[PPT] - in non-universal gaugino mass scenario Univ. of Tokyo Junichiro PowerPoint Presentation

SLIDE 1

Study of dark matter physics in non-universal gaugino mass scenario

Univ. of Tokyo

Junichiro Kawamura

collaboration with Hiroyuki Abe (Waseda U.), Yuji Omura (Nagoya U.)

PPP2017@Kyoto

1

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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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・ Every SM particle has superpartner ・ radiative electroweak symmetry breaking (EWSB) ・gauge coupling unification ・ dark matter candidate

MSSM is promising candidate for beyond SM

Minimal Supersymmetric Standard Model

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SM MSSM

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・ little hierarchy problem ・ testability at LHC

low-scale SUSY

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 motivation  LHC bound: e.g.) 𝑛 ෤

𝑕 > 2.0TeV

 Higgs mass 125 GeV

SLIDE 5

SM-like Higgs boson mass

 MSSM Higgs boson mass

𝑛ℎ

2 ≃ 𝑛𝑎 2cos22𝛾 + 3𝑛𝑢 2

8𝜌2𝑤𝑣

2 log 𝑁𝑡𝑢𝑝𝑞 2

𝑛𝑢

2

+ 2𝐵𝑢

2

𝑁𝑡𝑢𝑝𝑞

2

1 − 𝐵𝑢

2

12𝑁𝑡𝑢𝑝𝑞

2

125 GeV needs large quantum correction (∼ 35 GeV) 𝑁𝑡𝑢𝑝𝑞 ≃ 10TeV if Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≪ 1

 maximal mixing scenario

Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞

last term is maximized at

Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ∼ 6

( maximal mixing )

2𝐵𝑢

2

𝑁𝑡𝑢𝑝𝑞

2

1 − 𝐵𝑢

2

12𝑁𝑡𝑢𝑝𝑞

2

𝑁𝑡𝑢𝑝𝑞 = 𝑛ሚ

𝑢1𝑛ሚ 𝑢2

ℒ ⊃ 𝑧𝑢𝐵𝑢 𝐼𝑣 ǁ 𝑢𝑀 ǁ 𝑢𝑆

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SLIDE 6

✓ fine-tuning is required if 𝑛𝑎 ≪ 𝜈, 𝑛𝐼𝑣 ✓ at least 𝜈 must be small since it’s unique SUSY parameter ✓ small 𝜈 means small 𝑛𝐼𝑣 around EW scale

little hierarchy problem

SUSY searches and Higgs mass indicate high-scale SUSY  Higgs potential minimization condition hierarchy between SUSY scale and EW scale

𝑛𝑎

2 ≃ −2 𝜈 2 + 2|𝑛𝐼𝑣 2 |

EW scale SUSY scale

𝜈 ∶ higgsino mass 𝑛𝐼𝑣

2 : up-type Higgs mass

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SLIDE 7

Higgs mass vs little hierarchy

little hierarchy problem relates to the Higgs boson mass  RG equation of 𝑛𝐼𝑣

2

16𝜌2 𝑒𝑛𝐼𝑣

2

𝑒𝑢 ≃ 6𝑧𝑢

2 𝑛𝐼𝑣 2 + 𝑛ሚ 𝑢𝑀 2 + 𝑛ሚ 𝑢𝑆 2 + 𝐵𝑢 2 − 6𝑕2 2 𝑁2 2 − 6

5 𝑕1

2 𝑁1 2

top squark parameters 𝑛ሚ

𝑢𝑀 2 , 𝑛ሚ 𝑢𝑆 2 , 𝐵𝑢 appear

heavy top squark leads larger |𝑛𝐼𝑣

2 |

✓ 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?

