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研究内容

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研究内容

  1. 1. カラーを持たない新粒粒⼦子を軸に 新しい物理理を探る Takahiro  Yoshinaga  (Univ.  of  Tokyo) Based  on    T.  Kitahara  and  T.Y    JHEP  05  035  (2013)    M.  Endo,  K.  Hamaguchi,  S.  Iwamoto,  and  T.Y  JHEP  01  123  (2014)    M.  Endo,  K.  Hamaguchi,  T.  Kitahara,  and  T.Y    JHEP  11  013  (2013)    M.  Endo,  T.  Kitahara,  and  T.Y    JHEP  04  139  (2014) 33  Slides
  2. 2.   研究テーマ 2 「Muon  g-‐‑‒2を説明する超対称模型の現象論論」 Muon  g-‐‑‒2 >3σ  dev. eB e`L e`R eg eq fW ··· ⇡ ≫1TeV O(100)GeV Muon  g-‐‑‒2  Motivated  SUSY mee = m eµ = m e⌧ m ee = m eµ ⌧ m e⌧ 46 Dissertation / Takahiro Yoshinaga µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL W0 H0 d γ (c) µL µR µL B H0 d γ (d) µL µR µR H0 d B γ (e) Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigenstates. The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(e) are from the neutralino–smuon diagram. fW eH 46 Dissertation / Takahiro Yoshinaga µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL W0 H0 d γ (c) µL γ µR γ fW eH ≫1TeV ⇡ O(100)GeV eg eq ··· eB fW eH e` LHC LHC  &  ILC
  3. 3.   研究での⾃自分の役割 3 「どのような切切り⼝口で物理理を引き出すか」 CHAPTER 2. FOUNDATION 23 µ µ γ (A) µ µ γ (B) µ µ γ (C) Figure 2.1: (A) The Feynman diagram which contributes to the anomalous magnetic moment of the muon. (B) The hadronic vacuum-polarization contributions to the muon g −2. (C) The hadronic light-by-light contributions to the muon g − 2. The amplitude can be interpreted as the Born approximation to the scattering of the electron from a potential (For detail, see textbook [19]). The interaction Hamiltonian which corresponds to such potential is given by Hint = −〈−→µ 〉 · −→ B , (2.17) where 〈−→µ 〉 = 2 F1(0) + F2(0) × eQℓ 2mℓ ξ′† −→σ 2 ξ. (2.18) The factor ξ′† (−→σ /2)ξ can be interpreted as the spin of the leptons, −→ S . Comparing Eq. (2.18) with Eqs. (2.3) and (2.4), the coefficient 2 F1(0) + F2(0) becomes SUSY 超対称模型のMuon  g-‐‑‒2への寄与 -‐‑‒  全て考慮すると複雑、物理理が⾒見見えづらい -‐‑‒  加速器シミュレーションの計算が⼤大変 本質的に重要なセットアップに近似 1.  Chargino-‐‑‒sneutrino    2.  Neutralino-‐‑‒smuon Multi-‐‑‒lepton  signalが重要 真空の安定性が重要
  4. 4.   本⽇日の内容 4 Intro. Muon  g-‐‑‒2 Muon  g-‐‑‒2  Motivated  SUSY  Models Main Neutralino-‐‑‒Smuon  Constribution Chargino-‐‑‒Sneutrino  Constribution Conc. Summary
  5. 5.   本⽇日の内容 5 Intro. Muon  g-‐‑‒2 Muon  g-‐‑‒2  Motivated  SUSY  Models Main Neutralino-‐‑‒Smuon  Constribution Chargino-‐‑‒Sneutrino  Constribution Conc. Summary
  6. 6.   素粒粒⼦子物理理学の⽬目標 6 「万物を説明する理理論論の解明」 現状 標準模型の問題点 ü  標準模型(SM)が確⽴立立 ü  ほとんどの実験結果を説明できる ü  究極の素粒粒⼦子模型とは考えられていない ü  重⼒力力が含まれていない ü  暗⿊黒物質の候補がいない         … ü  Muon  g-‐‑‒2の不不⼀一致 標準模型の粒粒⼦子 将来3〜~5年年の実験で新しい素粒粒⼦子模型 を探索索するための重要なヒント
  7. 7. ミューオンの異異常磁気モーメント  (Muon  g-‐‑‒2) Muon g-2 ✓ g = 2 at tree level (Dirac equation) ✓ g ≠ 2 by radiative corrections Magnetic moment g-factor   Muon  g-‐‑‒2 7 l  ミューオンの磁気モーメント l  g-‐‑‒factor H = !m · ! B , !m = Ç e 2mµ å !sg -‐‑‒  g  =  2  :  Tree  Level -‐‑‒  g  ≠  2  :  Radiative  Correction aµ ⌘ g 2 2
  8. 8.   Muon  g-‐‑‒2 8 SM  Prediction Contributions Value  (10-‐‑‒10) QED  (O(α5)) 11658471.8951  (0.0080) EW  (NLO) 15.36  (0.1) Hadronic (LO) [HLMNT] 694.91  (4.27) [DHMZ] 692.3  (4.2) Hadronic  (HO) -‐‑‒9.84  (0.07) Hadronic (LbL) [RdRV] 10.5  (2.6) [NJN] 11.6  (3.9) Total  SM [HLMNT] 11659182.8  (4.9) CHAPTER 2. FOUNDATION µ µ γ (A) µ (B Figure 2.1: (A) The Feynman diagram which c of the muon. (B) The hadronic vacuum-polariz hadronic light-by-light contributions to the mu The amplitude can be interpreted as th electron from a potential (For detail, see textb corresponds to such potential is given by Hint = −〈−→µ where 〈−→µ 〉 = 2 F1(0) + F2(0 The factor ξ′† (−→σ /2)ξ can be interpreted as the with Eqs. (2.3) and (2.4), the coefficient 2 F1( 2 F1(0) + F2(0) = It is just the g-value. 2.2.2 The Standard Model predictio The SM prediction of the muon g − 2 has bee several groups of theorists. Fig. 2.1 (A) shows muon g − 2. The theoretical uncertainty reach review the SM prediction of the muon g − 2. QED Contribution The quantum electromagnetic dynamics (QED to the muon g − 2 (99.993%), and come from CHAPTER 2. FOUNDATION µ µ γ (A) µ µ γ (B) µ Figure 2.1: (A) The Feynman diagram which contributes to the ano of the muon. (B) The hadronic vacuum-polarization contributions to hadronic light-by-light contributions to the muon g − 2. The amplitude can be interpreted as the Born approximatio electron from a potential (For detail, see textbook [19]). The intera corresponds to such potential is given by Hint = −〈−→µ 〉 · −→ B , where 〈−→µ 〉 = 2 F1(0) + F2(0) × eQℓ 2mℓ ξ′† −→σ 2 ξ. CHAPTER 2. FOUNDATION 23 µ µ γ (A) µ µ γ (B) µ µ γ (C) Figure 2.1: (A) The Feynman diagram which contributes to the anomalous magnetic moment of the muon. (B) The hadronic vacuum-polarization contributions to the muon g −2. (C) The hadronic light-by-light contributions to the muon g − 2. The amplitude can be interpreted as the Born approximation to the scattering of the electron from a potential (For detail, see textbook [19]). The interaction Hamiltonian which had QED,  EW had Experiment [E821  Muon  g-‐‑‒2実験のHome  pageより] 11659208.9  (6.3)  ×  10-‐‑‒10aexp µ = >3σの不不⼀一致が観測 26.1  (8.0)  ×  10-‐‑‒10aµ ⌘ aexp µ ath µ =  素粒粒⼦子物理理学の⽂文化…不不⼀一致が3σ:兆候  5σ:発⾒見見 (標準模型)
  9. 9.   Muon  g-‐‑‒2 9 Future 35 26 25 40 Fermilab  &  J-‐‑‒PARC Next  3-‐‑‒5  years e+e-‐‑‒→hadrons実験 中⼼心値が変わらなければ 近い将来>5σの感度度が期待 [Snowmass  white  paperより] SMXX 181.5±3.5
  10. 10.   Muon  g-‐‑‒2 10 中⼼心値が変わらなければ 近い将来>5σの感度度が期待 >3σの不不⼀一致が観測 26.1  (8.0)  ×  10-‐‑‒10aµ ⌘ aexp µ ath µ = 「今」Muon  g-‐‑‒2の不不⼀一致の原因 を調べることは⾮非常に重要 本研究の⽴立立場
