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

PPP2017@Kyoto 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.) 1

Outline 1. Brief review of MSSM 2. Non-universal gaugino mass scenario 3. Phenomenology of NUGM 4. Conclusion 2/40

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 3/40

low-scale SUSY  motivation ・ little hierarchy problem ・ testability at LHC  LHC bound: e.g.) 𝑛 ෤  Higgs mass 125 GeV 𝑕 > 2.0 TeV 4/40

SM-like Higgs boson mass 𝑁 𝑡𝑢𝑝𝑞 = 𝑛 ሚ 𝑢 1 𝑛 ሚ  MSSM Higgs boson mass 𝑢 2 ℒ ⊃ 𝑧 𝑢 𝐵 𝑢 𝐼 𝑣 ǁ 𝑢 𝑀 ǁ 𝑢 𝑆 2 2 2 2 2 log 𝑁 𝑡𝑢𝑝𝑞 2 cos 2 2𝛾 + 3𝑛 𝑢 + 2𝐵 𝑢 𝐵 𝑢 2 ≃ 𝑛 𝑎 𝑛 ℎ 1 − 2 2 2 8𝜌 2 𝑤 𝑣 𝑛 𝑢 𝑁 𝑡𝑢𝑝𝑞 12𝑁 𝑡𝑢𝑝𝑞 125 GeV needs large quantum correction ( ∼ 35 GeV) Τ 𝑁 𝑡𝑢𝑝𝑞 ≃ 10 TeV if 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ≪ 1 2 2 2𝐵 𝑢 𝐵 𝑢 1 −  maximal mixing scenario 2 2 𝑁 𝑡𝑢𝑝𝑞 12𝑁 𝑡𝑢𝑝𝑞 last term is maximized at Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ∼ 6 ( maximal mixing ) Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 5/40

little hierarchy problem SUSY searches and Higgs mass indicate high-scale SUSY hierarchy between SUSY scale and EW scale  Higgs potential minimization condition 2 ≃ −2 𝜈 2 + 2|𝑛 𝐼 𝑣 2 | 𝑛 𝑎 𝜈 ∶ higgsino mass 2 : up-type Higgs mass 𝑛 𝐼 𝑣 EW scale SUSY scale ✓ fine-tuning is required if 𝑛 𝑎 ≪ 𝜈, 𝑛 𝐼 𝑣 ✓ at least 𝜈 must be small since it’s unique SUSY parameter ✓ small 𝜈 means small 𝑛 𝐼 𝑣 around EW scale 6/40

Higgs mass vs little hierarchy little hierarchy problem relates to the Higgs boson mass 2  RG equation of 𝑛 𝐼 𝑣 2 16𝜌 2 𝑒𝑛 𝐼 𝑣 2 𝑁 2 2 − 6 2 + 𝑛 ሚ 2 + 𝐵 𝑢 2 𝑛 𝐼 𝑣 2 + 𝑛 ሚ 2 − 6𝑕 2 2 𝑁 1 2 ≃ 6𝑧 𝑢 5 𝑕 1 𝑢 𝑀 𝑢 𝑆 𝑒𝑢 2 , 𝑛 ሚ 2 , 𝐵 𝑢 appear • top squark parameters 𝑛 ሚ 𝑢 𝑀 𝑢 𝑆 2 | • heavy top squark leads larger |𝑛 𝐼 𝑣 ✓ 10 TeV top squark forces 10 −3 % tuning 7/40

Outline 1. Brief review of MSSM 2. Non-universal gaugino mass scenario 3. phenomenology of NUGM 4. Conclusion 8/40

What we need for low-scale SUSY?  little hierarchy problem 2 ≃ −2 𝜈 2 + 2|𝑛 𝐼 𝑣 2 | 𝑛 𝑎 |𝑛 𝐼 𝑣 𝑛 𝑇𝑉𝑇𝑍 | ≃ 𝜈 ≃ 𝑛 𝑎 to avoid the fine-tuning  MSSM Higgs boson mass 2 4 2 2 2 log 𝑁 𝑡𝑢𝑝𝑞 2 cos 2 2𝛾 + 3𝑛 𝑢 + 2𝐵 𝑢 𝐵 𝑢 2 ≃ 𝑛 𝑎 𝑛 ℎ 1 − 2 2 2 8𝜌 2 𝑤 𝑣 𝑛 𝑢 𝑁 𝑡𝑢𝑝𝑞 12𝑁 𝑡𝑢𝑝𝑞 Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ≃ 6 to avoid heavy top squark 9/40