 MSSM Higgs boson mass 𝑛ℎ

2 ≃ 𝑛𝑎 2cos22𝛾 + 3𝑛𝑢 4

8𝜌2𝑤𝑣

2 log 𝑁𝑡𝑢𝑝𝑞 2

𝑛𝑢

2

+ 2𝐵𝑢

2

𝑁𝑡𝑢𝑝𝑞

2

1 − 𝐵𝑢

2

12𝑁𝑡𝑢𝑝𝑞

2

Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≃ 6 to avoid heavy top squark

 little hierarchy problem

𝑛𝑎

2 ≃ −2 𝜈 2 + 2|𝑛𝐼𝑣 2 | |𝑛𝐼𝑣 𝑛𝑇𝑉𝑇𝑍 | ≃ 𝜈 ≃ 𝑛𝑎 to avoid the fine-tuning

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Higgs boson mass in NUGM

 Universal Gaugino Masses

𝑁2 = 𝑁3 ≫ 𝑛0

✓ 125 GeV Higgs boson requires heavy top squark ≳ sub TeV  top squark parameters at 𝑛𝑇𝑉𝑇𝑍 = 1.0TeV

𝑛ሚ

𝑢𝑀 2 𝑛𝑇𝑉𝑇𝑍 ≃ +0.35𝑁2 2 + 3.21 𝑁3 2 + 0.60 𝑛0 2

𝑛ሚ

𝑢𝑆 2

𝑛𝑇𝑉𝑇𝑍 ≃ −0.16𝑁2

2 + 2.77𝑁3 2 + 0.29𝑛0 2

𝐵𝑢 𝑛𝑇𝑉𝑇𝑍 ≃ −0.24𝑁2 − 1.42𝑁3 + 0.27𝐵0 unification scale Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≃ 6 is necessary to avoid heavy top squark

10

𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≃ 1.422 × 𝑁3

2

3.21 ⋅ 2.77 × 𝑁3

2 ≃ 0.67

𝑁𝑡𝑢𝑝𝑞 ≡ 𝑛ሚ

𝑢𝑆𝑛ሚ 𝑢𝑀

SLIDE 11

Higgs boson mass in NUGM

 top squark parameters at 𝑛𝑇𝑉𝑇𝑍 = 1.0TeV

𝑛ሚ

𝑢𝑀 2 𝑛𝑇𝑉𝑇𝑍 ≃ +0.35𝑁2 2 + 3.21 𝑁3 2 + 0.60 𝑛0 2

𝑛ሚ

𝑢𝑆 2

𝑛𝑇𝑉𝑇𝑍 ≃ −0.16𝑁2

2 + 2.77𝑁3 2 + 0.29𝑛0 2

𝐵𝑢 𝑛𝑇𝑉𝑇𝑍 ≃ −0.24𝑁2 − 1.42𝑁3 + 0.27𝐵0 unification scale Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≃ 6 is necessary to avoid heavy top squark

 Non-Universal Gaugino Masses (NUGM)

