Dark Matter Inverse-Seesaw Models · 2019. 12. 3. · ANGY LIU Universität Würzburg 5/ 19....

Motivation Models and Results Conclusion

Dark Matter

In Minimal Supersymmetric

Inverse-Seesaw Models

YANG LIU

Universität Würzburg

YANG LIU Universität Würzburg 1/ 19


arXiv:1909.11686

Prof. Werner Porod from Universität Würzburg&

Prof. Joel Jones-Pérez from Ponticia UniversidadCatolica del Peru



Motivation

Dark matter (DM) need to be explained

Supersymmetry provides candidates

lightest νR (keV range), νR (superpartner of νR)



Minimal Inverse-Seesaw Model: Structure

Superpotential

W =WMSSM +1

2(MR)ij νR,iνR,j + (Yν)ijLi · HuνR,j (1)

Soft-breaking terms

The corresponding soft breaking terms are

Vsoft = VsoftMSSM+(m2νR)ij ν

∗R,iνR,j +

1

2(Bν)ij νR,iνR,j + (T )ijLi ·HuνR,j .

(2)



Parameterization(Casas-Ibarra-like):arXiv:1505.05880With this parametrization, the neutrino Yukawa coupling is:

Yν = −i√

2

vuU∗PMNSH

∗m12

l (mlR† +RTMh)M

− 12

h H.

The neutrino mixing matrix U is a function of ml = diag(m1,m2,m3),Mh = diag(M4,M5,M6), UPMNS matrix and matrix H and R. Where Hs are:

H = (I + m1/2l R†M−1

h Rm−1/2l )−1/2 H = (I + M

1/2h Rm−1

l R†M−1/2h )−1/2,

and the matrix R is parametrized as:

R =

1c56 s56

−s56 c56

c46 s46

1−s46 c46

c45 s45

−s45 c45

1

where cij = cos θ′ij and θ

′ij are the mixing angles in this 3× 3 mixing

matrix, θ′ij = ρij + iγij .

Upshot

γ change the magnitude of Yν exponentially: minimal inverse-seesaw



Minimal Inverse-Seesaw Model: Decay Processes

Three-Body Decay

νj

νi

νl

νk

pk1

Z

k2k3

νj

νi

νl

νk

pk1

H/A

k2k3

Radiative Decay

νj

νi

γ

W+

l

l

νj

νi

γ

l

χ+

χ+

νj

νi

γ

H+

l

l



Numerical Results: ν4 (keV)Our Results:

Γ ≈ 10−47GeV,

BR(ν4 → νγ) ' 10%

sin2 2θ =∑3i |Ui,4|2,

Γ ∝ sin2(2θ)(mν4keV

)5s−1

Mν4(keV) min. sin2 2θ7 3.38462×10−9

20 1.18462×10−9

30 7.89744×10−10

40 5.92308×10−10

50 4.73847×10−10

NuSTAR Results(arXiv:1609.00667):

Condition: neutrinos are produced by Shi-Fuller mechanism.



Numerical Results: ν

ν

ν f

f

h

Calculated with SPheno and micrOMEGAS

Variation

Variable Values Magn. of Ωh2

Yν 10−12 107

M2ν 8000( GeV)2 102

M2ν , Tν M2

ν = 8000( GeV)2, Tν = 100 10−1

M2ν , Tν , Yν,1 M2

ν = 6000( GeV)2, Tν = 100, Yν,1 = 10−5 10−2

Tν = AνYν = 100, Aν = 107 → charge breaking minimum



BLSSM (B-L Supersymmetric Standard Model) : Structure

Gauge Group

U(1)Y × SU(3)c × SU(2)L × U(1)B−L

Structure

MSSM particles + η, η

W =WMSSM + Y ijν LiHuνj − µ′η ˆη + Y ijx νiηνj ,

LSB =LMSSM −m2η|η|2 −m2

η|η|2 + ...(3)

Idea:

Typical 2 light H: 1 MSSM, 1 singlet

Build up Higgs funnel with one of the light Higgs which is mainlyη-like: Mh ' 2Mν , controlled by tanβ′ =

vηvη

This will exhaust ν DM and produce ν4



Varied Yx(1, 1)

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

10-9

10-8

10-7

10-6

10-5

10-4

10-3

0

20

40

60

80

100

Ω h

2

% i

n t

ota

l

YX(1,1)