  11. 11.   Muon  g-‐‑‒2 11 /21Dec 2, 2013 SUSY: Model-building and Phenomenology Teppei KITAHARA -The Univ. of Tokyo Status of the muon g-2 SM Value experiment DHMZ (11) The latest result of the muon g-2 [Hagiwara,Liao,Martin,Nomura,Teubner,J. Phys. G 38 (2011)085033] [Davier,Hoecker,Malaescu,Zhang,Eur. Phys. J. C 71(2011)1515] 3.3 σ 3.6 σ (possibly a signal of new physics)muon g-2 anomaly 3 SM+NP Exp Muon  g-‐‑‒2の不不⼀一致は新しい物理理(NP)の寄与が原因 新しい物理理 -‐‑‒  超対称模型(SUSY)を仮定 :新粒粒⼦子の質量量が加速器実験の探索索可能領領域に⼊入る -‐‑‒  model-‐‑‒independent  approachを採⽤用 CHAPTER 2. FOUNDATION µ µ γ (A) µ µ γ (B) µ Figure 2.1: (A) The Feynman diagram which contributes to the anom of the muon. (B) The hadronic vacuum-polarization contributions to hadronic light-by-light contributions to the muon g − 2. The amplitude can be interpreted as the Born approximation electron from a potential (For detail, see textbook [19]). The intera corresponds to such potential is given by Hint = −〈−→µ 〉 · −→ B , where 〈−→µ 〉 = 2 F1(0) + F2(0) × eQℓ 2mℓ ξ′† −→σ 2 ξ. The factor ξ′† (−→σ /2)ξ can be interpreted as the spin of the leptons, −→ S with Eqs. (2.3) and (2.4), the coefficient 2 F1(0) + F2(0) becomes 2 F1(0) + F2(0) = 2(1 + aℓ) = gℓ. It is just the g-value. 2.2.2 The Standard Model prediction of the muon g − The SM prediction of the muon g − 2 has been precisely evaluated NP 本研究の⽴立立場
  12. 12.   本⽇日の内容 12 Intro. Muon  g-‐‑‒2 Muon  g-‐‑‒2  Motivated  SUSY  Models Main Neutralino-‐‑‒Smuon  Constribution Chargino-‐‑‒Sneutrino  Constribution Conc. Summary
  13. 13.   Muon  g-‐‑‒2  Motivated  SUSY  Models 13 超対称性  (SUSY):BosonとFermionの間の対称性 MSSM=Minimal  Supersymmetric  Standard  Model SM粒粒⼦子のパートナー(超対称粒粒⼦子,  superparticle)を予⾔言
  14. 14.   Muon  g-‐‑‒2  Motivated  SUSY  Models 14 超対称性  (SUSY):Muon  g-‐‑‒2の不不⼀一致を説明 aSUSY µ ⇠ ↵2 tan 4⇡ m2 µ m2 SUSY 46 Dissertatio µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µL µR µL B H0 d γ (d) µL µ µR H0 d B γ (e) Figure 3.4: The diagrams of the SUSY contributions to the muon g − The diagram (a) comes from the chargino–muon sneutrino diagram, t from the neutralino–smuon diagram. ∆aχ0 µ = − mµ 48π2 6 X=1 4 A=1 1 m2 ℓX mµ 4 N L(e) 2AX 2 + N R(e) 2AX 2 F fW eH Chargino-‐‑‒sneutrino Neutralino-‐‑‒smuon Ç ⇠ 150 ⇥ 10 10 ⇥ ✓ 100GeV mSUSY ◆2 ⇥ ✓ tan 10 ◆å mSUSY  :  典型的なSUSY粒粒⼦子の質量量,    tanβ  :  Higgsの真空期待値の⽐比 mSUSY  =  O(100)GeV,  tanβ  =  O(10)のとき 超対称粒粒⼦子の寄与によりMuon  g-‐‑‒2の不不⼀一致を説明可能 [Lopez,  Nanopoulos,  Wang,  ʼ’93] [Chattopadhyay,  Nath,  ʼ’95] [Moroi,  ʼ’95] 26.1  (8.0)  ×  10-‐‑‒10aµ ⌘ aexp µ ath µ =
  15. 15.   Muon  g-‐‑‒2  Motivated  SUSY  Models 15 Muon  g-‐‑‒2:典型的なパターン Contributions O(100)GeV  particles Diagram Chagino-‐‑‒ sneutrino Wino,  Higgsinos,   (Bino),  smuons   Neutralino-‐‑‒ smuon Bino,  smuons 46 Dissertation / Takah µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µL W0 H (c) µL µR µL B H0 d γ µL µR µR H0 d B γ fW eH 46 µL µR W± νµ γ (a) µL µL µR B (b) µL µR µL B H0 d γ (d) Figure 3.4: The diagrams of the SUSY contributio The diagram (a) comes from the chargino–muon s from the neutralino–smuon diagram. 6 4 fW eH Minimalにはカラー電荷を持たない粒粒⼦子 のみが軽ければMuon  g-‐‑‒2を説明可能
  16. 16.   Muon  g-‐‑‒2  Motivated  SUSY  Models 16 知りたいこと -‐‑‒  どのような性質を持つか -‐‑‒  実験(特に加速器)で検証できるか Muon  g-‐‑‒2  Motivated  SUSY  models ≫1TeV ⇡ O(100)GeV eg eq ··· eB fW eH e` eB e`L e`R eg eq fW ···≫1TeV ⇡ O(100)GeV Chagino-‐‑‒sneutrino Neutralino-‐‑‒smuon 思い切切って単純なセットアップを考える [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14] [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13]
  17. 17.   本⽇日の内容 17 Intro. Muon  g-‐‑‒2 Muon  g-‐‑‒2  Motivated  SUSY  Models Main Neutralino-‐‑‒Smuon  Constribution Chargino-‐‑‒Sneutrino  Constribution Conc. Summary
  18. 18.   Chargino-‐‑‒Sneutrino  Contribution 18 どうやって探すか ⇡ ≫1TeV O(100)GeV l  通常の解析:Multi-‐‑‒jet l  カラーを持つ粒粒⼦子が重すぎて通常の⽅方法では探索索不不可能* eB fW eH e` eg eq ··· Cascade   Decay Multi-‐‑‒jets Large  missing   transverse  energy LHCで⽣生成されない *  Gaugino間に関係がつく場合  (ex.  ⼤大統⼀一理理論論)はGluino対⽣生成から間接的にWinoなどを探索索可能 [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14]
  19. 19. l  Cross  section  at  LHC  (8TeV) l  現在のLHCのデータ:L=O(10)fb-‐‑‒1 l  Multi-‐‑‒lepton  signal   Chargino-‐‑‒Sneutrino  Contribution 19 どうやって探すか ⇡ ≫1TeV O(100)GeV l  通常の解析:Multi-‐‑‒jet l  Electroweak  gaugino  production:Winoを直接探索索すればよい eB fW eH e` eg eq ··· Decoupled Electroweak  gaugino  production (pp ! e± 1 e0 2 ) ⇠ O (0.1) pb @Wino ⇠ O (100)GeV O(100)-‐‑‒O(1000)  eventが期待 質量量がWino  >  slepton  >  Binoの場合にenhance pp ! e± 1 e0 2 ! 3` + Emiss T [ATLAS  Collaboration,  ʼ’14]
  20. 20. Excluded M2 [GeV] meµL [GeV]   Chargino-‐‑‒Sneutrino  Contribution 20 -‐‑‒  Mass -‐‑‒  LHC LHC  Status Muon  g-‐‑‒2を説明できるパラメータ領領域の⼀一部は 現在のLHCのデータですでに排除 [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14] M2 = 2M1, µ = 2M2 meµR = mstau = 3 TeV (結果に影響しない)   e`e` e0 1e0 1 ` ` e0 2 e± 1 ` pp ! e± 1 e0 2 ! 3` + Emiss T tan = 40 1σ:Δaμ SUSY  =  (26.1±8.0)×10-‐‑‒10 2σ:Δaμ SUSY  =  (26.1±16.0)×10-‐‑‒10 1σ 2σ
  21. 21.   Chargino-‐‑‒Sneutrino  Contribution 21 Future  Prospects LHCが14TeVにアップグレードした場合 ほぼすべてのパラメータ領領域が探索索可能 [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14] -‐‑‒  Multi-‐‑‒lepton  :  より感度度が上がる -‐‑‒  SM  boson Excluded M2 [GeV] meµL [GeV] tan = 40 e0 1e0 1 e0 2 e± 1 Z, H W pp ! e± 1 e0 2 ! W Z or W H + Emiss T Wino  mass  <  ~∼1TeV@14TeV [Berggren,et.al,  ʼ’13]  (snowmass  paper) [ATLAS-‐‑‒PHYS-‐‑‒PUB-‐‑‒2013-‐‑‒007] [CMS-‐‑‒NOTE-‐‑‒13-‐‑‒002] SM  boson (300-‐‑‒3000fb-‐‑‒1)  
  22. 22.   Chargino-‐‑‒Sneutrino  Contribution 22 Muon  g-‐‑‒2を説明できるパラメータ領領域の⼀一部は 現在のLHCのデータですでに排除 残りの質量量領領域も将来のLHC実験 で探索索可能な⾒見見通し カラーを持つ超対称粒粒⼦子が重くても 直接Winoを⽣生成して探索索可能 まとめ