✓ 𝑛ሚ

𝑢𝑆 𝑛𝑇𝑉𝑇𝑍 decreases, |𝐵𝑢 𝑛𝑇𝑉𝑇𝑍 | increases as 𝑁2 increases

✓ upper bound is 𝑁2/𝑁3≲ 4.2 for 𝑛ሚ

𝑢𝑆 2 (𝑛𝑇𝑉𝑇𝑍) > 0

Τ 𝐵𝑢 𝑁𝑡𝑢𝑝𝑞 ≲ 6

`07 H.Abe, T.Kobayashi, Y.Omura

𝑁𝑡𝑢𝑝𝑞 ≡ 𝑛ሚ

𝑢𝑆𝑛ሚ 𝑢𝑀

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SLIDE 12

𝑛𝐼𝑣

2

𝑛𝑇𝑉𝑇𝑍 ≃ +0.20𝑁2

2 − 0.13𝑁2𝑁3 − 1.56𝑁3 2 − 0.07𝑛0 2

 RG-running of 𝑛𝐼𝑣

2

naturalness in NUGM

𝑁2 ≃ 3.1 × 𝑁3 → 𝑛𝐼𝑣

2

𝑛𝑇𝑉𝑇𝑍 ≃ 𝑛𝐹𝑋

2

unification scale

12

large wino mass reduces 𝑛𝐼𝑣

2

≃ 𝜈 2 large wino mass enhances the Higgs boson mass

+

SLIDE 13

 we assume universal soft mass 𝑛0 and A-term 𝐵0

Higgs boson mass in NUGM

13

Δ𝜈 ≡ 𝑒 ln 𝑛𝑎

2

𝑒 ln 𝜈(Λ𝐻𝑉𝑈)2

𝑛ℎ = 124 𝑛ℎ = 126 no EWSB 𝑁3 = 𝑛0 = 1.0TeV tan𝛾 = 15 1-loop RGE + 1-loop RG Higgs mass

𝐵0 = −1.0TeV 𝑛𝑇𝑉𝑇𝑍 ≡ 𝑛ሚ

𝑢1𝑛ሚ 𝑢2 , 𝑠𝑗 = 𝑁𝑗/𝑁3

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14

NGUM is a good scenario for low-scale SUSY

summary of NUGM

𝜈-parameter can be small due to large wino mass
the Higgs boson mass is also enhanced by large wino mass
both 𝑛ℎ ∼ 125 GeV and 𝜈 ∼ 𝑛𝐹𝑋 can be achieved
the degree of tuning is relaxed above 1% level,
nce gaugino mass ratios are fixed

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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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typical mass spectrum

✓ higgsinos are light ✓ right-handed stop can be lighter than others ✓ most of sparticles are heavy

these are determined by gluino mass 𝑁3

2 TeV 1 TeV 100 GeV ෤ g, ǁ 𝑢2, ෨ 𝑐1,2, ෤ 𝑟, ሚ 𝑚, ෤ 𝜓3,4

0 , ෤

𝜓2

±

ǁ 𝑢1 ≃ ǁ 𝑢𝑆 ෤ 𝜓1,2

0 , ෤

𝜓1

± ≃ ෨

ℎ

16

as a result of large wino mass

SLIDE 17

decays of higgsinos

 higgsinos are light and degenerate Δm෥

𝜓 ≲ 2.0 GeV

decay products are too soft to be reconstructed
c𝜐 < 𝑃(10−3𝑑𝑛): no disappearing track unlike pure wino

higgsino searches are difficult at LHC soft soft

ATLAS collab.

invisible

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typical mass spectrum

✓ higgsinos are light, but suitably degenerate ✓ right-handed stop is lighter than others ✓ most of sparticles are heavy