Varied with YX(1,1), tanβ’=0.97

Ωh2

ν4ν5ν6

gd3e3u2A

WmWph1Z

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

10-9

10-8

10-7

10-6

10-5

10-4

10-3

0

20

40

60

80

100



Varied tan β′, Yx(1, 1) = 10−5

10-5

10-4

10-3

10-2

10-1

100

101

102

103

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Ω h

2

tanβ'

Ωh2

10-5

10-4

10-3

10-2

10-1

100

101

102

103

0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1



Varied Mass Ratio

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

1.5 2 2.5 3 3.5 4 0

50

100

150

200Ω

h2

Mas

s (G

eV)

mh'/mν~ 1P

Ω h2 mν~ 1P mh'/2 mh/2



Conclusion

Minimal Inverse-Seesaw model:

keV range neutrino DM, excluded if νR are produced throughShi-Fuller mechanism

excluded for ν DM if ν4 in keV range.

BLSSM

Exists regions where ν DM allowed : observed relic density, colliderexperiments.



THANK YOU!

For your attention.



BACK UP



MSSM (minimal supersymmetric standard model)

Superpotential

WMSSM = µHu · Hd − ˆUYuQ · Hu − ˆDYdQ · Hd − ˆEYeL · Hd. (4)

Soft-breaking Terms

LSOFT =− 1

2(M3g

α · gα +M2Wα · Wα +M1B · B + h.c.)

−m2Qij

Q†i · Qj −m2˜Uij

˜U†i˜Uj −m2

˜Dij

˜D†i˜Dj

−m2˜Lij

˜L†i · ˜Lj −m2˜Eij

˜E†i˜Ej

−m2HuH

†u ·Hu −m2

HdH†d ·Hd − (bHu ·Hd + h.c.)

− aiju ˜UiQj ·Hu + aijd˜DiQj ·Hd + aije

˜EiLj ·Hd + h.c.

(5)



Approximations for the Integrals1

Loop integrals I, J,K, I2 appear in the decay width, and the originalforms can have numerical problems when setting the light neutrino massto 0.

I =1

m2j −m2

i

∫ 1

0

dx

1− xlog

(m2x+M2(1− x)−m2

jx(1− x)

m2x+M2(1− x)−m2ix(1− x)

)(6)

J =1

m2j −m2

i

∫ 1

0

dx

xlog

(m2x+M2(1− x)−m2

jx(1− x)

m2x+M2(1− x)−m2ix(1− x)

)(7)

I2 =1

m2j −m2

i

∫ 1

0

dx log

(m2x+M2(1− x)−m2

jx(1− x)

m2x+M2(1− x)−m2ix(1− x)

)(8)

K =−1

m2j −m2

i

∫ 1

0

dx

[1 +

m2x+M2(1− x)−m2jx(1− x)

x(1− x)(m2j −m2

i )

× log

(m2x+M2(1− x)−m2

jx(1− x)

m2x+M2(1− x)−m2ix(1− x)

)].

(9)

m: loop fermion mass, M : loop boson mass, mj : sterile neutrino mass,mi: light neutrino mass.

1H.E. Haber and D. Wyler. Radiative neutralino decay. Nuclear Physics,

B323:267310, 1989.



Approximations

Basic idea

Mj ,m << M , expand the integrals with x =M2j

M2 , y = m2

M2 to the secondorder around 0.

For example:

I =1

36M2[2x2(93y2 + 42y + 11)

+ 6(2x2(18y2 + 6y + 1) + 3x(8y2 + 4y + 1)

+ 6(2y2 + 2y + 1)) log(y) + 9x(8y2 + 6y + 1) + 36]

(10)



BLSSM: Method

Paramters

tanβ′ =vηvη: controls the Higgs mass and sneutrino masses;

Yx: Yukawa coupling of the singlet Higgs;

Induced variables: M2ν , Bµ′ = m2

A0sin 2β′

2 ,Tx(1, 1) = Ax(1, 1)Yx(1, 1)

Idea

set the mass dierence: mνS1−mνP1

= 0.5 GeV

vary one variable at a time, solve out the induced varibles

calculate with SPheno-4.0.3 and micrOMEGAS-4.3.5


Dark Matter Inverse-Seesaw Models · 2019. 12. 3. · ANGY LIU Universität Würzburg 5/ 19....

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