Post on 08-Oct-2020
Motivation Models and Results Conclusion
Dark Matter
In Minimal Supersymmetric
Inverse-Seesaw Models
YANG LIU
Universität Würzburg
YANG LIU Universität Würzburg 1/ 19
Motivation Models and Results Conclusion
arXiv:1909.11686
Prof. Werner Porod from Universität Würzburg&
Prof. Joel Jones-Pérez from Ponticia UniversidadCatolica del Peru
YANG LIU Universität Würzburg 2/ 19
Motivation Models and Results Conclusion
Motivation
Dark matter (DM) need to be explained
Supersymmetry provides candidates
lightest νR (keV range), νR (superpartner of νR)
YANG LIU Universität Würzburg 3/ 19
Motivation Models and Results Conclusion
Motivation
Dark matter (DM) need to be explained
Supersymmetry provides candidates
lightest νR (keV range), νR (superpartner of νR)
YANG LIU Universität Würzburg 3/ 19
Motivation Models and Results Conclusion
Motivation
Dark matter (DM) need to be explained
Supersymmetry provides candidates
lightest νR (keV range), νR (superpartner of νR)
YANG LIU Universität Würzburg 3/ 19
Motivation Models and Results Conclusion
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)
YANG LIU Universität Würzburg 4/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 5/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 6/ 19
Motivation Models and Results Conclusion
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.
YANG LIU Universität Würzburg 7/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 8/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 9/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 10/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 11/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 12/ 19
Motivation Models and Results Conclusion
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.
YANG LIU Universität Würzburg 13/ 19
Motivation Models and Results Conclusion
THANK YOU!
For your attention.
YANG LIU Universität Würzburg 14/ 19
Motivation Models and Results Conclusion
BACK UP
YANG LIU Universität Würzburg 15/ 19
Motivation Models and Results Conclusion
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)
YANG LIU Universität Würzburg 16/ 19
Motivation Models and Results Conclusion
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.
YANG LIU Universität Würzburg 17/ 19
Motivation Models and Results Conclusion
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)
YANG LIU Universität Würzburg 18/ 19
Motivation Models and Results Conclusion
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
YANG LIU Universität Würzburg 19/ 19