  23. 23.   本⽇日の内容 23 Intro. Muon  g-‐‑‒2 Muon  g-‐‑‒2  Motivated  SUSY  Models Main Neutralino-‐‑‒Smuon  Constribution Chargino-‐‑‒Sneutrino  Constribution Conc. Summary
  24. 24.   Neutralino-‐‑‒Smuon  Contribution 24 右巻きと左巻きsmuonの混合に⽐比例例   ü  Large  μ  tanβ  :  enhanced ü  Large  smuon  mass  :  suppressed 46 Dis µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL B H0 d γ (d) µL µR H0 d (e) Figure 3.4: The diagrams of the SUSY contributions to the mu The diagram (a) comes from the chargino–muon sneutrino diag from the neutralino–smuon diagram. ∆aχ0 µ = − mµ 2 6 4 1 2 mµ N L(e) 2AX 2 + N R 2 fW eH eµL eµR m2 e`LR SmuonがO(1)TeVでも極端に⼤大きな混合を 取ればMuon  g-‐‑‒2の不不⼀一致を説明できてしまう Muon  g-‐‑‒2 1σ 2σ 加速器実験の探索索可能領領域を超えてしまう!? [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] 1σ:Δaμ SUSY  =  (26.1±8.0)×10-‐‑‒10 2σ:Δaμ SUSY  =  (26.1±16.0)×10-‐‑‒10 Slepton間の混合の⼤大きさが重要 m2 e`LR ' m`µtan
  25. 25.   Neutralino-‐‑‒Smuon  Contribution 25 46 Dis µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL B H0 d γ (d) µL µR H0 d (e) Figure 3.4: The diagrams of the SUSY contributions to the mu The diagram (a) comes from the chargino–muon sneutrino diag from the neutralino–smuon diagram. ∆aχ0 µ = − mµ 2 6 4 1 2 mµ N L(e) 2AX 2 + N R 2 fW eH eµL eµR m2 e`LR SmuonがO(1)TeVでも極端に⼤大きな混合を 取ればMuon  g-‐‑‒2の不不⼀一致を説明できてしまう Muon  g-‐‑‒2 1σ 2σ 加速器実験の探索索可能領領域を超えてしまう!? [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] 安定性条件 により禁⽌止 Slepton間の混合の⼤大きさが重要 右巻きと左巻きsmuonの混合に⽐比例例   ü  Large  μ  tanβ  :  enhanced ü  Large  smuon  mass  :  suppressed m2 e`LR ' m`µtan  スカラーポテンシャルの安定性条件   により上限が存在する
  26. 26.   Neutralino-‐‑‒Smuon  Contribution 26 真空の安定性条件 -‐‑‒  SleptonとHiggsの3点結合 v  :  真空期待値,  h  :  SM  Higgs,  混合はμ>0のときnegative   EW  vacuumの寿命  >  宇宙年年齢とすると 混合の⼤大きさに上限が付く EW  vacuum Charge-‐‑‒breaking  minima ⼤大きすぎる混合
  27. 27.   Neutralino-‐‑‒Smuon  Contribution 27 真空の安定性条件 -‐‑‒  数値公式* Slepton  mass  bound [Kitahara,  TY,  ʻ‘13] [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] *  Calculated  by  CosmoTransitions            η~∼1,  (leptonのフレーバーに弱く依存)   Muon  g-‐‑‒2の不不⼀一致を説明するという 条件と合わせるとsmuon  <  ~∼500GeV (すべて縮退)のとき Stau-‐‑‒Higgsポテンシャルで強く制限 Vacuum  bound 〜~400GeV
  28. 28.   Neutralino-‐‑‒Smuon  Contribution 28 -‐‑‒  Mass -‐‑‒  混合 -‐‑‒  LHC mee = meµ = me⌧ (縮退) 真空の安定性条件を満たす 中で最⼤大の値を各点で選ぶ LHC  Status e`e` e0 1e0 1 ` ` Muon  g-‐‑‒2を1σで説明できる領領域  (1σ  Region) のほとんどは現在のLHCのデータですでに排除 Excluded [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] pp ! e`e`⇤ ! `+ ` + Emiss T
  29. 29.   Neutralino-‐‑‒Smuon  Contribution 29 -‐‑‒  Cross  section  (LO) Future  Prospects Smuonの質量量がNeutralinoの質量量より ⼗十分⼤大きい領領域は14TeV  LHCで探索索可能 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] (eµ1 eµ1) = 8 >>< >>: 1fb  (√s  =  8TeV,                                          のとき)meµ = 330GeV meµ = 450GeV1fb  (√s  =  14TeV,                                          のとき) ↔  現在のLHCの制限 ↔  (Naïveな)将来の感度度 LHC
  30. 30.   Neutralino-‐‑‒Smuon  Contribution 30 Future  Prospects Smuonの質量量とNeutralinoの質量量が 近い領領域は1TeV  ILCで探索索可能 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] -‐‑‒  ILC kinematicalに許される質量量領領域ならば探索索可能 Closing the loopholes At the ILC, a systematic search for the NLSP is possible without leaving loopholes, covering even the cases that may be very difficult to test at the LHC. In the case of a very small mass difference between the LSP and the NLSP - less than a few GeV - the clean environment at the ILC nevertheless allows for a good detection efficiency. If √ s is much larger than the threshold for the NLSP-pair production, the NLSPs themselves will be highly boosted in the detector frame, and most of the spectrum of the decay products will be easily detected. In this case, the precise knowledge of the initial state at the ILC is of paramount importance to recognize the signal, by the slight discrepancy in energy, momentum and acolinearity between signal and background from pair production of the NLSP’s SM partner. In the case the threshold is not much below √ s, the background to fight is γγ → f ¯f where the γ’s are virtual ones radiated off the beam-electrons. The beam-electrons themselves are deflected so little that they leave the detector undetected through the outgoing beam-pipes. Under the clean conditions at the ILC, this background can be kept under control by demanding that there is a visible ISR photon accompanying the soft NLSP decay products. If such an ISR is present in a γγ event, the beam-remnant will also be detected, and the event can be rejected. If the LSP is unstable due to R-parity violation, the ILC reach would be better or equal to the R- conserving case, both for long-lived and short-lived LSP’s and whether the LSP is charged or neutral. Also in the case of an NLSP which is a mass-state mixed between the hyper-charge states, the procedure is viable. One will have one more parameter - the mixing angle. However, as the couplings to the Z of both states are known from the SUSY principle, so is the coupling with any mixed state. There will then be one mixing-angle that represents a possible “worst case”, which allows to determine the reach whatever the mixing is - namely the reach in this “worst case”. Finally, the case of “several” NLSPs– i.e. a group of near-degenerate sparticles– can be disentangled due to the possibility to precisely choose the beam energy at the ILC. This will make it possible to study the “real” NLSP below the threshold of its nearby partner. 0 50 100 150 200 250 0 50 100 150 200 250 Exclusion Discovery Excludable at95% C L NLSP : µ˜R MNLSP [GeV] MLSP[GeV] 0 50 100 150 200 250 240 242 244 246 248 250 Exclusion Discovery NLSP : µ˜R MNLSP [GeV] MLSP[GeV] Figure 3: Discovery reach for a ˜µR NLSP after collecting 500 fb−1 at √ s = 500 GeV. Left: full scale, Right: zoom to last few GeV before the kinematic limit. The strategy At an e+ e− -collider, the following typical features of NLSP production and decay can be exploited: missing [Baer,  et.al.,  ʻ‘13] ex)  √s  =  500GeV   Δm=O(10-‐‑‒100)MeV Massの差はO(10)GeV ILCで探索索可能
