4th / B George W.S. Hou (NTU) ITEP, 7/24/06 1 Fourth Generation Manifestations in B Decays July 24, 2006, ITEP, Moscow.

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4th / B George W.S. Hou (NTU) ITEP, 7/24/06 1 Fourth Generation Manifestations in B Decays July 24, 2006, ITEP, Moscow

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 2 Outline I Introduction: Rates vs CPV 7  A II  A = A K  +     A K  +     0 10  S LO PQCD;  S in QCDF; Towards NLO PQCD III Consistency and b  s Predictions 4 sin2  B s b  s ll vs  m B s ; sin2  B s ; A K *  ; IV 4 x 4 Unitarity: Z  bb and Kaon constraints sin2  B d Predictions — K L    ; (  m D ;) sin2  B d ; 6 A K + J/  & A K + J/  3 V Conclusion 1 coworkers M. Nagashima, G. Raz, A. Soddu + H.n. Li, S. Mishima _

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 3 I. Introduction Rates vs CPV Rates: Pure EWP Z dominance for heavy top Measured Belle ’02 nondecoupling WSH, Soni, Willey, PRL’87 Rates: P-EWP Interference Deshpande and He, PRL’95 (also Buras and Fleischer) Deshpande, He, WSH and Pakvasa, PRL’99 KK KK KK KK _d_d d  KK u u BB sb KK KK KK KK Stimulated by CLEO ‘98 Precursor to R c - R n

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 4 CKM05

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 5 CKM05 Comment These ratios are “bad” expt’lly: sensitive to K  and   systematics Absolute rates, even ratios, are subject to theoretical uncertainty. Direct CPV (or TCPV) are better ratios expt’lly, and theoretically: subject to strong phase only. No CPV Phase in V ts ? Great ! New Physics — Probe New Physics Arhrib and WSH, EPJC’03 4th Generation as template

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 6 On Boxes and Z Penguins GIM, charm, ε K small ε’ K, K   (still waiting) heavy top, sin2    Z dominance for heavy top 1986  2002 nondecoupling All w/ 3-gen., Just wait if there’s 4th D ! b’, t LHC BsBs

4th / B George W.S. Hou (NTU) ITEP, 7/24/ th 4 th generation? — The jury is out … Particle mass ~ EW scale Natural: W, Z, H; top the only fermion, so … N = 3 N = 3, ca. 1989: b’ stock collapsed … Well, now neutrino has mass Something extra out there ➯ Pls attend A. Soddu talk at ICHEP Trouble with S parameter (PDG04, 06) ? - Possible if neutral lepton N relatively light, m N ~ 55 GeV (Maltoni,) Novikov, Okun, Razanov, Vysotsky - PDG: Direct b’/t’ search; Unitarity (CKM) listings EW  |m t’ –m b’ | ≲ M W In era of LHC, can Directly Search for b’, t ’ Once and For All ! 4 th Generation eV Seesaw and 4 th Generation Flavour

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 8 March of the B Penguins EMP:B  K*  1993 (CLEO) b  s  1995 (CLEO) Strong P:B  K  ’K1998 (CLEO) Direct CPV2004 (BaBar/Belle) 4th gen. effect subdued … EWP:B  K ℓ  ℓ  2002 (Belle) b  s ℓ  ℓ  2002 (Belle) no apparent 4th gen. effect So why bother ?

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 9 Belle PRL’04 Started theory work after this.

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 10 II  A = A K  +     A K  +     0 WSH, Nagashima, Soddu, PRL’05

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 11 Why  A = A K  +     A K  +    > 0 a Puzzle ? ?  A ~ 0 expected  10.8  1.7 %  4  4 %

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 12 _d_d d  KK u u BB sb Why  A = A K  +     A K  +    > 0 a Puzzle ? Large C ? Large EWPenguin ? Suppress Tree CPV Phase Need NP CPV Phase ∵ T and P EW ≈ same strong phase ? t, t ’ 4th Gen. in EWP Natural  A ~ 0 expected  10.8  1.7 %  4  4 %

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 13 SM 3 Effective b  s Hamiltonian and t’ Effect

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 14 SM 4 SM 3 new unitarity condition new penguin from t’ Effective b  s Hamiltonian and t’ Effect

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 15 Tree QCD penguin EW penguin SM4 naturally Impact on EWP Wilson Coefficients at M W Scale (No New Operators) nondecoupling

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 16 Factorizable Non- Factorizable Penguin Annihilation w/ Strong Phase LO PQCD TP PaPa Li, Sanda, Keum 2001

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 17

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 18 _d_d d  KK u u s b BB Factorizable Non- Factorizable P EW (Ta)(Ta) C LO PQCD

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 19 EWP

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 20 From Constraints Some parameter space allowed  sb ~  /2 favored by both A CP ( K    ) and ⊕ A CP ( K    ) ~  11, A CP ( K    ) ~ ? Independently Unchanged by  m B s measurement WSH, Nagashima, Soddu, PRL’05