Higgs boson mass in NUGM Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ≃ 6 is necessary to avoid heavy top squark  top squark parameters at 𝑛 𝑇𝑉𝑇𝑍 = 1.0 TeV 2 𝑛 𝑇𝑉𝑇𝑍 ≃ +0.35𝑁 2 2 + 3.21 𝑁 3 2 + 0.60 𝑛 0 2 𝑛 ሚ 𝑢 𝑀 2 + 2.77𝑁 3 2 + 0.29𝑛 0 2 2 𝑛 ሚ 𝑛 𝑇𝑉𝑇𝑍 ≃ −0.16𝑁 2 unification scale 𝑢 𝑆 𝐵 𝑢 𝑛 𝑇𝑉𝑇𝑍 ≃ −0.24𝑁 2 − 1.42𝑁 3 + 0.27𝐵 0  Universal Gaugino Masses 𝑁 𝑡𝑢𝑝𝑞 ≡ 𝑛 ሚ 𝑢 𝑆 𝑛 ሚ 𝑢 𝑀 1.42 2 × 𝑁 3 2 𝐵 𝑢 ≃ 2 ≃ 0.67 𝑁 2 = 𝑁 3 ≫ 𝑛 0 𝑁 𝑡𝑢𝑝𝑞 3.21 ⋅ 2.77 × 𝑁 3 ✓ 125 GeV Higgs boson requires heavy top squark ≳ sub TeV 10

Higgs boson mass in NUGM Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ≃ 6 is necessary to avoid heavy top squark  top squark parameters at 𝑛 𝑇𝑉𝑇𝑍 = 1.0 TeV 2 𝑛 𝑇𝑉𝑇𝑍 ≃ +0.35𝑁 2 2 + 3.21 𝑁 3 2 + 0.60 𝑛 0 2 𝑛 ሚ 𝑢 𝑀 2 + 2.77𝑁 3 2 + 0.29𝑛 0 2 2 𝑛 ሚ 𝑛 𝑇𝑉𝑇𝑍 ≃ −0.16𝑁 2 unification scale 𝑢 𝑆 𝐵 𝑢 𝑛 𝑇𝑉𝑇𝑍 ≃ −0.24𝑁 2 − 1.42𝑁 3 + 0.27𝐵 0  Non-Universal Gaugino Masses (NUGM) `07 H.Abe, T.Kobayashi, Y.Omura ✓ 𝑛 ሚ 𝑢 𝑆 𝑛 𝑇𝑉𝑇𝑍 decreases, |𝐵 𝑢 𝑛 𝑇𝑉𝑇𝑍 | increases as 𝑁 2 increases 𝑁 𝑡𝑢𝑝𝑞 ≡ 𝑛 ሚ 𝑢 𝑆 𝑛 ሚ Τ 𝐵 𝑢 𝑁 𝑡𝑢𝑝𝑞 ≲ 6 𝑢 𝑀 2 (𝑛 𝑇𝑉𝑇𝑍 ) > 0 ✓ upper bound is 𝑁 2 /𝑁 3 ≲ 4.2 for 𝑛 ሚ 𝑢 𝑆 11/40

naturalness in NUGM 2  RG-running of 𝑛 𝐼 𝑣 unification 2 − 0.13𝑁 2 𝑁 3 − 1.56𝑁 3 2 − 0.07𝑛 0 2 2 𝑛 𝐼 𝑣 𝑛 𝑇𝑉𝑇𝑍 ≃ +0.20𝑁 2 scale 2 2 𝑁 2 ≃ 3.1 × 𝑁 3 → 𝑛 𝐼 𝑣 𝑛 𝑇𝑉𝑇𝑍 ≃ 𝑛 𝐹𝑋 2 ≃ 𝜈 2 large wino mass reduces 𝑛 𝐼 𝑣 + large wino mass enhances the Higgs boson mass 12

Higgs boson mass in NUGM 𝑁 3 = 𝑛 0 = 1.0 TeV  we assume universal soft mass 𝑛 0 and A-term 𝐵 0 tan𝛾 = 15 2 𝑒 ln 𝑛 𝑎 1-loop RGE + 𝑛 𝑇𝑉𝑇𝑍 ≡ 𝑛 ሚ 𝑢 1 𝑛 ሚ 𝑢 2 , 𝑠 𝑗 = 𝑁 𝑗 /𝑁 3 Δ 𝜈 ≡ 1-loop RG Higgs mass 𝑒 ln 𝜈(Λ 𝐻𝑉𝑈 ) 2 𝐵 0 = −1.0 TeV no EWSB 𝑛 ℎ = 126 𝑛 ℎ = 124 13

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 𝑛 ℎ ∼ 125 GeV and 𝜈 ∼ 𝑛 𝐹𝑋 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 15/40