  31. 31.   Neutralino-‐‑‒Smuon  Contribution 31 Muon  g-‐‑‒2を1σで説明できる領領域  (1σ  Region) のほとんどは現在のLHCのデータですでに排除 残りの質量量領領域も将来のLHC,  ILC実験 で探索索可能な⾒見見通し* Stau-‐‑‒Higgsポテンシャルの安定性条件から slepton  mass  <  500GeVに制限される まとめ *  ILCにおけるStau探索索に関して、HiggsとDiphotonの結合の情報も有効 [Kitahara,  TY,  ʻ‘13] [Endo,  Kitahara,  TY,  ʻ‘14]
  32. 32.   本⽇日の内容 32 Intro. Muon  g-‐‑‒2 Supersymmetry(SUSY) Main Muon  g-‐‑‒2  Motivated  SUSY  model Neutralino-‐‑‒smuon  constribution Chargino-‐‑‒sneutrino  constribution Conc. Summary
  33. 33.   まとめ 33 「超対称模型は近い将来探索索可能」 Muon  g-‐‑‒2 >3σ  dev. eB e`L e`R eg eq fW ··· ⇡ ≫1TeV O(100)GeV Muon  g-‐‑‒2  Motivated  SUSY mee = m eµ = m e⌧ m ee = m eµ ⌧ m e⌧ 46 Dissertation / Takahiro Yoshinaga µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL W0 H0 d γ (c) µL µR µL B H0 d γ (d) µL µR µR H0 d B γ (e) Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 in gauge eigenstates. The diagram (a) comes from the chargino–muon sneutrino diagram, the diagrams (b)–(e) are from the neutralino–smuon diagram. fW eH 46 Dissertation / Takahiro Yoshinaga µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL W0 H0 d γ (c) µL γ µR γ fW eH ≫1TeV ⇡ O(100)GeV eg eq ··· eB fW eH e` LHC LHC  &  ILC (Muon  g-‐‑‒2を説明する)
  34. 34.   他の研究内容 34 l 卒業研究:群上の調和解析   -‐‑‒  曲がった空間上でのFourier解析の理理論論 l 修⼠士課程:B中間⼦子の物理理   -‐‑‒  B中間⼦子の崩壊現象、CP対称性の破れを軸にした       超対称模型の探索索 l 博⼠士課程:Muon  g-‐‑‒2   -‐‑‒  Higgs粒粒⼦子の崩壊現象を⽤用いたStau探索索   -‐‑‒  新しいレプトンを含む模型の制限   -‐‑‒  Muon  g-‐‑‒2と暗⿊黒物質を説明する超対称模型の探索索
  35. 35.   補⾜足パート 35 Backup
  36. 36.   Muon  g-‐‑‒2 36 測り⽅方 磁場中でのMuonの歳差運動の周波数から求める ①  ⼀一様磁場中に偏極した(反)muonを⼊入れる ②  サイクロトロン運動(磁場)&歳差運動(スピン) ③  g=2  :  歳差運動はサイクロトロン運動に追従 g≠2  :  歳差運動の⽅方がわずかに速くなる(異異常歳差運動) ④  崩壊先の陽電⼦子の数の時間変動の測定から歳差運動の振動数を求める ⑤  歳差運動の振動数からg-‐‑‒2を読み取る !a ' e mµ aµ ! B
  37. 37.   Muon  g-‐‑‒2 37 BNLとJ-‐‑‒PARCの違い* l  BNL:Magic  momentum l  J-‐‑‒PARC:電場ゼロ 電場速度度 Lorentz因⼦子 異異常歳差運動の振動数 γ=29.4  (p  =  3.094GeV/c)  のとき、第⼆二項が無視できる *  Fermilab  (FNAL)  はBNLと同じsetup   極冷冷muonを⽤用いることで、収束電場を不不要にする EDMの観測も⽬目標 !a = e mµ 2 4aµ ! B ✓ aµ 1 2 1 ◆ ! ⇥ ! E c ⌘ 2 ⇣! ⇥ ! B ⌘ 3 5 EDM(無視)
  38. 38.   Muon  g-‐‑‒2 38 >3σの不不⼀一致が観測 26.1  (8.0)  ×  10-‐‑‒10aµ ⌘ aexp µ ath µ = Status of the muon g-2 SM Value experiment DHMZ (11) The latest result of the muon g-2 [Hagiwara,Liao,Martin,Nomura,Teubner,J. Phys. G 38 (2011)085033] [Davier,Hoecker,Malaescu,Zhang,Eur. Phys. J. C 71(2011)1515] 3.3 σ 3.6 σ aμ  ×  1010  -‐‑‒  11659000 SM Exp [Hagiwara,  Liao,  Martin,  Nomura,  Teubner,  ʼ’11]
  39. 39.   Muon  g-‐‑‒2 39 (Naive)  NP  contribution aNP µ ⇠ ↵NP 4⇡ mµ m2 NP ✓ g = 2 at tree level (Dirac equation) ✓ g ≠ 2 by radiative corrections Magnetic moment g-factor gNP gNP mNP 条件:SM  EW  contributionと同程度度 26.1  (8.0)  ×  10-‐‑‒10aµ ⌘ aexp µ ath µ = aSM EW µ ⇠ ↵2 4⇡ m2 µ m2 W = 15.36  (0.1)  ×  10-‐‑‒10 αNP,  mNP  ~∼  O(EWボソンの結合,  質量量) そのような粒粒⼦子が存在したら既に発⾒見見されているはず…
  40. 40.   Muon  g-‐‑‒2 40 (Naive)  NP  contribution aNP µ ⇠ ↵NP 4⇡ mµ m2 NP ✓ g = 2 at tree level (Dirac equation) ✓ g ≠ 2 by radiative corrections Magnetic moment g-factor gNP gNP mNP 2種類の可能性 l  αNP~∼  O(10-‐‑‒6)  (weak),  mNP~∼  O(100)MeV  (small) l  αNP~∼  O(0.1-‐‑‒1)  (strong),  mNP~∼  O(100-‐‑‒1000)GeV  (heavy) e.g.  Hidden  Photon e.g.  Supersymmetry
  41. 41.   Supersymmetry 41 Higgs  mass l  Tree  level  :   l  Large  top-‐‑‒stop  correction mtree h ' mZ m2 h ⇠ m2 Z cos2 2 + 3 4⇡2 Y 2 t sin2 ñ m2 t log M2 S m2 t + X2 t M2 S Ç 1 X2 t 12M2 S å + ··· ô Ms = p met1 met2 , Xt = At µcot -‐‑‒  Heavy  stop  :  Ms  ≫  1TeV,  Xt  =  0 -‐‑‒  Maximal  mixing  :  Ms  ~∼  1TeV,  Xt  =  √6Ms   Scalar  top  >  1TeV
  42. 42.   Supersymmetry 42 CMSSM  (mSUGRA) m0 A0 m1/2 sgn(µ) tan Scalar  mass Scalar  coupling m0 Masses  of  Hu,d Gaugino  mass Other  parameters  :  
  43. 43.   Supersymmetry 43 Muon  g-‐‑‒2  vs  CMSSM CMSSMの枠組では現在のLHCの制限とHiggs  massと Muon  g-‐‑‒2を同時に説明することができない [Endo,  Hamaguchi,  Iwamoto,  Nakayama,  Yokozaki  ʻ‘11] [GeV]0m 0 1000 2000 3000 4000 5000 6000 [GeV]1/2 m 300 400 500 600 700 800 900 1000 (2400GeV)q~ (1600GeV) q~ (1000 GeV) g ~ (1400 GeV)g ~ h(122GeV) h(124GeV) h(126GeV) Expected Observed Expected Observed Expected Observed Expected Observed Expected Observed Expected Observed > 0µ,0= -2m 0 ) = 30, AβMSUGRA/CMSSM: tan( Status: ICHEP 2014 ATLAS Preliminary = 8 TeVs, -1 L dt = 20.1 - 20.7 fb∫ τ∼ LSP not included.theory SUSY σ95% CL limits. 0-lepton, 2-6 jets 0-lepton, 7-10 jets 0-1 lepton, 3 b-jets 1-lepton + jets + MET 1-2 taus + 0-1 lept. + jets + MET 3 b-jets≥2SS/3 leptons, 0 - arXiv: 1405.7875 arXiv: 1308.1841 arXiv: 1407.0600 ATLAS-CONF-2013-062 arXiv: 1407.0603 arXiv: 1404.2500 mh  ~∼126GeV* g-‐‑‒2 tanβ=20 m0[GeV] m1/2[GeV] *  Higgs  massは  (b→sγの制限を満たす範囲で)  A-‐‑‒termを調節して説明
  44. 44.   Supersymmetry 44 Muon  g-‐‑‒2  vs  Higgs  mass  and  LHC  (model) l  Messenger  sectorを拡張 l  Extra  vector-‐‑‒like  matterを加える l  新しいgauge対称性を加える [Endo,  Hamaguchi,  Iwamoto,  Yokozaki,    ʼ’11,12] [Endo,  Hamaguchi,  Ishikawa,  Iwamoto,  Yokozaki,    ʼ’12] [Moroi,  Sato,  Yanagida,  ʼ’12] [Evans,  Ibe,  Yanagida,  ʼ’11] [Evans,  Ibe,  Shirai,  Yanagida,  ʼ’11] [Ibe,  Matsumoto,  Yanagida,  Yokozaki,  ʼ’12] [Bhattacharyya,  Bhattacherjee,  Yanagida,  Yokozaki  ʼ’13]   [Endo,  Hamaguchi,  Iwamoto,  Nakayama,  Yokozaki,    ʼ’11]