these are determined by gluino mass 𝑁3

2 TeV 1 TeV 100 GeV ෤ g, ǁ 𝑢2, ෨ 𝑐1,2, ෤ 𝑟, ሚ 𝑚, ෤ 𝜓3,4

0 , ෤

𝜓2

±

ǁ 𝑢1 ≃ ǁ 𝑢𝑆 ෤ 𝜓1,2

0 , ෤

𝜓1

± ≃ ෨

ℎ

18

due to large wino mass
DM searches are important

SLIDE 19

constraints form indirect detection

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

𝜏𝑤 𝑤=0 is determined by higgsino mass itself

≃ ෨ ℎ

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20

constraints form indirect detection

𝜈 < 300 GeV excluded by Fermi-LAT
𝜈 < 800 GeV excluded by AMS-02

 non-thermal: Ω𝑀𝑇𝑄 = Ω𝑝𝑐𝑡  thermal: Ω𝑀𝑇𝑄 = Ω𝑢ℎ𝑓𝑠𝑛𝑏𝑚

no constraint on 𝜈

Fermi-LAT, AMS-02, (`16 Cooco, Kramer et.al.) softsusy, SDECAY micrOMEGA

𝜊 ≡ Ω𝑀𝑇𝑄/Ω𝑝𝑐𝑡

𝜊 = 1 𝜊 = Ω𝑢ℎ𝑓𝑠𝑛𝑏𝑚/Ω𝑀𝑇𝑄

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21

direct detection for higgsino LSP

cross section

𝜇ℎ𝜓𝜓 = 𝑕 2 1 ± 𝑡2𝛾 𝑑𝑋 𝑛𝑎 𝑁2 − 𝜈 + 𝑢𝑋

2

𝑛𝑎 𝑁1 − 𝜈

𝜏𝑂𝜓

𝑇𝐽 = 𝑕2

4𝜌 𝑛𝑂

2

𝑛ℎ

4𝑛𝑋 2

1 + 𝑛𝑂 𝑛𝜓

−2 2

9 + 7 9 ෍

𝑟=𝑣,𝑒,𝑡

𝑔

𝑈

𝑟

𝑂 2

𝜇ℎ𝜓𝜓

2

: gauge-basis

gaugino masses are crucial for higgsino-gaugino mixing
sign of 𝜈 is also important for smaller tan𝛾

SLIDE 22

constraints from direct detection

tan𝛾 = 10 𝑛0 = 1TeV

softsusy+sdecay +micrOMEGA

there are significant bounds on 𝑁1 even when 𝑛 ෤

𝑕 ≃ 3.2TeV

SI cross section is on the “neutrino floor” everywhere

`13 Billard, Strigari, Figueroa-Feliciano

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𝑁3 = 1.5TeV, 𝑁2 ∼ 4.5TeV

SLIDE 23

constraints from direct detection

tan𝛾 = 10 𝑛0 = 1TeV

softsusy+sdecay +micrOMEGA

XENON1T fully covers 𝜈 > −100 GeV in non-thermal case
nly 𝜈 ≲ 1.0TeV is covered in thermal case
LHC is sensitive to small 𝜈 , while DD is sensitive to large 𝜈

23/40

𝑁3 = 1TeV, 𝑁2 ∼ 4.0TeV

SLIDE 24

typical mass spectrum

✓ higgsinos are light, but suitably degenerate ✓ right-handed stop is lighter than others ✓ most of sparticles are heavy

