effective scalar interaction after EWSB

[〈H〉 =(

0 v)T

and φ = vφ + σ]

∆V (h, σ) = λHφ

(h2σ2

4+

v√2hσ2)

16

SM→ Nν N

L

L N

N

H

Dominantly two step production

SM σ N1 2

SM → σf

f̄

σ

σh

V

σ

σh

h

σ

σh

h

σ

σh

σ

σ → N

σ

N

Several approximations:

g∗ = const,

no finite T effects, . . .17

SM→ Nν N

L

L N

N

H

Dominantly two step production

SM σ N1 2

SM → σf

f̄

σ

σh

V

σ

σh

h

σ

σh

h

σ

σh

σ

σ → N

σ

N

Several approximations:

g∗ = const,

no finite T effects, . . .17

Dark Matter Abundance

104 1000 100 10 110-13

10-11

10-9

10-7

10-5

T @GeVD

Ymσ = 500GeV; λHφ = 2.7 · 10−7

Tin = 8.8 GeV

Yσ

YN

104 1000 100 10 110-13

10-11

10-9

10-7

10-5

T @GeVD

Y

mσ = 30GeV; λHφ = 3.7 · 10−9

Tin = 17 GeV

Yσ

YN

Higgs annihilation solid (decay dashed), ZZ (solid), WW (dashed); tt̄

mN = 7.1 keV;λφ = 0.5

Dark matter abundance [Ωsh2 ' 0.1199± 0.0027 Planck 1303.5076]

ΩN 'mσ Y

∞N T

30

g s∗(T0)g s∗(Tin)

ρc

Higgs decays dominant contribution when kinematically accessible18

Free-Streaming Horizon rFS '√teqtnraeq

(5 + ln teq

tnr

)

5 10 15 20mN[keV]0.005

0.010

0.050

0.100

0.500rFS[Mpc]

HDM

CDM

WDM

Ly-α

mth[keV]2

3.35

10

20

500

170

60

30

mN = 〈p(Tnr )〉 '√π

2Tnr ⇒ tnr '

π

16

m2σm2N

(g s∗ (T0)

g s∗ (Tin)

)2/3tin

19

Conclusions

• keV sterile neutrinois a viable DM candidate

• Freeze-in production via scalar decay is aninteresting alternative to oscillations

• Can be both cold or warm DM

19

13th International Symposium on Cosmology and Particle Astrophysics

(CosPA 2016),Sydney, Nov 28 – Dec 2, 2016

LOC: Jan Hamann (USyd), Gary Hill (Adelaide), Archil Kobakhidze (USyd), Geraint Lewis (USyd), Michael Schmidt (USyd), Kevin Varvell (USyd), Yvonne Wong (UNSW)

https://indico.cern.ch/event/491882

https://indico.cern.ch/event/491882/https://indico.cern.ch/event/491882

In thermal equilibrium decay SM+N+H [1507.05694]Out-of-equilibrium decay SM+N+ [1409.4330]Conclusions