  45. 45.   Supersymmetry 45 Electron  g-‐‑‒2   11596521807.3(2.8)×10-‐‑‒13 aexp e = ath e = 11596521818.7(0.6)(0.4)(0.2)(7.6)(0.1)×10-‐‑‒13 ae = aexp e ath e = -‐‑‒11.4  (8.1)  ×  10-‐‑‒13 l  実験値と理理論論値はConsistent  (1.4σ) l  新しい物理理の寄与 ae = ✓ aµ 3 ⇥ 10 9 ◆ 0.7 ⇥ 10 13 (NaïveにYukawaでスケール) -‐‑‒  SUSYでSleptonが縮退している場合はMuon  g-‐‑‒2に⽐比べて感度度が弱い -‐‑‒  Non-‐‑‒universalの場合はElectron,  Muon  g-‐‑‒2の両⽅方がenhanceし得る (符号逆&LFV/CPVを誘発するのでちと厳しいが…) ae ⇠ 2 ⇥ 10 12 ex.)                                                                      のときmee = 100GeV, tan = 30
  46. 46.   Supersymmetry 46 超対称粒粒⼦子のCross  section  (14TeV  LHC)   [ATLAS-‐‑‒PHYS-‐‑‒PUB-‐‑‒2013-‐‑‒011]
  47. 47.   Supersymmetry 47 カラーを持たない超対称粒粒⼦子のCross  section  
  48. 48.   Chargino-‐‑‒Sneutrino  Contribution 48 Mass  spectrum ⇡ ≫1TeV O(100)GeV l  軽い(O(100)GeV)粒粒⼦子  :  Bino,  Wino,  Higgsino,  sleptons l  他の超対称粒粒⼦子  :  Decoupled* *  現在のLHCの制限および126GeV  Higgs  massと無⽭矛盾 eB fW eH e` eg eq ··· 46 µL µR W± νµ γ (a) µL µL γ fW eH [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14]
  49. 49.   Chargino-‐‑‒Sneutrino  Contribution 49 Mass  spectrum ⇡ ≫1TeV O(100)GeV l  軽い(O(100)GeV)粒粒⼦子  :  Bino,  Wino,  Higgsino,  sleptons l  他の超対称粒粒⼦子  :  Decoupled* *  現在のLHCの制限および126GeV  Higgs  massと無⽭矛盾 eB fW eH e` eg eq ··· 46 µL µR W± νµ γ (a) µL µL γ fW eH [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14] [GeV]0m 0 1000 2000 3000 4000 5000 6000 [GeV]1/2m 300 400 500 600 700 800 900 1000 (2400GeV)q~ (1600GeV) q~ (1000 GeV) g ~ (1400 GeV)g ~ h(122GeV) h(124GeV) h(126GeV) Expected Observed Expected Observed Expected Observed Expected Observed Expected Observed Expected Observed > 0µ,0= -2m 0 ) = 30, AβMSUGRA/CMSSM: tan( Status: ICHEP 2014 ATLAS Preliminary = 8 TeVs, -1 L dt = 20.1 - 20.7 fb∫ τ∼ LSP not included.theory SUSY σ95% CL limits. 0-lepton, 2-6 jets 0-lepton, 7-10 jets 0-1 lepton, 3 b-jets 1-lepton + jets + MET 1-2 taus + 0-1 lept. + jets + MET 3 b-jets≥2SS/3 leptons, 0 - arXiv: 1405.7875 arXiv: 1308.1841 arXiv: 1407.0600 ATLAS-CONF-2013-062 arXiv: 1407.0603 arXiv: 1404.2500 [GeV]g~m 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 [GeV] 1 0 χ∼m 200 400 600 800 1000 forbidden 1 0 χ∼tt →g~ = 8 TeVs),g~) >> m(q~, m(1 0 χ∼tt→g~production,g~g~ ICHEP 2014 ATLAS Preliminary Expected Observed Expected Observed Observed Expected 10 jets≥0-lepton, 7 - 3 b-jets≥0-1 lepton, 3 b-jets≥2SS/3 leptons, 0 - arXiv: 1308.1841 arXiv: 1407.0600 arXiv: 1404.2500 ]-1 = 20.3 fb int [L ]-1 = 20.1 fb int [L ]-1 = 20.3 fb int [L not included.theory SUSY σ95% CL limits. Colored  superparticles  >  ~∼1TeV [https://twiki.cern.ch/twiki/bin/view/AtlasPublic/SupersymmetryPublicResults#Summary_̲plots_̲status_̲July_̲2014]
  50. 50.   Chargino-‐‑‒Sneutrino  Contribution 50 Mass  spectrum ⇡ ≫1TeV O(100)GeV l  軽い(O(100)GeV)粒粒⼦子  :  Bino,  Wino,  Higgsino,  sleptons l  他の超対称粒粒⼦子  :  Decoupled* *  現在のLHCの制限および126GeV  Higgs  massと無⽭矛盾 eB fW eH e` eg eq ··· 46 µL µR W± νµ γ (a) µL µL γ fW eH [Endo,  Hamaguchi,  Iwamoto,  TY,  ʼ’14] Scalar  top  >>  1TeV [Hahn,  Heinemeyer,  Hollik,  Rzehak,  Weiglein,  ʼ’13] 3 FD approach in the e leading and sub- her up to a certain btained in the RGE all terms of Eq. (4) n terms of mt; the ven by 3αt)/(16π))] (5) e are no logarithmic MMS S and MOS S . beyond 2-loop order tion MA ≫ MZ, to ons can be incorpo- he φ2φ2 self-energy t 1/ sin2 β). In this ons enter not only other Higgs sector nHiggs. The latest 0, which is available roved predictions as etical uncertainties ns. Taking into ac- garithmic contribu- certainty of the re- tions. Accordingly, ng from corrections p sector is adjusted running top-quark s evaluated only for er than for the full 5000 10000 15000 20000 MS [GeV] 115 120 125 130 135 140 145 150 155 Mh [GeV] FH295 3-loop 4-loop 5-loop 6-loop 7-loop LL+NLL FeynHiggs 2.10.0 Xt = 0 Xt /MS = 2 5000 10000 15000 20000 MS [GeV] 115 120 125 130 135 140 145 150 155 Mh [GeV] 3-loop, O(αt αs 2 ) 3-loop full LL+NLL H3m FeynHiggs 2.10.0 A0 = 0, tanβ = 10 FIG. 1. Upper plot: Mh as a function of MS for Xt = 0 (solid) and Xt/MS = 2 (dashed). The full result (“LL+NLL”) is compared with results containing the logarithmic contribu- tions up to the 3-loop, . . . 7-loop level and with the fixed-order FD result (“FH295”). Lower plot: comparison of FeynHiggs (red) with H3m (blue). In green we show the FeynHiggs 3-loop 2 Mh  :  Higgs  mass Ms  :  Scalar  top  mass
  51. 51.   Chargino-‐‑‒Sneutrino  Contribution 51 Electroweak  gaugino探索索   ) [GeV] 2 0 χ∼(=m 1 ± χ∼m 100 200 300 400 500 600 700 [GeV]0 1 χ∼m 0 100 200 300 400 500 600 Expected limits Observed limits arXiv:1402.70293L,,ν∼/LL ~ via0 2 χ∼± 1 χ∼ arXiv:1403.52942l,,ν∼/LL ~ via− 1 χ∼+ 1 χ∼ arXiv:1402.70293L,,τν∼/L τ∼via0 2 χ∼± 1 χ∼ arXiv:1407.0350,τ2≥,τν∼/Lτ∼via0 2 χ∼± 1 χ∼ arXiv:1407.0350,τ2≥,τν∼/Lτ∼via − 1 χ∼+ 1 χ∼ arXiv:1403.52942l+3L,via WZ,0 2 χ∼± 1 χ∼ arXiv:1501.07110+3L, ± l ± +lγγlbb+lvia Wh,0 2 χ∼± 1 χ∼ arXiv:1403.52942l,via WW, − 1 χ∼+ 1 χ∼ All limits at 95% CL =8 TeV Status: Feb 2015s,-1 Preliminary 20.3 fbATLAS ) 2 0 χ∼+ m 1 0 χ∼= 0.5(mν∼/L τ∼/L l ~m τ/µL = e/ µl = e/ 1 0 χ∼ = m 2 0 χ∼ m Z + m 1 0 χ∼ = m 2 0 χ∼ m h + m 1 0 χ∼ = m 2 0 χ∼ m 1 0 χ∼ = 2m 2 0 χ∼m Wino>slepton>Binoの場合はWino〜~数百GeVまで排除