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 21 Right trend for S  K, S  K S  K , S K    hep-ph/ WSH, Nagashima, Raz, Soddu QCDF NLO s3 PQCD LO NF (QCDF-LO)

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 22 Robustness Against Hadronic Uncertainty Vary H ard spectator Weak A nnihilation around QCDF “s3” value of BRs: hadr. uncertainty S  K, S  K Robust S  ’K diluted away 3  BR range QCDF

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 23 WSH, Nagashima, Soddu, PRL’05 LO PQCD ⊕ 4th Gen.  A  12% vs 15% (data) Toward NLO PQCD WC + VC + QL + MP Li, (Sanda,) Mishima NLO PQCD ⊕ 4th Gen.  A  15%  S   0.11 SM3 input vs  0.38  0.26 (data) WSH, Li, Mishima, Nagashima, in prep.

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 24 III Consistency and b  s Predictions

flavor/4th generation George W.S. Hou (NTU) JC 3/27// th generation not excluded favored allowed Arhrib and WSH Yanir Hattori, Hasuike and Wakaizumi Independently Constraints WSH, Nagashima, Soddu, PRL’05

flavor/4th generation George W.S. Hou (NTU) JC 3/27//06 26 and Prospects Just Around Corner! (SM3-like) ~  to   ! Defintely BSM if measured ! Phase Could Tevatron Measure These !? Update at ICHEP ’ 06 WSH, Nagashima, Soddu, PRL’05

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 27 Consistency and b  s  Predictions BR OK A CP ~ 0 far away beyond SuperB PDG ’06 SM3 Heavy t ’ effect decoupled for b  s 

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 28 A K     +   A K       14%  0.02  0.04  0.02  0.13 HFAG K 0  Predictions Not in good agreement — Await further test R c ≲ R n ≈ 1.08 R ≈ 0.94 (  0.11  0.18  0.08) Belle

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 29 IV 4 x 4 Unitarity: Z  bb and Kaon constraints _ WSH, Nagashima, Soddu, PRD’05 hep-ph/ ➯ A K   J/   0 ?

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 30 Parameterization for B ( ’n K; ’n b’) WSH, Soni, Steger, PLB ’87 SM3 3 new angles, 2 new CPV phases s  bs  b

4th / B George W.S. Hou (NTU) ITEP, 7/24/ x 4 Unitarity ➯ Constraints We need to deal with mixing matrix in detail to keep Unitarity From b → s study SM3 Kaon b  s b  d impose Cross Check !

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 32 Constrain s  d from K Physics (J. Bijnens et al.) (E. Pallante et al.) Therefore…. well-satisfy ! “Standard” No SM3 solution (shaded )

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 33 well-satisfy Hard to tell apart (non-trivial) with present precision ∵ stringent s  d vs V ub ~ 0.01 e -i  Disfavored

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 34 Implication for Rate enhanced up to almost two orders !! Grossman-Nir Current E391A U.L. Very hard to measure SM 3 enhanced to or even higher !! In general larger than !! ∵ Large CPV Phase

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 35 Double Cabibbo (Too) Large/Imaginary x ~ 0.22 “Typical” CKM Matrix b  s b  d

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 36 Intriguing “Prediction”: A J/  K +  0 ? _c_c c J/  KK u u BB sb t, t ’ B  J/  K + dominated by color suppressed b  ccs (a 2 ) - Inclusion of SM3 Penguin does not alter Weak Phase ~ 0 Strong Phase The amplitude above likely has Strong Phase  - B  J/  K + Rate is enhanced: “hadronic” - Analogous to enhancement seen in B   D     ➯  ° - Further support from Strong Phase in B  J/  K*:  ° Enter t ’ effect: Weak Phasee i  sb - Weak Phase e i  sb - Factorized amplitude : J/  spits off from virtual Z ➯  ° Likely Retained Expt Making of DCPV ! Interference WSH, Nagashima, Soddu, hep-ph/

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 37 Another hint: Low S J/  K ? ± ± HFAG ± UTfit vs. indirect Belle/BaBar PDG ’06 A J/  K +  0 ? PDG ’05 similar to  S  °

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 38 PDG ’06 A J/  K + is getting serious: careful studies started Systematics Study becomes Theme — Needed towards SuperB !! Could be seen by 2008 ?! Better than  A and  S ? Prognosis for A J/  K + Measurement Sign flip

4th / B George W.S. Hou (NTU) ITEP, 7/24/06 39 b  s CPV Phenomena Is Current NP Frontier S f in b  sqq A K +   -  A K +   0 Puzzle S f in b  scc ? Two Hints Can All 3 Arise from P EW w/ 4th Generation ? Seemingly Yes. Three ? Check A J/    K + V. Conclusion sin2  B s < 0 A J/    K +  0 Best Bets may be sin2  B s < 0 and A J/    K +  0 Model-indep. treatmennt: Sinha, Basuda, WSH, hep-ph/