1. 1 Effects of New Physics on CP violation in B decays July 17, 2003 HEP2003, Aachen

2. 17 July, HEP2003George W.S. Hou 2 Outline b ⇄ s Phenomena: Current Frontier for NP Flavor Models w/ 1 Extra CP Phase in b ⇄ s 4th Generation Large s R -b R Mixing w/ SUSY: Light Squark 4th Generation & b → s ℓ + ℓ −,  m B s, sin2  B s — Does Not Touch EM/Strong Penguins Much Light and S  K s, S  ’K s,  m B s, sin2  B s Survive b → s  Tune for S  K s, S  ’K s Possible Consequences:  m B s, sin2  B s, wrong  helicity Conclusion Based on A. Arhrib and WSH, EPJC 27, 555 (2003) A. Arhrib, C.K. Chua and WSH, PRD 65, 017701 (2001) C.K. Chua, WSH and M. Nagashima, to appear

3. 17 July, HEP2003George W.S. Hou 3 Present b ⇄ s Phenomena: Current NP Frontier CP Phase sin2  B d ≅ 0.8 Agree with CKM Fit but  3 ≅ 60 ∘ CKM Fit v.  3 ~ 90 ∘ B → K  /  Modes Although sin2  B d →  ’K s ≅ sin2  B d but sin2  B d →  K s Opposite Sign !? b → s ℓ + ℓ − > SM?  m B s “Just Around the Corner ” but if sin2  B s ≠ 0 ➯ NP b → s  L ? Wrong Helicity Component? Test via B s →    Mixing-dep CPV  b →     Polarization (Near) Future

4. 17 July, HEP2003George W.S. Hou 4 4th Generation: In general 3 New CP Phases Restrict to b ⇄ s Only: Just One New CP Phase Phase  s Neglected in Literature ! Large s R -b R Mixing w/ SUSY: Light Squark Just One New CP Phase Models w/ 1 Extra CP Phase in b ⇄ s  Flavor-driven Light s-b Flavored Squark Flavor Symmetry ⊕ Supersymmetry

5. 17 July, HEP2003George W.S. Hou 5 4th Generation 4th Generation Effect Formalism Take Hamiltonian for b → s  Phase  s has been Neglected in Literature usual term Satisfies GIM Parameters ≅ −0.04 ~ 0.0006

6. 17 July, HEP2003George W.S. Hou 6 b → s ,  m B s Complementary - b → s  Weak m t’ –dep ➯ Not So Constraining -  m B s Strong m t’ –dep ➯ Not Constructive Interf.  s =  /,  /  s =  /2, 3  /2 Most Forgiving ∵ Add in quadrature Constraints: b → s ,  m B s Expt. dashed: b → s , solid:  m B s Choose param. ➯ SM Values

7. 17 July, HEP2003George W.S. Hou 7 Constraint/Test: b → s ℓ + ℓ − Rate EW Penguin has Strong m t’ –dep., Just Like B s Mixing Yet to Settle (a bit high) SM ~ NNLO SM3 ~ (0.8−1.7) x 10 -6 ~ (0.5−0.8) x 10 -6 Less hadronic uncertainty Maybe high vs. NNLO More Stringent than  m B s Improve Soon ➯ Improve Soon !  s ~  /,  /  s ~  /2, 3  /2 r s Allow Larger r s May be Needed If NNLO Remains Low No Further Info in m 2 (ℓℓ) Constrained by BR ➯ A FB ~ SM

8. 17 July, HEP2003George W.S. Hou 8 sin 2  B d Agree with SM3, but May be Affected by Any sin 2  B s ≠ 0 Implies NP !! sin 2  B s = 0 Strictly in SM3 ➯ Any sin 2  B s ≠ 0 Implies NP !! The Highlight: Large sin2  B s ≠ 0 Def. A, B, C are quadratic fns of m t, m t’ 250 GeV 350 GeV rsrs rsrs 0.02 0.01 0.002 0.005 0.004 0.002 r s Even for Small r s sin 2  B s sin 2  B s Can be Large Both Signs Possible Largest If  m B s “Just Around Corner”  s ~  /,  / i.e. when  s ~  /2, 3  /2  m B s Quite Measurable sin 2  B s ~ ± 1 Good at Tevatron !

9. 17 July, HEP2003George W.S. Hou 9 But, … 4th Generation Not Effective on EM & Strong Penguins b → s  affected only when r s (and m t’ ) gets large No Mixing CPV because (L) Chirality Same as SM b → sg* Even Less Affected ➯ Cannot Touch S  K s, S  ’K s etc. Turn to one that Can

10. 17 July, HEP2003George W.S. Hou 10 Light Light & S  K s, S  ’K s,  m B s, sin2  B s 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

11. 11 Right-handed Quarks Inert in SM S  Right-handed Squarks SUSY Assume RR Sector Impact b ⇄ s SUSY thru SUSY also important

12. 17 July, HEP2003George W.S. Hou 12 Level Splitting by Large Mixing  Drive One State Light 100 GeV Possible 1 CP Phase Focus on 200 GeV

13. 17 July, HEP2003George W.S. Hou 13 Rates B →  K s,  ’K s Rates More Conservative Survive b → s  Constraint Cannot Account of  ’K s Rate  K s Rate also a bit Low But, Not New Problems

14. 17 July, HEP2003George W.S. Hou 14 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

15. 17 July, HEP2003George W.S. Hou 15 Tune for 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 ! S  K s Lower gluino mass lowers S  K s Hadronic Parameters CP phase enters B →  K s via Lower q 2, larger S  K s ➯ Larger | S  K s | If B →  ’K s rate due to (SM) S  ’K s QCD Effect ➯ S  ’K s drops a bit Could  ≃ 3  /2 be it? noticed also by Khalil & Kou Murayama et al.

16. 17 July, HEP2003George W.S. Hou 16  m B s, sin2  B s Consequences:  m B s, sin2  B s Take  ≃ 3  /2 as example 800 GeV gluino “preferred”  m B s ~ 20-40 ps -1 -  m B s ~ 20-40 ps -1 “Easy” sin2  B s ~ −1 - sin2  B s ~ −1 Super Lighter gluino at 500 GeV  m B s > 60 ps -1 -  m B s > 60 ps -1 Tougher sin2  B s ~ −1 - 0 - sin2  B s ~ −1 - 0 For lighter gluino, periodicity change ∵ a -term dominant (two exch.) 100 GeV 100 GeV ~ 200 GeV case Direct Detection ! Except, Direct Detection !

17. 17 July, HEP2003George W.S. Hou 17 Strength of Mixing-dep. CPV B s →  in, e.g. B s →   L Test  L component (Atwood, Gronau, Soni, 1997) (Atwood, Gronau, Soni, 1997)  L Can also test  L comp. via  Polarization in  b →    (Mannel, Recksiegel, 1997) (Mannel, Recksiegel, 1997) Wrong Helicity Photon in b → s  L More: Wrong Helicity Photon in b → s  L All Testable at Tevatron and Beyond and Beyond

18. 17 July, HEP2003George W.S. Hou 18 Conclusion New CP Phase Impact of 4th Generation (Emphasized New CP Phase) B s Mixing & CPV Prominent in - B s Mixing & CPV - EW b → s Penguin Mild in EM/Strong Penguin A Light Flavor-mixed Squark? Survive b → s  S  K s S  ’K s Can Account for S  K s, S  ’K s  m B s sin2  B s  L Strong Impact on:  m B s, sin2  B s, b → s  L ➯ Study at B Factories, Tevatron, and …