  52. 52.   Chargino-‐‑‒Sneutrino  Contribution 52 Electroweak  gaugino探索索(Future)   ATLAS 24 5 Discovery Potential: Supersymmetry too massive and ˜c± 1 and ˜c0 2 are wino-like, which suppresses neutralino-pair production relative to neutralino-chargino production. The analysis is based on a three-lepton search, with electrons, muons, and at most one hadron- ically decaying t lepton. In order to get an estimate for the sensitivity at 14 TeV two different Scenarios (A and B) are considered, as discussed earlier. The results are shown in Fig. 21. The chargino mass sensitivity can be increased to 500–600 GeV, while discovery potential for neu- tralinos ranges from 150 to almost 300 GeV. P1 P2 ˜± 1 ˜0 2 W Z ˜0 1 ˜0 1 (a) [GeV]0 2 χ∼= m± 1 χ∼m 100 200 300 400 500 600 700 [GeV]0 1 χ∼m 0 50 100 150 200 250 300 350 400 450 500 -1 8 TeV, 20 fb (scenario A)-1 14 TeV, 300 fb (scenario B)-1 14 TeV, 300 fb ± 1 χ∼0 2 χ∼→pp 0 1 χ∼Z→ 0 2 χ∼ 0 1 χ∼W→ ± 1 χ∼ CMS Preliminary Based on SUS-13-006 discovery reachσEstimated 5 (b) Figure 21: The simplified model topology for direct ˜c± 1 ˜c0 2 production decaying to the WZ+Emiss T final state (a), and the projected 5s discovery projections for this model (b). assumptions and analysis strategies. 6.1 Direct Production of Weak Gauginos Weak gauginos can be produced in decays of squarks and gluinos or directly in weak production. For weak gaugino masses of several hundred GeV, as expected from naturalness arguments [20], the weak production cross section is rather small, ranging from 10 2 to 10 pb, and a dataset corresponding to high integrated luminosity is necessary to achieve sensitivity to high-mass weak gaugino production. Results with the 2012 data exclude charginos masses of 300 to 600 GeV for small LSP masses, depending on whether sleptons are present in the decay chain. For LSP masses greater than 100 GeV there are currently no constraints from the LHC if the sleptons are heavy . The weak gauginos can decay via ˜0 2 ! Z ˜0 1 or ˜± 1 ! W± ˜0 1, and both of these decays lead to a final state with three leptons and large missing transverse momentum. SM back- ground for this final state is dominated by the irreducible WZ process, even with a high missing transverse momentum requirement of 150 GeV. Boosted decision trees can be trained to use kinematic variables, such as the leptons0 transverse momenta, the pT of the Z-boson candidate, the summed ET in the event, and the transverse mass mT of the lepton from the W and the missing transverse momentum. The expected sensitivity for the search is calculated using a simplified model in which the ˜0 2 and ˜± 1 are nearly degenerate in mass. With a ten-fold increase in integrated luminosity from 300 to 3000 fb 1 , the discovery reach extends to chargino masses above 800 GeV, to be compared with the reach of 350 GeV from the smaller dataset. The extended discovery reach and comparison are shown in Fig. 10. Mass (GeV)2 0 χ∼and1 ± χ∼ 100 200 300 400 500 600 700 800 Mass(GeV)1 0 χ∼ 100 200 300 400 500 600 700 ATLAS Simulation , 95% exclusion limit-1 3000 fb discovery reachσ, 5-1 3000 fb , 95% exclusion limit-1 300 fb discovery reachσ, 5-1 300 fb =14 TeVs Figure 10: Discovery reach (solid lines) and exclusion limits (dashed lines) for charginos and neutralinos in ˜± 1 ˜0 2 ! W(?) ˜0 1Z(?) ˜0 1 decays. The results are shown for the 300 fb 1 and 3000 fb 1 datasets. CMS 14TeV  LHCでWino〜~1TeVまで探索索可能 [ATLAS-‐‑‒PHYS-‐‑‒PUB-‐‑‒2013-‐‑‒007] [CMS-‐‑‒NOTE-‐‑‒13-‐‑‒002]
  53. 53.   Neutralino-‐‑‒smuon  contribution 53 Muon  g-‐‑‒2  (Higher  order  corr.  1,  ~∼10%) l  QEDのLeading  Log  correction   l  Bino  couplingに重い粒粒⼦子がdecoupleした効果 1 + 2loop = Ç 1 4↵ ⇡ ln msoft mµ å 1 + 1 4⇡ ✓ 2↵Y b + 9 4 ↵2 ◆ ln Msoft msoft egL = gY + egL ' gY  1 + 1 4⇡ ✓ ↵Y b + 9 4 ↵2 ◆ ln Msoft msoft egR = gY + egR ' gY  1 + ↵Y 4⇡ b ln Msoft msoft aµ = (1 + 2loop ) ⇥ a1loop µ Leading  Log Bino  coupling 重い粒粒⼦子のスケール 軽い粒粒⼦子のスケール b = 41 6 (# of the generations of light sleptons)
  54. 54.   Neutralino-‐‑‒Smuon  Contribution 54 Mass  spectrum eB e`L e`R eg eq fW ··· ⇡ ≫1TeV O(100)GeV l  軽い(O(100)GeV)粒粒⼦子  :  Bino,  sleptons l  他の超対称粒粒⼦子  :  Decoupled* *  現在のLHCの制限および126GeV  Higgs  massと無⽭矛盾 46 Dissertation / µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL W µL γ µR γ fW eH [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13]
  55. 55.   Neutralino-‐‑‒smuon  contribution 55 Muon  g-‐‑‒2  (Higher  order  corr.  2,  ~∼10%) l  Yukawaの補正  (Non-‐‑‒Holomorphic  Yukawa) -‐‑‒  MSSMのYukawaとSMのYukawaのmatchingの際に出現 m` = `L `R + hHdi hHui `L `R SUSYSUSY Y MSSM ` = m` v cos 1 1 + ` `
  56. 56.   Neutralino-‐‑‒smuon  contribution 56 Bino  coupling SUSY  limitではU(1)Y  ゲージ結合と等しい (重い粒粒⼦子の)  SUSY  breakingの効果でズレが発⽣生 Coupling EnergyMsoftmsoft egBino = gY gY egBino egBino 重い粒粒⼦子 decouple  くりこみ群の runが変化 イメージを表示できません。メモリ不足のためにイメージを開くことができないか、イメージが破損している可能性が あります。コンピューターを再起動して再度ファイルを開いてください。それでも赤い x が表示される場合は、イメー ジを削除して挿入してください。 -‐‑‒  Interaction -‐‑‒  Bino  coupling egL = gY + egL ' gY  1 + 1 4⇡ ✓ ↵Y b + 9 4 ↵2 ◆ ln Msoft msoft egR = gY + egR ' gY  1 + ↵Y 4⇡ b ln Msoft msoft b = 41 6 (# of the generations of light sleptons)
  57. 57.   Slepton  Mass  Bound 57 スカラーポテンシャル l  Up-‐‑‒type  HiggsとSlepton l  Slepton-‐‑‒Higgsの3点相互作⽤用 l  Sleptonの4点相互作⽤用 V = (m2 Hu + µ2 )|Hu|2 + m2 e`L |e`L|2 + m2 e`R |e`R|2 (Y`µH⇤ u e`⇤ L e`R + h.c.) + Y 2 ` |e`⇤ L e`R|2 + g2 8 (|e`L|2 + |Hu|2 )2 + g2 Y 8 (|e`L|2 2|e`R|2 |Hu|2 )2 + g2 + g2 Y 8 H |Hu|4 mixing Flavor  dep. -‐‑‒  Sleptonの混合に⽐比例例 -‐‑‒  極端に⼤大きいとEW  vacuumが不不安定になる -‐‑‒  LeptonのYukawaに⽐比例例  (=tanβが⼤大きい極限でにtanβに⽐比例例) -‐‑‒  tanβを⼤大きくすると真空の安定性条件をゆるくする⽅方向に働く -‐‑‒  Stauの場合は若若⼲干依存、Selectron/Smuonは依存性無視できる
  58. 58.   Slepton  Mass  Bound 58 真空崩壊 l  Decay  rate /(Volume) = A· e B ~∼(100GeV)4 Bounce解から評価 -‐‑‒  偽の真空の基底状態のエネルギーの虚部から出現 -‐‑‒  境界条件 -‐‑‒  境界条件のもとでの運動⽅方程式の解:Bounce解 = 2ImE0, E0 = lim T!1 1 T ln ÇZ [D ]exp( SE[ ]) å Φ=Up-‐‑‒type  Higgs,  Sleptons,  SE  はユークリッド作⽤用 lim T!1 ✓ !x ,± T 2 ◆ = f イメージを表示できません。メモリ不足のためにイ メージを開くことができないか、イメージが破損し 偽の真空での場の配位 [Coleman,  ʻ‘77] [Callan,  Coleman,  ʻ‘77]
