PPP2017@Kyoto

Study of dark matter physics
in non-universal gaugino mass scenario
Univ. of Tokyo
Junichiro Kawamura
collaboration withHiroyuki Abe (Waseda U.), Yuji Omura (Nagoya U.)
1Outline

1. Brief review of MSSM
2. Non-universal gaugino mass scenario

3. Phenomenology of NUGM
4. Conclusion

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Minimal Supersymmetric Standard Model・ Every SM particle has superpartner・ radiative electroweak symmetry breaking (EWSB)
・gauge coupling unification
SM・ dark matter candidate
MSSM

MSSM is promising candidate for beyond SM
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low-scale SUSY motivation
・ little hierarchy problem
・ testability at LHC
 LHC bound: e.g.) 𝑚𝑔෤ > 2.0 TeV

 Higgs mass 125 GeV

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SM-like Higgs boson mass
 MSSM Higgs boson mass

𝑀𝑠𝑡𝑜𝑝 = 𝑚𝑡ሚ1 𝑚𝑡ሚ2ℒ ⊃ 𝑦𝑡 𝐴𝑡 𝐻𝑢 𝑡ǁ𝐿 𝑡ǁ𝑅

2222
𝑀
3𝑚2𝐴𝐴𝑠𝑡𝑜𝑝𝑡𝑡𝑡𝑚ℎ2 ≃ 𝑚𝑍2 cos 2 2𝛽 + 2 2 log+1−228𝜋 𝑣𝑢
𝑚𝑡2
𝑀𝑠𝑡𝑜𝑝
12𝑀𝑠𝑡𝑜𝑝125 GeV needs large quantum correction (∼ 35 GeV)

𝑀𝑠𝑡𝑜𝑝 ≃ 10 TeV if 𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ≪ 1

 maximal mixing scenario

2𝐴2𝑡𝐴2𝑡
1−22𝑀𝑠𝑡𝑜𝑝
12𝑀𝑠𝑡𝑜𝑝last term is maximized at𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ∼ 6( maximal mixing )𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝
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little hierarchy problem
SUSY searches and Higgs mass indicate high-scale SUSYhierarchy between SUSY scale and EW scale Higgs potential minimization condition
2
𝑚𝑍2 ≃ −2 𝜇 2 + 2|𝑚𝐻|𝑢

EW scale

SUSY scale𝜇 ∶ higgsino mass
2𝑚𝐻
: up-type Higgs mass𝑢✓ fine-tuning is required if 𝑚𝑍 ≪ 𝜇, 𝑚𝐻𝑢✓ at least 𝜇 must be small since it’s unique SUSY parameter✓ small 𝜇 means small 𝑚𝐻𝑢 around EW scale

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Higgs mass vs little hierarchy
little hierarchy problem relates to the Higgs boson mass
2
 RG equation of 𝑚𝐻
𝑢2𝑑𝑚
6 2𝐻𝑢2222222216𝜋≃ 6𝑦𝑡 𝑚𝐻𝑢 + 𝑚𝑡ሚ𝐿 + 𝑚𝑡ሚ𝑅 + 𝐴𝑡 − 6𝑔2 𝑀2 − 𝑔1 𝑀1 2𝑑𝑡
5• top squark parameters 𝑚𝑡2ሚ𝐿 , 𝑚𝑡2ሚ𝑅 , 𝐴𝑡 appear2• heavy top squark leads larger |𝑚𝐻|𝑢✓ 10 TeV top squark forces 10−3 % tuning
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Outline

1. Brief review of MSSM
2. Non-universal gaugino mass scenario

3. phenomenology of NUGM
4. Conclusion

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What we need for low-scale SUSY?
 little hierarchy problem
2𝑚𝑍2 ≃ −2 𝜇 2 + 2|𝑚𝐻|𝑢|𝑚𝐻𝑢 𝑚𝑆𝑈𝑆𝑌 | ≃ 𝜇 ≃ 𝑚𝑍 to avoid the fine-tuning MSSM Higgs boson mass
2422𝑀
3𝑚2𝐴𝐴𝑠𝑡𝑜𝑝𝑡𝑡𝑡
𝑚ℎ2 ≃ 𝑚𝑍2 cos 2 2𝛽 + 2 2 log+1−228𝜋 𝑣𝑢
𝑚𝑡2
𝑀𝑠𝑡𝑜𝑝
12𝑀𝑠𝑡𝑜𝑝

𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ≃ 6 to avoid heavy top squark
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Higgs boson mass in NUGM𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ≃ 6 is necessary to avoid heavy top squark top squark parameters at 𝑚𝑆𝑈𝑆𝑌 = 1.0 TeV
𝑚𝑡2ሚ𝐿 𝑚𝑆𝑈𝑆𝑌 ≃ +0.35𝑀22 + 3.21 𝑀32 + 0.60 𝑚02
𝑚𝑡2ሚ𝑅 𝑚𝑆𝑈𝑆𝑌 ≃ −0.16𝑀22 + 2.77𝑀32 + 0.29𝑚02

unification scale

𝐴𝑡 𝑚𝑆𝑈𝑆𝑌 ≃ −0.24𝑀2 − 1.42𝑀3 + 0.27𝐴0

 Universal Gaugino Masses
𝑀2 = 𝑀3 ≫ 𝑚0𝑀𝑠𝑡𝑜𝑝 ≡𝑚𝑡ሚ𝑅 𝑚𝑡ሚ𝐿𝐴𝑡
1.422 × 𝑀32≃≃ 0.67
2𝑀𝑠𝑡𝑜𝑝3.21 ⋅ 2.77 × 𝑀3

✓ 125 GeV Higgs boson requires heavy top squark ≳ sub TeV
10

Higgs boson mass in NUGM𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ≃ 6 is necessary to avoid heavy top squark top squark parameters at 𝑚𝑆𝑈𝑆𝑌 = 1.0 TeV
𝑚𝑡2ሚ𝐿 𝑚𝑆𝑈𝑆𝑌 ≃ +0.35𝑀22 + 3.21 𝑀32 + 0.60 𝑚02
𝑚𝑡2ሚ𝑅 𝑚𝑆𝑈𝑆𝑌 ≃ −0.16𝑀22 + 2.77𝑀32 + 0.29𝑚02

unification scale

𝐴𝑡 𝑚𝑆𝑈𝑆𝑌 ≃ −0.24𝑀2 − 1.42𝑀3 + 0.27𝐴0

 Non-Universal Gaugino Masses (NUGM)`07 H.Abe, T.Kobayashi, Y.Omura✓ 𝑚𝑡ሚ𝑅 𝑚𝑆𝑈𝑆𝑌 decreases, |𝐴𝑡 𝑚𝑆𝑈𝑆𝑌 | increases as 𝑀2 increases

𝐴𝑡 Τ𝑀𝑠𝑡𝑜𝑝 ≲ 6✓ upper bound is 𝑀2 /𝑀3 ≲ 4.2 for 𝑚𝑡2ሚ𝑅 (𝑚𝑆𝑈𝑆𝑌 ) > 0𝑀𝑠𝑡𝑜𝑝 ≡𝑚𝑡ሚ𝑅 𝑚𝑡ሚ𝐿

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naturalness in NUGM2
 RG-running of 𝑚𝐻𝑢2𝑚𝐻𝑚𝑆𝑈𝑆𝑌𝑢≃ +0.20𝑀22 − 0.13𝑀2 𝑀3 − 1.56𝑀32 − 0.07𝑚02

unificationscale

22𝑀2 ≃ 3.1 × 𝑀3 → 𝑚𝐻𝑚≃𝑚𝑆𝑈𝑆𝑌𝐸𝑊𝑢

22large wino mass reduces 𝑚𝐻≃𝜇𝑢+
large wino mass enhances the Higgs boson mass
12

Higgs boson mass in NUGM
𝑀3 = 𝑚0 = 1.0 TeV
 we assume universal soft mass 𝑚0 and A-term 𝐴0tan𝛽 = 15𝑚𝑆𝑈𝑆𝑌 ≡𝑚𝑡ሚ1 𝑚𝑡ሚ2 , 𝑟𝑖 = 𝑀𝑖 /𝑀3

𝑑 ln 𝑚𝑍2Δ𝜇 ≡𝑑 ln 𝜇(Λ𝐺𝑈𝑇 )21-loop RGE +1-loop RG Higgs mass𝐴0 = −1.0 TeV
no EWSB𝑚ℎ = 126𝑚ℎ = 124

13

summary of NUGM
•𝜇-parameter can be small due to large wino mass•the Higgs boson mass is also enhanced by large wino mass•

both 𝑚ℎ ∼ 125 GeV and 𝜇 ∼ 𝑚𝐸𝑊 can be achieved•

the degree of tuning is relaxed above 1% level,
once gaugino mass ratios are fixed
NGUM is a good scenario for low-scale SUSY
14

Outline
1. Brief review of MSSM
2. Non-universal gaugino mass scenario
3. Phenomenology of NUGM
4. Conclusion

