1. Flavor A Two Particle SUSY/ Flavor Perspective on CPV in B →  K S December 15, 2003 @ 6 th ACFA LC Workshop

2. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 2 Prologue: Is there a Link btwn LC and B? Super B Upgrade Does Take Aim at SUSY Effects ! But... Could B Factory Impact on Tevatron/LHC/LC !?

3. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 3 Introduction: Intuitive Grasp of S  K s Data * * Cheon’s talk

4. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 4 Still 2.7  from 0.73 (~ 2002) World Average sin 2  1eff (  K S ) =  0.39±0.41 2002 sin 2  1eff (  K S ) =  0.15±0.33 2003 158 fb  1 : 250 fb  1 : Large Large Effective s-b Mixing New New CPV Phase Right-handed Right-handed Interaction Large,NewPhysics, Large, New Physics, b → s CPV Effect [ to get sin 2  1eff (  ’ K S ) ~ sin 2  1 ] Flavor Call for Synergies of Flavor & SUSY ?

5. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 5 Penguins (Vertex Loops) S  K S = sin 2  1 SM (KM) Prediction Possible SUSY FCNC/CPV Loop Real 

6. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 6 Flavor (approximate) Abelian Flavor Symmetry ⊕ SUSY Right-handed s-b Mixing AFSHas Right-handed s-b Mixing Right-handed Dynamics SUSYBrings in Right-handed Dynamics AFS Model Pre-existed Nir-Seiberg, PLB’93; Leurer-Nir-Seiberg, NPB’94 More Definite, yet Generic, Model Context ⇨ Constraints/Predictions ⇦ Has All Ingredients Framework

7. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 7 Abelian Flavor Symmetry and SUSY?

8. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 8 Abelian Flavor Symmetry Commuting Charges Nir-Seiberg, PLB’93; Leurer-Nir-Seiberg, NPB’94 Prominent but right-handed N.B. Need 4 Texture Zeros (Chua-WSH, PRL’01) : Set [..] = 0 Arhrib-Chua-WSH, PRD’01 Decouple d flavor Mass/Mixing Hierarchy Alternative Picture: Chang, Masiero, Murayama AFS: Independently Well Motivated GUT Diag: Mass Up-right: V CKM

9. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 9 Right-handed Quarks Inert in SM S  Right-handed Squarks SUSY Assume RR Sector Impact b ⇄ s SUSY thru SUSY also important

10. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 10 Level Splitting by Large Mixing  Drive One State Light 100 GeV Possible 1 CP Phase Focus on 200 GeV strange-beauty squark

11. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 11 Why TeV Scale SUSY? Large Flavor Violation (s-b) ⇔ Stringent Low Energy Constraints Chua-WSH, hep-ph/0110106

12. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 12 Facing B Data Arhrib-Chua-WSH, PRD’01 Chua-WSH-Nagashima, hep-ph/0308298

13. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 13 A Little Note on Formalism … Besides O 1,2 Tree O 3-6 Strong Penguin O 7-10 EM/EW Penguin also O 11,12  /g Dipole Matrix Elements evaluated via Naïve Factorization

14. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 14 B →  K s,  ’K s Rates First, Rate Constraints Survive b → s  Constraint  K s Rate “Sees Red” Cannot Account for  ’K s Rate Not a New Problem Combine b → s  and B →  K s →  ~  /2, 3  /2 ? →  ~  /2, 3  /2 ? 1, 0.5 TeV 2, 0.5 1, 0.8 TeV 2, 0.8 More Conservative

15. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 15 Tuning for S  K s ≲ 0, S  ’K s ~ S  K s Possible S  K s S  K s ≲ 0 prefers lower  -plane S  ’K s ➯ S  ’K s ≅ sin2  B d as well ! Lower gluino mass S  K s Lower gluino mass lowers S  K s Hadronic Parameters CP phase enters B →  K s via Lower q 2, and/or larger S  K s ➯ Larger | S  K s | ∴ Prefer to keep gluino mass above 500 GeV (L.E. Constraints) Could  ≲  /2 be it? Noticed also by Khalil & Kou [Murayama et al.] 0.5 TeV Preferred

16. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 16 Flavor A Two(Three)-particle SUSY/ Flavor Model?

17. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 17 The Upshot? Two-Particle SUSY Model Why TeV Scale SUSY? Large Flavor Violation (s-b) ⇔ Stringent Low Energy Constraints In fact, all other SUSY particles a “nuisance”: ), hence pushed high. Strange-beauty Squark TeV Scale SUSY w/ Strange-beauty Squark “Light” Particles: ≲ 200 GeV ≳ (≲?) 500 GeV likely LSP? unlikely ~ TeV

18. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 18 Allowed Generic Squark Bounds

19. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 19 b, s ∴ (bb+sb+bs+ss) Diluted

20. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 20 Collider Study w/ Kingman Cheung ~ 200 GeV ~ 500 GeV

21. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 21 Cross Sections at Tevatron ~ 0.1-1 pb ≲ 0.01 pb A few hundred events at few fb − 1

22. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 22 Cross Sections at LHC Now Dominant Both ~ 10 pb Somewhat forward More massive event Distinct, probe s → b

23. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 23 Cross Sections at LC ~ 10 fb

24. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 24 Detection Basically, just a light “b”-squark in Production so, Discovery not a problem. Question is Decay: bino LSP or gravatino Can be Stable? (LSP) To be studied... But, need Good b-tagging ! [s-tagging?]

25. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 25 Conclusion S  K s S  ’K s S  K s, S  ’K s Data (May) Call for - Large s-b Mixing, w/ New CPV Phase - New Right-handed Interaction Hint at a Light Flavor-mixed Squark? Independtly Well Motivated (Flavor & SUSY) S  K s ≲ 0, S  ’K s >0 Survive b → s  Account for S  K s ≲ 0, S  ’K s >0 Wait for Confirmation at B Factory [ ⇨SuperB ] ➯ Study Collider Aspect Nonstandard, Flavorful TeV SUSY Strangebeauty w/ light Strangebeauty CP Phase !? B Factory Could Impact on Tevatron/LHC/LC !

26. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 26 Backup Slides …

27. 27 2002 Status of New Phases in b  s Penguins3

28. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 28 Results stronger, but consistent (~ doubling of data) 3.5  3.5  from sin 2  1 = 0.73 Statistics dominated 2002: published (PRD’03) 2003: submitted to PRL (8/03), accepted 11/03 Belle B →  K S : 2002 vs 2003 sin 2  1eff (  K S ) =  0.73±0.64±0.22 sin 2  1eff (  K S ) =  0.96±0.50 78 fb  1 : 140 fb  1 : +0.09  0.11

29. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 29 BaBar 2003:B →  K S Systematic Issues sin 2  1eff (  K S ) =  0.18±0.51±0.09 sin 2  1eff (  K S ) = +0.45±0.43±0.07 81 fb  1 : 110 fb  1 : Data size increased and was reprocessed. Extensive checks with data and Toy MC. The large change is attributed to a 1σ statistical fluctuation. Browder @ LP03 consistent w/ 0.73 New 29 fb  1 : Gives > +1 !!

30. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 30 Abelian Flavor Symmetry Commuting Charges Nir-Seiberg, PLB’93; Leurer-Nir-Seiberg, NPB’94 Prominent but right-handed N.B. Need 4 Texture Zeros (Chua-WSH, PRL’01) : Set [..] = 0 Arhrib-Chua-WSH, PRD’01 Decouple d flavor Mass/Mixing Hierarchy Alternative Picture: Chang, Masiero, Murayama AFS: Independently Well Motivated GUT Diag: Mass Up-right: V CKM

31. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 31 Amplitudes V ∓ A S  K s vs S  ’K s Reason behind Opposite Trend in S  K s vs S  ’K s

32. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 32 B s Situation for B s Mixing and S K*   New Prospect for S K*  

33. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 33 Lighter gluino ~ 500 GeV Needed  m B s > 70 ps -1 -  m B s > 70 ps -1 Tough ! sin2  B s ~ 0 - 1 - sin2  B s ~ 0 - 1 Tough ? Would’ve preferred heavier gluino S  K s ≲ 0 but for … S  K s ≲ 0 For lighter gluino, periodicity change ∵ a -term dominant (two exch.) 100 GeV 100 GeV ? ~ 200 GeV case Direct Detection ! Except, Easier Direct Detection !  m B s, sin2  B s Consequences:  m B s, sin2  B s Take  ≲  /2 as example Tough (!?)

34. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 34  m B s Experimental Prospects for  m B s What about LHCb/BTeV ? CDF Cannot Observe (already optimistic) Nakada: Can; but CPV Program B s for B s Diificult?

35. Dec. 15, 2003 @ ACFA-LC6George W.S. Hou 35 Strength of Mixing-dep. CPV  L Test  L component (Atwood, Gronau, Soni, 1997 ) (Atwood, Gronau, Soni, 1997 ) S K s    nowPromising S K s    now Promising Free from Hadronic Uncert. Free from Hadronic Uncert. B s →  In contrast, B s →  probably washed out  L Can also test  L comp. via  Polarization in  b →    (Mannel, Recksiegel, 1997) (Mannel, Recksiegel, 1997) Wrong Helicity Photon in b → s  L Implications: Wrong Helicity Photon in b → s  L