these are determined by gluino mass 𝑁3

2 TeV 1 TeV 100 GeV ෤ g, ǁ 𝑢2, ෨ 𝑐1,2, ෤ 𝑟, ሚ 𝑚, ෤ 𝜓3,4

0 , ෤

𝜓2

±

ǁ 𝑢1 ≃ ǁ 𝑢𝑆 ෤ 𝜓1,2

0 , ෤

𝜓1

± ≃ ෨

ℎ

24

due to large wino mass

stop / gluino searches are important at LHC

DM searches are important
large bino/wino is necessary for 𝑁෤

𝑕 ≲ 3.0 TeV

SLIDE 25

top squark decays

 right-handed top squark is light in NUGM

𝑋

𝑁𝑇𝑇𝑁 ∋ 𝑧𝑢 𝑢𝑀 ෨

ℎ𝑣

0 − 𝑐𝑀 ෨

ℎ𝑣

+

ǁ 𝑢𝑆

top squark decays to 𝑢 + ෤

𝜓1,2

0 or 𝑐 + ෤

𝜓1

±

right-handed top squark couples to quark/higgsinos universally
Br

ǁ 𝑢1 → 𝑐 ෤ 𝜓1

± = 1 − Br

ǁ 𝑢1 → 𝑢 ෤ 𝜓1,2 ≃ 0.5 unless 𝑛ሚ

𝑢1 ≃ 𝑛෥ 𝜓1 ±

25

25 % 25 % 50 %

SLIDE 26

top squark search

26

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

[1] ATLAS-CONF-2015-066 [2] ATLAS-CONF-2016-077

tan𝛾 = 15 𝑛0 = 𝑁3 = 1TeV

softsusy+sdecay+MG5 +pythia6+delphes3

𝑀 = 3.2 𝑔𝑐−1 𝑀 = 13.3 𝑔𝑐−1

SLIDE 27

top squark search

27

✓ 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

[3] ATLAS-CONF-2017-038 [4] ATLAS-CONF-2017-020

tan𝛾 = 15 𝑛0 = 𝑁3 = 1TeV

softsusy+sdecay+MG5 +pythia6+delphes3

𝑀 = 36.1 𝑔𝑐−1 preliminary 1l+bb+MET had+MET

SLIDE 28

gluino search

28

✓ gluino decays to top and stop: ෤ 𝑕 → 𝑢 ǁ 𝑢1 → 𝑢 + 𝑢 ෤ 𝜓1,2

0 /𝑐 ෤

𝜓1

±

✓ signals are characterized by 4𝑐 + jets or lepton + MET ✓ 13TeV data [5] with 14.8 fb−1cover 𝑛 ෤

𝑕 ≤ 1.8TeV for 𝜈 ≤ 800 GeV

[5] ATLAS-CONF-2016-052

tan𝛾 = 15 𝑛0 = 1TeV 𝑁1 = 12TeV

softsusy+sdecay+MG5 +pythia6+delphes3

𝑀 = 14.8 𝑔𝑐−1

SLIDE 29

gluino search

29

✓ gluino decays to top and stop: ෤ 𝑕 → 𝑢 ǁ 𝑢1 → 𝑢 + 𝑢 ෤ 𝜓1,2

0 /𝑐 ෤

𝜓1

±

✓ signals are characterized by 4 bottoms and large MET ✓ latest 13TeV data [6] cover 𝑛 ෤

𝑕 ≤ 1.9TeV for 𝜈 ≤ 1000 GeV

[6] ATLAS-CONF-2017-021

𝑀 = 36.1 𝑔𝑐−1 preliminary 4t+MET(1l) 4b+MET 4t+MET(ol) tan𝛾 = 15 𝑛0 = 1TeV 𝑁1 = 12TeV

softsusy+sdecay+MG5 +pythia6+delphes3

SLIDE 30

Conclusion

NUGM realize 125 GeV Higgs and small 𝜈-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
𝑛ሚ

𝑢1 ≲ 860 GeV, 𝑛 ෤ 𝑕 ≲ 1.9TeV are excluded by the 2017 data

30

SLIDE 31

backup

31

SLIDE 32

32

𝑁 Τ

1 2 =

𝐺𝑈 𝑈 + 𝑈 + 𝑕0

2

16𝜌2 𝑐𝑏 𝐺𝐷 𝐷

Realization of NUGM

 mixed moduli / anomaly mediation  F-terms of non-trivial GUT representations  non-universal gauge kinetic function

𝑐𝑏 = 33 5 , 1, −3

ex ) 𝑁1: 𝑁2: 𝑁3 = 1 ∶ 3 ∶ −2 for 24 of SU(5)

suitable linear combi. of 𝐺1 and 𝐺24

`12 J.E.Younkin, S.P.Martin

𝑔

𝑏 = 𝑑𝑏 + 𝑚𝑏 𝐽 𝑈𝐽

𝑏 = 𝑉 1 𝑍, 𝑇𝑉 2 𝑀, 𝑇𝑉 3 𝐷

`05 K.Choi, K.S.Jeong, K.Okumura `05 R.Kitano, Y.Nomura

SLIDE 33

33

scenarios for DM relic abundance

Ω𝑀𝑇𝑄 = Ω𝑝𝑐𝑡 @ 𝜈 ≃ 1.0TeV and reduces for smaller 𝜈
dark matter is augmented by other particle(s)

 thermal scenario: Ω𝑀𝑇𝑄 = Ω𝑢ℎ𝑓𝑠𝑛𝑏𝑚 ≤ Ω𝑝𝑐𝑡  Non-thermal scenario: Ω𝑀𝑇𝑄 = Ω𝑝𝑐𝑡

LSP is produced by certain non-thermal production
DM searches become the most efficient