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typical mass spectrum0g෤ , 𝑡ǁ2 , 𝑏෨1,2 , 𝑞,
෤ 𝑙,ሚ 𝜒෤3,4, 𝜒෤2±✓ most of sparticles are heavy

2 TeV• these are determined by gluino mass 𝑀3
1 TeV

𝑡1ǁ ≃ 𝑡ǁ𝑅

✓ right-handed stop can be lighter than others• as a result of large wino mass0𝜒෤1,2, 𝜒෤1± ≃ ℎ෨

✓ higgsinos are light

100 GeV16decays of higgsinos
 higgsinos are light and degenerateΔm𝜒෥ ≲ 2.0 GeV

softinvisible
ATLAS
collab.

soft• decay products are too soft to be reconstructed• c𝜏 < 𝑂(10−3 𝑐𝑚): no disappearing track unlike pure wino

higgsino searches are difficult at LHC
17

typical mass spectrum
0g෤ , 𝑡ǁ2 , 𝑏෨1,2 , 𝑞,
෤ 𝑙,ሚ 𝜒෤3,4, 𝜒෤2±✓ most of sparticles are heavy
2 TeV
1 TeV

• these are determined by gluino mass 𝑀3
𝑡1ǁ ≃ 𝑡ǁ𝑅

✓ right-handed stop is lighter than others• due to large wino mass0𝜒෤1,2, 𝜒෤1± ≃ ℎ෨

100 GeV✓ higgsinos are light, but suitably degenerate• DM searches are important18

constraints form indirect detection≃ ℎ෨

http://www.hap-astroparticle.org/184.php

𝜎𝑣 𝑣=0 is determined by higgsino mass itself
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constraints form indirect detection𝜉 ≡ Ω𝐿𝑆𝑃 /Ω𝑜𝑏𝑠
𝜉=1Fermi-LAT, AMS-02,(`16 Cooco, Kramer et.al.)𝜉 = Ω𝑡ℎ𝑒𝑟𝑚𝑎𝑙 /Ω𝐿𝑆𝑃 non-thermal: Ω𝐿𝑆𝑃 = Ω𝑜𝑏𝑠
- 𝜇 < 300 GeV excluded by Fermi-LAT- 𝜇 < 800 GeV excluded by AMS-02

softsusy, SDECAY
micrOMEGA thermal: Ω𝐿𝑆𝑃 = Ω𝑡ℎ𝑒𝑟𝑚𝑎𝑙- no constraint on 𝜇20

direct detection for higgsino LSP: gauge-basis

cross section

𝑔𝑚𝑍𝑚𝑍2𝜆ℎ𝜒𝜒 =1 ± 𝑠2𝛽 𝑐𝑊+ 𝑡𝑊2𝑀2 − 𝜇𝑀1 − 𝜇2 𝑚2𝑔𝑚𝑁𝑁𝑆𝐼𝜎𝑁𝜒=1+24𝜋 𝑚ℎ4 𝑚𝑊𝑚𝜒−22 7+
෍ 𝑓𝑇𝑁𝑞9 92𝜆2ℎ𝜒𝜒

𝑞=𝑢,𝑑,𝑠•gaugino masses are crucial for higgsino-gaugino mixing•

sign of 𝜇 is also important for smaller tan𝛽21

constraints from direct detection
𝑀3 = 1.5 TeV, 𝑀2 ∼ 4.5 TeVtan𝛽 = 10𝑚0 = 1 TeV
softsusy+sdecay+micrOMEGA•

there are significant bounds on 𝑀1 even when 𝑚𝑔෤ ≃ 3.2 TeV•SI cross section is on the “neutrino floor” everywhere`13 Billard, Strigari, Figueroa-Feliciano
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constraints from direct detection
𝑀3 = 1 TeV, 𝑀2 ∼ 4.0 TeV

tan𝛽 = 10𝑚0 = 1 TeV
softsusy+sdecay+micrOMEGA•XENON1T fully covers 𝜇 > −100 GeV in non-thermal case•only 𝜇 ≲ 1.0 TeV is covered in thermal case•

LHC is sensitive to small 𝜇 , while DD is sensitive to large 𝜇23/40

typical mass spectrum
0g෤ , 𝑡ǁ2 , 𝑏෨1,2 , 𝑞,
෤ 𝑙,ሚ 𝜒෤3,4, 𝜒෤2±✓ most of sparticles are heavy
2 TeV
1 TeV

• these are determined by gluino mass 𝑀3𝑡1ǁ ≃ 𝑡ǁ𝑅✓ right-handed stop is lighter than others• due to large wino mass0𝜒෤1,2, 𝜒෤1± ≃ ℎ෨