  59. 59.   Slepton  Mass  Bound 59 真空崩壊 l  Bounce解  (Path  deformation  method) -‐‑‒  運動⽅方程式  (O(4)  symmetric,  zero  temp.  :  α  =  3) -‐‑‒  最初にPathにあたりをつける -‐‑‒  Pathを変形させて運動⽅方程式の解になるものを探す ! guess = ! (x), d ! dx = 1 (仮定) Figure 4: Path deformation in two dimensions. The normal force exerted on path (blue straight line) pushes it in the direction of the true tunneling so curved line). [CosmoTransitions,  ʻ‘11] d2 ! d⇢2 + ↵ ⇢ d ! d⇢ = rV( ! ) d2 x d⇢2 + ↵ ⇢ dx d⇢ = @ @ x V( ! ) d2 ! d⇢2 ✓ dx d⇢ ◆2 = r?V( ! ) (Path⽅方向) (垂直⽅方向) V true false cf.)  Overshoot/Undershoot  method Multi-‐‑‒dimensionだと⼀一意に求められない
  60. 60.   Slepton  Mass  Bound 60 Fitting  Formula   200 300 400 500 600 200 300 400 500 600 l  Stauの場合 µtan , tan = 70 30 20TeV 40 50 60 70 90 80 [Kitahara,  TY,  ʻ‘13] [Endo,  Kitahara,  TY,  ʻ‘14]
  61. 61.   Slepton  Mass  Bound 61 Fitting  Formula   l  tanβ依存性 20 40 60 80 100 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 -‐‑‒  スカラーの4点はYukawaに依存  (                                            ) -‐‑‒  tanβが⼤大きい極限で(tanβ)2に⽐比例例 -‐‑‒  tanβを⼤大きくするとVacuumの制限が若若⼲干改善* [Kitahara,  TY,  ʻ‘13] 改善悪化 ここで1に規格化 *  1,2世代のsleptonの場合は、Yukawaが⼩小さいため、tanβ依存性は無視できる
  62. 62.   Slepton  Mass  Bound 62 Stau  mass  dependence Massの制限はstauとsmuonのmassの⽐比に依存 Vacuum  bound 〜~400GeV 〜~600GeV me⌧/meµ = 1 me⌧/meµ = 2 me⌧/meµ 1 stauによって制限 (3点結合はYukawaに⽐比例例) meµ Æ 500GeV smuonによって制限 (stauがdecoupleしたとき) meµ Æ 2TeV [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] stauが重くなると 制限が弱くなる
  63. 63.   Universal  Case 63 -‐‑‒  Mass -‐‑‒  混合 -‐‑‒  LHC mee = meµ = me⌧ (縮退) 真空の安定性条件を満たす 中で最⼤大の値を各点で選ぶ LHC  Status e`e` e0 1e0 1 ` ` [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] Smuon  mass  <  500GeVに制限される g-‐‑‒2 1σ 2σ Excluded  by  long-‐‑‒lived  stau  search pp ! e`e`⇤ ! `+ ` + Emiss T
  64. 64.   Universal  Case 64 -‐‑‒  Mass -‐‑‒  混合 -‐‑‒  LHC mee = meµ = me⌧ (縮退) 真空の安定性条件を満たす 中で最⼤大の値を各点で選ぶ LHC  Status e`e` e0 1e0 1 ` ` (Dilepton  search)が有効 [ATLAS  Collaboration,  JHEP  05  (2014)  035] [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] pp ! e`e`⇤ ! `+ ` + Emiss T pp ! e`e`⇤ ! `+ ` + Emiss T
  65. 65.   Universal  Case 65 ILC  (smuon) [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] Smuonにmassの差がある場合はILCが有効 偏極ビームを⽤用いることで断⾯面積がenhance p s = 1TeV p s = 1TeV Polarization
  66. 66.   Universal  Case 66 ILC  (selectron) [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] t-‐‑‒channel  Bino  exchangeのため断⾯面積がenhance Bino  couplingの測定にも有効 p s = 1TeV -‐‑‒  Diagram  (t-‐‑‒channel) -‐‑‒  Bino  coupling eB ee ee⇤ e+ e ü  重い粒粒⼦子の効果でO(%)変化 ü  ⾼高精度度のCouplingの測定から重いスケールを探れるかも [Nojiri,  Fujii,  Tsukamoto,  ʻ‘96] [Nojiri,  Pierce,  Yamada,  ʼ’97]
  67. 67.   Non-‐‑‒Universal  Case 67 Smuon  mass  bound 500 1000 1500 2000 500 1500 2500 3500 meµ < me0 1 Smuon-‐‑‒Higgsポテンシャルの安定性条件から   smuon  mass  <  2TeVに制限される -‐‑‒  Mass -‐‑‒  混合 mee = meµ ⌧ me⌧ (stauはdecouple) meµL = meµR , tan = 40 真空の安定性条件を満たす 中で最⼤大の値を各点で選ぶ Smuon  mass  <2TeVは 加速器実験の探索索可能領領域を超えている [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13]
  68. 68.   Non-‐‑‒Universal  Case 68 Fermionを対⾓角にする基底で Slepton質量量⾏行行列列に⾮非対⾓角項が出現 Sleptonの質量量が縮退していない場合、 GIM機構が働かないため、LFV/CPVを誘発 LFV/CPV                         (対⾓角)  である模型でも Fermionを対⾓角にする基底とは⼀一般に揃わない ⇣ m2 e` ⌘ i j = diag ⇣ m2 ee , m2 eµ, m2 e⌧ ⌘ LFV/CPVはSlepton質量量⾏行行列列の⾮非対⾓角項に敏感
  69. 69.   Non-‐‑‒Universal  Case 69 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] Flavor  mixingの定義 l  SleptonがFlavor  diagonalである基底でのYukawa: l  Fermion  massを対⾓角にする基底でのYukawa: l  Mixing  matrix:世代間の混合をparameterize Mixing  matrix  :  基底間のズレ
  70. 70.   Non-‐‑‒Universal  Case 70 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] ex)  Lepton  FCNCs l  Effective  operator  (双極⼦子型) l  Wilson係数 l  Flavor  mixing Leff ⌘ e m`i 2 `i µ⌫ ⇣ AL i j PL + AR i j PR ⌘ `j Fµ⌫ + h.c. Higher-‐‑‒order   correction Loop  function AL i j = (1 + 2loop ) ↵Y 8⇡ M1µtan m`j X a,b=1,2,3 h UR i ib h M` i ba h U† L i aj Fa,b AR i j = (1 + 2loop ) ↵Y 8⇡ M1µtan m`j X a,b=1,2,3 h UL i ia h M† ` i ab h U† R i bj Fa,b h UL i 1a h M† ` i ab h U† R i b2 Fa,b = mµ 1 + µ ( L)12 Ä F1,2 F2,2 ä + m⌧ 1 + ⌧ ( L)13( R)⇤ 23 Ä F1,2 F1,3 F3,2 + F3,3 ä SelectronとSmuonが縮退 していればキャンセル Sleptonが全て縮退 していればキャンセル 46 Dissertation µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL W µL µR µL B H0 d γ (d) µL µR µR H0 d B γ (e) Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 The diagram (a) comes from the chargino–muon sneutrino diagram, the from the neutralino–smuon diagram. χ0 mµ 6 4 1 mµ L(e) 2 R(e) 2 N fW eH eµL eµReeR eR
  71. 71.   Non-‐‑‒Universal  Case 71 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] ex)  Lepton  FCNCs l  μ→eγ崩壊 l  電⼦子の電気双極⼦子モーメント l  Muon  g-‐‑‒2との相関 46 Dissertation µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL W µL µR µL B H0 d γ (d) µL µR µR H0 d B γ (e) Figure 3.4: The diagrams of the SUSY contributions to the muon g − 2 The diagram (a) comes from the chargino–muon sneutrino diagram, the from the neutralino–smuon diagram. χ0 mµ 6 4 1 mµ L(e) 2 R(e) 2 N fW eH eµL eµReeR eR de e = me 2 Im î AL 11 AR 11 ó B(µ ! e ) ' 48⇡3 ↵ G2 F Ä |AL 12|2 + |AR 12|2 ä Br(µ ! e ) ⇣ aNeutralino µ ⌘2 ' 1 (µ ! all) ↵mµ 16 13 23 2 Ç m⌧ mµ å2 + (higher order) de/e aNeutralino µ ' 1 2mµ Im[( R)13( L)⇤ 13] m⌧ mµ + (higher order) Stauが⼗十分重いとき、SUSY粒粒⼦子の質量量と独⽴立立