ǁ typical mass spectrum 0 , ෤ ± 𝑢 2 , ෨ 𝑟, ሚ g, ǁ ෤ 𝑐 1,2 , ෤ 𝑚, ෤ 𝜓 3,4 𝜓 2 ✓ most of sparticles are heavy 2 TeV • these are determined by gluino mass 𝑁 3 𝑢 1 ≃ ǁ 1 TeV 𝑢 𝑆 ✓ right-handed stop can be lighter than others • as a result of large wino mass ± ≃ ෨ 0 , ෤ 𝜓 1,2 ෤ 𝜓 1 ℎ ✓ higgsinos are light 100 GeV 16

decays of higgsinos  higgsinos are light and degenerate Δm ෥ 𝜓 ≲ 2.0 GeV soft invisible soft ATLAS collab. • decay products are too soft to be reconstructed • c𝜐 < 𝑃(10 −3 𝑑𝑛) : no disappearing track unlike pure wino higgsino searches are difficult at LHC 17

ǁ typical mass spectrum 0 , ෤ ± 𝑢 2 , ෨ 𝑟, ሚ g, ǁ ෤ 𝑐 1,2 , ෤ 𝑚, ෤ 𝜓 3,4 𝜓 2 ✓ most of sparticles are heavy 2 TeV • these are determined by gluino mass 𝑁 3 𝑢 1 ≃ ǁ 1 TeV 𝑢 𝑆 ✓ right-handed stop is lighter than others • due to large wino mass ± ≃ ෨ 0 , ෤ 𝜓 1,2 ෤ 𝜓 1 ℎ ✓ higgsinos are light, but suitably degenerate • DM searches are important 100 GeV 18

constraints form indirect detection ≃ ෨ ℎ http://www.hap-astroparticle.org/184.php 𝜏𝑤 𝑤=0 is determined by higgsino mass itself 19/40

constraints form indirect detection 𝜊 ≡ Ω 𝑀𝑇𝑄 /Ω 𝑝𝑐𝑡 𝜊 = 1 Fermi-LAT, AMS-02, (`16 Cooco, Kramer et.al.) softsusy, SDECAY 𝜊 = Ω 𝑢ℎ𝑓𝑠𝑛𝑏𝑚 /Ω 𝑀𝑇𝑄 micrOMEGA  non-thermal : Ω 𝑀𝑇𝑄 = Ω 𝑝𝑐𝑡  thermal: Ω 𝑀𝑇𝑄 = Ω 𝑢ℎ𝑓𝑠𝑛𝑏𝑚 - no constraint on 𝜈 - 𝜈 < 300 GeV excluded by Fermi-LAT - 𝜈 < 800 GeV excluded by AMS-02 20

direct detection for higgsino LSP : gauge-basis 𝜇 ℎ𝜓𝜓 = 𝑕 𝑛 𝑎 𝑛 𝑎 2 2 1 ± 𝑡 2𝛾 𝑑 𝑋 𝑁 2 − 𝜈 + 𝑢 𝑋 𝑁 1 − 𝜈  cross section −2 2 2 𝑇𝐽 = 𝑕 2 2 𝑛 𝑂 1 + 𝑛 𝑂 9 + 7 𝑂 2 𝜏 𝑂𝜓 ෍ 𝑔 𝜇 ℎ𝜓𝜓 𝑈 4 𝑛 𝑋 2 4𝜌 𝑛 𝜓 9 𝑟 𝑛 ℎ 𝑟=𝑣,𝑒,𝑡 • gaugino masses are crucial for higgsino-gaugino mixing • sign of 𝜈 is also important for smaller tan𝛾 21

constraints from direct detection 𝑁 3 = 1.5 TeV, 𝑁 2 ∼ 4.5 TeV tan𝛾 = 10 𝑛 0 = 1 TeV softsusy+sdecay +micrOMEGA • there are significant bounds on 𝑁 1 even when 𝑛 ෤ 𝑕 ≃ 3.2 TeV • SI cross section is on the “neutrino floor” everywhere `13 Billard, Strigari, Figueroa-Feliciano 22/40

constraints from direct detection 𝑁 3 = 1 TeV, 𝑁 2 ∼ 4.0 TeV tan𝛾 = 10 𝑛 0 = 1 TeV softsusy+sdecay +micrOMEGA • XENON1T fully covers 𝜈 > −100 GeV in non-thermal case • only 𝜈 ≲ 1.0 TeV is covered in thermal case • LHC is sensitive to small 𝜈 , while DD is sensitive to large 𝜈 23/40

ǁ typical mass spectrum 0 , ෤ ± 𝑢 2 , ෨ 𝑟, ሚ g, ǁ ෤ 𝑐 1,2 , ෤ 𝑚, ෤ 𝜓 3,4 𝜓 2 ✓ most of sparticles are heavy 2 TeV • these are determined by gluino mass 𝑁 3 𝑢 1 ≃ ǁ 1 TeV 𝑢 𝑆 ✓ right-handed stop is lighter than others • due to large wino mass ✓ higgsinos are light, but suitably degenerate ± ≃ ෨ 0 , ෤ 𝜓 1,2 ෤ 𝜓 1 ℎ • DM searches are important 100 GeV • large bino/wino is necessary for 𝑁 ෤ 𝑕 ≲ 3.0 TeV stop / gluino searches are important at LHC 24