✓ higgsinos are light, but suitably degenerate• DM searches are important

100 GeV• large bino/wino is necessary for 𝑀𝑔෤ ≲ 3.0 TeVstop / gluino searches are important at LHC
24top squark decays
 right-handed top squark is light in NUGM𝑊𝑀𝑆𝑆𝑀 ∋ 𝑦𝑡 𝑡𝐿 ℎ෨ 𝑢0 − 𝑏𝐿 ℎ෨ 𝑢+ 𝑡ǁ𝑅0
• top squark decays to 𝑡 + 𝜒෤1,2or 𝑏 + 𝜒෤1±

• right-handed top squark couples to quark/higgsinos universally0• Br 𝑡1ǁ → 𝑏 𝜒෤1± = 1 − Br 𝑡1ǁ → 𝑡 𝜒෤1,2≃ 0.5 unless 𝑚𝑡ሚ1 ≃ 𝑚𝜒±෥125 %

50 %

25 %

25

top squark search✓ signals are tt (25%) / tb (50%) / bb (25%) + MET✓ bb+MET channel[1] is sensitive to mass degenerate region✓ had + MET channel[2] is sensitive to high-stop mass region

tan𝛽 = 15
𝑚0 = 𝑀3 = 1 TeV

𝐿 = 3.2 𝑓𝑏 −1
𝐿 = 13.3 𝑓𝑏 −1

softsusy+sdecay+MG5+pythia6+delphes3[1] ATLAS-CONF-2015-066 [2] ATLAS-CONF-2016-077

26top squark search✓ signals are tt (25%) / tb (50%) / bb (25%) + MET✓ bb+MET channel[3] is sensitive to heavy higgsino region✓ had + MET channel[4] is sensitive to light higgsino region

𝐿 = 36.1 𝑓𝑏 −1

preliminarytan𝛽 = 15
𝑚0 = 𝑀3 = 1 TeV
softsusy+sdecay+MG5+pythia6+delphes3

had+MET
1l+bb+MET[3] ATLAS-CONF-2017-038 [4] ATLAS-CONF-2017-020

27gluino search0✓ gluino decays to top and stop: 𝑔෤ → 𝑡 𝑡1ǁ → 𝑡 + 𝑡𝜒෤1,2/𝑏 𝜒෤1±

✓ signals are characterized by 4𝑏 + jets or lepton + MET✓ 13TeV data [5] with 14.8 fb−1 cover 𝑚𝑔෤ ≤ 1.8 TeV for 𝜇 ≤ 800 GeV
𝐿 = 14.8 𝑓𝑏 −1
tan𝛽 = 15𝑚0 = 1 TeV
𝑀1 = 12 TeV
softsusy+sdecay+MG5+pythia6+delphes328[5] ATLAS-CONF-2016-052

gluino search0✓ gluino decays to top and stop: 𝑔෤ → 𝑡 𝑡1ǁ → 𝑡 + 𝑡𝜒෤1,2/𝑏 𝜒෤1±

✓ signals are characterized by 4 bottoms and large MET✓ latest 13TeV data [6] cover 𝑚𝑔෤ ≤ 1.9 TeV for 𝜇 ≤ 1000 GeV4b+MET

softsusy+sdecay+MG5+pythia6+delphes3

4t+MET(ol)preliminary

4t+MET(1l)tan𝛽 = 15
𝑚0 = 1 TeV
𝑀1 = 12 TeV

𝐿 = 36.1 𝑓𝑏 −1

29[6] ATLAS-CONF-2017-021

Conclusion•NUGM realize 125 GeV Higgs and small 𝜇-parameter•stop/gluino searches are important for NUGM scenario•DM searches exclude wide region if DM is dominated by LSP•

heavy bino/wino help to avoid the direct detection constraints•𝑚𝑡ሚ1 ≲ 860 GeV, 𝑚𝑔෤ ≲ 1.9 TeV are excluded by the 2017 data30

backup31Realization of NUGM
 mixed moduli / anomaly mediation`05 K.Choi, K.S.Jeong, K.Okumura`05 R.Kitano, Y.Nomura

𝑔02
𝐹𝐶
𝑀1Τ2 =+𝑏𝑎2
𝐶𝑇 + 𝑇 16𝜋
𝐹𝑇33
𝑏𝑎 =, 1, −35

 F-terms of non-trivial GUT representationsex ) 𝑀1 : 𝑀2 : 𝑀3 = 1 ∶ 3 ∶ −2for 24 of SU(5)suitable linear combi. of 𝐹1 and 𝐹 24