  72. 72.   Non-‐‑‒Universal  Case 72 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] ex)  μ→eγ崩壊 Br(µ ! e ) ⇣ aNeutralino µ ⌘2 ' 1 (µ ! all) ↵mµ 16 13 23 2 Ç m⌧ mµ å2 + (higher order) l  Stauは1,2世代のSleptonより重い: l  SelectronとSmuonは縮退:1-‐‑‒2世代間の混合の寄与はsuppress mee = meµ ⌧ me⌧ 仮定 Stauが1,2世代のSleptonより⼗十分重い場合 μ→eγとMuon  g-‐‑‒2の⽐比はBino,  slepton  massと独⽴立立 Flavor  mixingの定義 46 Diss µL µR W± νµ γ (a) µL µR µL µR B γ (b) µL µR µL B H0 γ µL µR H0 fW eH eµL eµReeR eR
  73. 73.   Non-‐‑‒Universal  Case 73 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] Non-‐‑‒Universality Smuonが重いほどMuon  g-‐‑‒2の説明のために ⼤大きなNon-‐‑‒Universalityが要求される
  74. 74.   Non-‐‑‒Universal  Case 74 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] ex)  μ→eγ崩壊 SleptonがLHC,  ILCで発⾒見見されなくても レプトンフレーバー実験から⾼高感度度で探索索可能 =Non-‐‑‒Universality 現在の Bound 将来の 感度度 -‐‑‒  Mass -‐‑‒  Formula mee = meµ ⌧ me⌧ Br(µ ! e ) Br(µ ! e ) ⇣ aNeutralino µ ⌘2 ' 1 (µ ! all) ↵mµ 16 13 23 2 Ç m⌧ mµ å2 + (higher order) Stauが⼗十分重い(R≫1)とき L 13 R ⇤ 23 Æ 3 ⇥ 10 6 L 13 R ⇤ 23 Æ 10 7⇠8 (Current) (Future) VubVcb ⇠ 10 4 cf)  CKM-‐‑‒like
  75. 75.   Non-‐‑‒Universal  Case 75 [Endo,  Hamaguchi,  Kitahara,  TY,  ʻ‘13] SleptonがLHC,  ILCで発⾒見見されなくても レプトンフレーバー実験から⾼高感度度で探索索可能 =Non-‐‑‒Universality 現在の Bound 将来の 感度度 -‐‑‒  Mass -‐‑‒  Formula mee = meµ ⌧ me⌧ Stauが⼗十分重い(R≫1)とき (Current) (Future) ex)  電⼦子の電気双極⼦子モーメント de/e aNeutralino µ ' 1 2mµ Im[( R)13( L)⇤ 13] m⌧ mµ + (higher order) Im L 13 R ⇤ 13 Æ 6 ⇥ 10 8 Im L 13 R ⇤ 13 Æ 6 ⇥ 10 9⇠10 de/e
  76. 76.   Non-‐‑‒Universal  Case 76 Sleptonのmassが縮退していない場合、 ⼀一般に⼤大きなLFV/CPVを誘発 Smuon-‐‑‒Higgsポテンシャルの安定性条件から smuon  mass  <  2TeVに制限される まとめ SleptonがLHC,  ILCで発⾒見見されなくても レプトンフレーバー実験から⾼高感度度で探索索可能
  77. 77.   Extra-‐‑‒Slides 77 Future  Prospects for  Stau Based  on    T.  Kitahara  and  T.Y    JHEP  05  035  (2013)    M.  Endo,  T.  Kitahara,  and  T.Y    JHEP  04  139  (2014)
  78. 78.   Stau 78 Higgs  Oblique  Correction   l  Loop-‐‑‒induced  Higgs  coupling l  新しい物理理にsensitive -‐‑‒  Higgs  to  digluon,  diphoton,  Zγ -‐‑‒  間接的に新しい物理理を制限 -‐‑‒  SM:tree  levelで出現しない -‐‑‒  新しい物理理の影響を受けやすい NPh V V制限 予⾔言 実験 新しい物理理
  79. 79.   Stau 79 Higgs  coupling  to  diphoton  κγ l  Current  accuracy  (LHC) l  Joint  analysis  ⌘ gh gh (SM) = 1 +  ,  ⇠ 15% -‐‑‒  Br(h→γγ)/Br(h→ZZ)はHL-‐‑‒LHCで精密測定  (3.6%と仮定) -‐‑‒  Br(h→ZZ)は初期ステージでのILCで精密測定  (sub%  level) -‐‑‒  両者の結果を合わせると単体での測定よりもκγを精密に決定可能  ⇠ 1 2% [Peskin,  ʻ‘13] 5% 4% 3% 2% 1% γ CMS-1 CMS-2 ILC ILC + LHC BR ratio CMS 250 500 500up 1000up1000 6% 7%  -‐‑‒  HL-‐‑‒LHC,  ILC単体だとO(1-‐‑‒10)% -‐‑‒  Joint  analysis
  80. 80.   Stau 80 Higgs  coupling  to  diphoton  κγ l  Loop-‐‑‒induced  Higgs  coupling l  新しい物理理にsensitive l  HL-‐‑‒LHCと初期のILCから1-‐‑‒2%の決定精度度が期待 将来excessが⾒見見えた場合に分かる 新しい物理理の性質を考察しておくことは重要 l  博⼠士論論⽂文では超対称模型を仮定 l  Muon  g-‐‑‒2を考慮すると、軽いStauが予想 l  初期のILCまでで数%のexcessが観測されたと仮定 新しい物理理
  81. 81. l  Stau  :  κγのみに⼤大きな寄与 l  3つのParameterでcontroll  (mass,  mixing  angle)   l  Stauが軽い&⼤大きな混合を持つ場合にenhance  (O(10)%) l  極端に⼤大きな混合は真空の安定性条件により制限   Stau 81 Stau  contribution  to  κγ Dissertation / Takahiro Yoshinaga τR τL h γ γ gure 3.6: Feynman diagram of the stau contribution to the Higgs coupling to di-photon. re OL,R are the unitary matrices, which diagonalize the chargino mass matrix, as seen in 3.3.1. δm2 fLL,RR and δm2 fLR are defined as m2 e⌧LR = 1 2 ⇣ m2 e⌧1 m2 e⌧2 ⌘ sin2✓e⌧ m2 e⌧1 , m2 e⌧2 , ✓e⌧ Ue⌧Me⌧U† e⌧ = diag(m2 e⌧1 , me⌧2 ) Ue⌧ = ✓ cos✓e⌧ sin✓e⌧ sin✓e⌧ cos✓e⌧ ◆ cf.)  Stauの質量量⾏行行列列
  82. 82.   Stau 82 Stau  contribution  to  κγ [Endo,  Kitahara,  TY,  ʻ‘14] 真空の安定性条件からκγの⼤大きさは制限 10-‐‑‒15%が取りうるexcessの最⼤大値 Large  mixing  angle:真空の安定性条件で制限
  83. 83.   Stau 83 Stau  mass  region [Endo,  Kitahara,  TY,  ʻ‘14] δκγ>4%ならば、      250GeVに制限 √s  =500GeV  ILCまでで発⾒見見可能 me⌧1 < Higgs  coupling  to  diphoton sin2✓e⌧ = 1 真空の安定性条件を満たす なかで最⼤大の値を選択tan = 20
  84. 84. l  仮定 l  Sample  point l  Reconstruction  (ILC  at  √s  =  500GeV)   Stau 84 Stau  searches  (Reconstruction) -‐‑‒  Stau1,2,  mixing  angle全てがILC  (√s  =  500GeV)で観測 -‐‑‒  κγは数%のexcessが観測、測定精度度は2%と仮定 88 Dissertation / Takahiro Yoshinaga Table 4.3: Model parameters at our sample point. In addition, tanβ = 5 and Aτ = 0 are set, though the results are almost independent of them. Parameters mτ1 mτ2 sin2θτ mχ0 1 δκγ Values 100 GeV 230 GeV 0.92 90 GeV 3.6% 4.3 Stau So far, we studied the prospects for the selection/smuon searches. In this section, we discuss the stau searches. If the staus have masses of (100)GeV and large left-right mixing, the Higgs coupling to the di-photon κγ is deviated from the SM prediction. Such a large left-right mixing is constrained by the vacuum meta-stability condition of the stau-Higgs potential, as mentioned in Sec 4.1.3. Then, we discussed that once the deviation from the SM prediction of κγ were observed, the mass region for the staus were determined by the condition in Sec. 4.1.4. Once the stau is discovered at ILC, its properties including the mass are determined. Par- ticularly, it is important to measure the mixing angle of the stau θτ. When sin2θτ is sizable, [Endo,  Kitahara,  TY,  ʻ‘14] me⌧1 ⇠ 0.1 GeV, me⌧2 ⇠ 6 GeV, sin2✓e⌧ sin2✓e⌧ ⇠ 2%  ⇠ 0.5% excessがStau起源かcheck可能
  85. 85. l  仮定 l  Sample  point  (stau2は√s  =  500GeVでは未発⾒見見) l  Prediction  for  stau2  (ILC  at  √s  =  1TeV)   Stau 85 Stau  searches  (Prediction) -‐‑‒  Stau1,  mixing  angleがILC  (√s  =  500GeV)で観測、stau2は未発⾒見見 -‐‑‒  κγは数%のexcessが観測、測定精度度は2%と仮定 [Endo,  Kitahara,  TY,  ʻ‘14] Table 1: Model parameters at our sample point. In addition, tanβ = 5 and Aτ = 0 are set, though the results are almost independent of them. Parameters mτ1 mτ2 sin2θτ mχ0 1 δκγ Values 150 GeV 400 GeV 0.91 140 GeV 5.6% me⌧1 ⇠ 0.1 GeV, sin2✓e⌧ sin2✓e⌧ ⇠ 2.5%,  ⇠ 2% √s  =  1TeV  ILCで発⾒見見が期待、ビームエネルギーを調節するためのヒントを与える

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