We consider “thermal” and “non-thermal” scenarios

SLIDE 34

 degree of tuning

tuning of soft parameters

Δ𝑏 ≡ 𝑒 ln 𝑛𝑎

2

𝑒 ln 𝑏(Λ𝐻𝑉𝑈)2

1. all parameters are independent
2. gaugino mass ratio and scalar parameters ratio are fixed
3. all ratios are fixed

Δ1 = max Δ𝑏

𝑏

𝑏 ∈ {𝑁1, 𝑁2, 𝑁3, 𝑛0, 𝐵0, 𝜈} Δ2 = max Δ𝑏

𝑏

𝑏 ∈ {𝑁1/2, 𝑛𝑡𝑑𝑏𝑚, 𝜈} Δ3 = max Δ𝑏

𝑏

𝑏 ∈ {𝑛𝑇𝑉𝑇𝑍, 𝜈}

Remark: σ𝑏 Δ𝑏 = 1 at tree level → Δ3 ∼ Δ𝑛𝑇𝑉𝑇𝑍 ∼ Δ𝜈

34/40

SLIDE 35

tuning of soft parameters

𝑁3 = 𝑛0 = −𝐵0= 1.0TeV Δ1 = max Δ𝑏

𝑏

𝑏 ∈ {𝑁1, 𝑁2, 𝑁3, 𝑛0, 𝐵0, 𝜈} Δ𝑁2 Δ𝑁3 Δ𝜈 Δ2 = max Δ𝑏

𝑏

𝑏 ∈ {𝑁1/2, 𝑛𝑡𝑑𝑏𝑚, 𝜈} Δ𝑁1/2 ∼ Δ𝜈

Δ2 can be small if 𝑠

2 ∼ 3.2 1-loop RGE + 1-loop EWSB

35/40

SLIDE 36

tuning of A-term

𝑁3 = 𝑛0 = 1.0TeV Δ2 = max Δ𝑏

𝑏

𝑏 ∈ {𝑁1/2, 𝑛𝑡𝑑𝑏𝑚, 𝜈} Δ𝑁1/2 ∼ Δ𝜈 𝐵0 = −1.0TeV 𝐵0 = −2.0TeV Δ𝑁1/2 ∼ Δ𝜈 Δ𝑛𝑡𝑑𝑏𝑚

Δ2 can not be small if 𝐵0 = −2.0TeV

36/40

SLIDE 37

tuning of soft parameters

𝑁3 = 𝑛0 = 1.0TeV Δ3 = max Δ𝑏

𝑏

𝑏 ∈ {𝑛𝑇𝑉𝑇𝑍, 𝜈} Δ𝑛𝑇𝑉𝑇𝑍 ∼ Δ𝜈 𝐵0 = −1.0TeV 𝐵0 = −2.0TeV Δ𝑛𝑇𝑉𝑇𝑍 ∼ Δ𝜈

Δ3 can be small in both cases

37/40

SLIDE 38

parameter settings

 parameters

universal soft scalar mass and A-term: 𝑛0, 𝐵0
non-universal gaugino masses : 𝑁1, 𝑁2, 𝑁3
Higgs bilinear, Higgs VEV ratio : 𝜈, 𝐶𝜈, tan𝛾 =

Τ 𝐼𝑣 𝐼𝑒

38

 constraints

electroweak symmetry breaking (EWSB) condition
Higgs boson mass : 𝑛ℎ = 125 GeV

 strategy

𝑁2 and 𝐶𝜈-term are tuned to satisfy EWSB condition
𝐵0 is tuned to realize 𝑛ℎ = 125 GeV

SLIDE 39

𝑁1 = 10TeV 𝑁1 = 5TeV

39/40

SLIDE 40

40/40