`12 J.E.Younkin, S.P.Martin non-universal gauge kinetic function
𝑓𝑎 = 𝑐𝑎 + 𝑙𝑎𝐼 𝑇 𝐼𝑎 = 𝑈 1 𝑌 , 𝑆𝑈 2 𝐿 , 𝑆𝑈 3 𝐶32

scenarios for DM relic abundance
We consider “thermal” and “non-thermal” scenarios
 thermal scenario: Ω𝐿𝑆𝑃 = Ω𝑡ℎ𝑒𝑟𝑚𝑎𝑙 ≤ Ω𝑜𝑏𝑠•

Ω𝐿𝑆𝑃 = Ω𝑜𝑏𝑠 @ 𝜇 ≃ 1.0 TeV and reduces for smaller 𝜇•dark matter is augmented by other particle(s) Non-thermal scenario: Ω𝐿𝑆𝑃 = Ω𝑜𝑏𝑠•

LSP is produced by certain non-thermal production•

DM searches become the most efficient33

tuning of soft parameters
𝑑 ln 𝑚𝑍2Δ𝑎 ≡𝑑 ln 𝑎(Λ𝐺𝑈𝑇 )2

 degree of tuning

1. all parameters are independent
Δ1 = max Δ𝑎𝑎𝑎 ∈ {𝑀1 , 𝑀2 , 𝑀3 , 𝑚0 , 𝐴0 , 𝜇}

2. gaugino mass ratio and scalar parameters ratio are fixed
Δ2 = max Δ𝑎𝑎𝑎 ∈ {𝑀1/2 , 𝑚𝑠𝑐𝑎𝑙 , 𝜇}3. all ratios are fixed
Δ3 = max Δ𝑎𝑎𝑎 ∈ {𝑚𝑆𝑈𝑆𝑌 , 𝜇}Remark: σ𝑎 Δ𝑎 = 1 at tree level → Δ3 ∼ Δ𝑚𝑆𝑈𝑆𝑌 ∼ Δ𝜇34/40

tuning of soft parameters
1-loop RGE +1-loop EWSB

𝑀3 = 𝑚0 = −𝐴0 = 1.0 TeV
Δ1 = max Δ𝑎 𝑎 ∈ {𝑀1 , 𝑀2 , 𝑀3 , 𝑚0 , 𝐴0 , 𝜇}𝑎Δ2 = max Δ𝑎𝑎𝑎 ∈ {𝑀1/2 , 𝑚𝑠𝑐𝑎𝑙 , 𝜇}

Δ𝑀2Δ𝑀3Δ𝑀1/2 ∼ Δ𝜇Δ𝜇Δ2 can be small if 𝑟2 ∼ 3.235/40

tuning of A-term
𝑀3 = 𝑚0 = 1.0 TeV
𝐴0 = −1.0 TeV

Δ2 = max Δ𝑎𝑎𝑎 ∈ {𝑀1/2 , 𝑚𝑠𝑐𝑎𝑙 , 𝜇}𝐴0 = −2.0 TeV

Δ𝑚𝑠𝑐𝑎𝑙Δ𝑀1/2 ∼ Δ𝜇

Δ𝑀1/2 ∼ Δ𝜇Δ2 can not be small if 𝐴0 = −2.0 TeV

36/40

tuning of soft parameters
𝑀3 = 𝑚0 = 1.0 TeV
𝐴0 = −1.0 TeV

Δ𝑚𝑆𝑈𝑆𝑌 ∼ Δ𝜇

Δ3 = max Δ𝑎𝑎𝑎 ∈ {𝑚𝑆𝑈𝑆𝑌 , 𝜇}𝐴0 = −2.0 TeV

Δ𝑚𝑆𝑈𝑆𝑌 ∼ Δ𝜇Δ3 can be small in both cases
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parameter settings
 parameters•

universal soft scalar mass and A-term: 𝑚0 , 𝐴0

• non-universal gaugino masses : 𝑀1 , 𝑀2 , 𝑀3
• Higgs bilinear, Higgs VEV ratio : 𝜇, 𝐵𝜇, tan𝛽 = 𝐻𝑢 Τ 𝐻𝑑

 constraints• electroweak symmetry breaking (EWSB) condition• Higgs boson mass : 𝑚ℎ = 125 GeV

 strategy• 𝑀2 and 𝐵𝜇-term are tuned to satisfy EWSB condition•

𝐴0 is tuned to realize 𝑚ℎ = 125 GeV38

𝑀1 = 10 TeV

𝑀1 = 5 TeV

39/40

40/40