fourth generation manifestations in b decays

4th/B George W.S. Hou (NTU) ITEP, 7/24/06 1

Fourth Generation Manifestationsin B Decays

July 24, 2006, ITEP, Moscow

http://www.ntu.edu.tw/chinese/PageN.php

http://www.ntu.edu.tw/chinese/PageB.php



Outline

I Introduction: Rates vs CPV 7

II AA = AK+ AK+ 0 10

LO PQCD; SS in QCDF; Towards NLO PQCD

III Consistency and b s Predictions 4

bsll vs mBs; sin2sin2BBss; AK*; IV 4 x 4 Unitarity: Z bb and Kaon constraints Predictions — KL ; (mD;) sin2sin2BBdd; 6

& AAKK ++J/J/ 3

V Conclusion 1coworkers M. Nagashima, G. Raz, A. Soddu + H.n. Li, S. Mishima

_



I. Introduction Rates vs CPV

Rates: Pure EWP

Z dominance for heavy top

Measured Belle ’02

nondecouplingWSH, 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

_dd

Ku u

Bsb K

K

K

K

Stimulated by CLEO ‘98

Precursor to Rc - Rn



Buras @ CKM05



Fleischer @ CKM05Comment• 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 Vts ? Great !— Probe New PhysicsNew Physics

Arhrib and WSH, EPJC’03

4th Generation as template



On Boxes and Z Penguins

GIM, charm, εK

small ε’K, K (still waiting)

heavy top, sin2

Z dominance for heavy top1986 2002

nondecoupling

All w/ 3-gen., Just wait if there’s 4th D !

b’, t ’ @ LHC

Bs



44thth generation? — The jury is out …

• Particle mass ~ EW scale Natural: W, Z, H; top the only fermion, so …

• NN = 3 = 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, mN ~ 55 GeV (Maltoni,) Novikov, Okun, Razanov, Vysotsky

- PDG: Direct b’/t’ search; Unitarity (CKM) listings

• EW|mt’ –mb’ | ≲ MW

In era of LHC, can Directly Search for b’, t ’ Once and For All !

eV Seesaw and 44thth Generation Generation

FlavourFlavour



March of the B Penguins

• EMP: B K*1993 (CLEO) b s1995 (CLEO)

• Strong P: B K’K1998 (CLEO)

Direct CPV2004 (BaBar/Belle)

4th gen. effect subdued …

• EWP: B K ℓℓ2002 (Belle)b s ℓℓ2002 (Belle)

no apparent 4th gen. effect

So why bother ?



Belle PRL’04

Started theory work after this.Started theory work after this.



II A = AK+ AK+ 0

WSH, Nagashima, Soddu, PRL’05



Why A = AK+ AK+ > 0 a Puzzle ?

?

A ~ 0 expected

10.81.7 % 44 %



_dd

Ku u

Bsb

Why A = AK+ AK+ > 0 a Puzzle ?

Large C ?

Large EWPenguin ?

Suppress Tree CPV Phase

Need NP CPV Phase∵ T and PEW

≈ same strong phase

?

t, t’ 4th Gen. in EWP Natural

A ~ 0 expected

10.81.7 % 44 %



SM 3

Effective b s Hamiltonian and t’ Effect



SM 4

SM 3

new unitarity condition

new penguin from t’

Effective b s Hamiltonian and t’ Effect



Tree

QCD penguin

EW penguin SM4 naturally Impact on EWP

Wilson Coefficients at MW Scale(No New Operators)

nondecoupling



Factorizable

Non-Factorizable

Penguin Annihilation w/ Strong Phase

LO PQCD

TP Pa

Li, Sanda, Keum 2001



_d

d

K

u u

sbB

Factorizable

Non-Factorizable

PEW (Ta) C

LO PQCD



EWP



From Constraints

• Some parameter space allowed• sb ~ /2 favored by both ACP(K) and ⊕

ACP(K) ~ 11, ACP(K) ~ +0.04 ?

IndependentlyUnchanged by

mBs measurement




Right trend for SK, SK

SK, SK

hep-ph/0603097WSH, Nagashima, Raz, Soddu

QCDF NLO s3PQCD LONF (QCDF-LO)



Robustness Against Hadronic Uncertainty

Vary H ard spectator Weak A nnihilation

around QCDF “s3” value of

• BRs: hadr. uncertainty• SK, SK Robust• S’K diluted away

3 BR range

QCDF



WSH, Nagashima, Soddu, PRL’05LO PQCD ⊕ 4th Gen.

A 12% vs 15% (data)

Toward NLO PQCDWC + VC + QL + MP Li, (Sanda,) Mishima

NLO PQCD ⊕ 4th Gen.

A 15% S 0.11

SM3 input

vs 0.380.26 (data)

WSH, Li, Mishima, Nagashima, in prep.



III Consistency and b s Predictions


flavor/4th generation George W.S. Hou (NTU) JC 3/27//06 25

4th generation not excluded

favored

allowed

Arhrib and WSH

YanirHattori, Hasuike and Wakaizumi

Independently

Constraints



flavor/4th generation George W.S. Hou (NTU) JC 3/27//06 26

and Prospects

Just Around Corner!(SM3-like)

~ to !Defintely BSMif measured !

Phase

Could Tevatron Measure These !?

Update at ICHEP ’06




Consistency and b s Predictions

BR OK ACP ~ 0 far awaybeyond SuperB

PDG ’06

SM3SM3

Heavy t’ effectdecoupledfor b s



AK+ AK 14%0.020.040.020.13 HFAG

K0 Predictions

Not in good agreement — Await further test

Rc ≲ Rn ≈ 1.08 R ≈ 0.94

(0.11 0.18 0.08) Belle



IV 4 x 4 Unitarity: Z bb and Kaon constraints_

WSH, Nagashima, Soddu, PRD’05 hep-ph/0605080

➯ AKJ/ 0 ?



Parameterization for B (’n K; ’n b’) WSH, Soni, Steger, PLB ’87

SM3

3 new angles, 2 new CPV phases

s b



4 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 dimpose

Cross Check !



Constrain s d from K Physics

(J. Bijnens et al.)

(E. Pallante et al.)

Therefore….

well-satisfy !

“Standard”

No SM3 solution

(shaded)



well-satisfy

Hard to tell apart (non-trivial) with present precision∵ stringent s d

vs Vub ~ 0.01 e-i

Disfavored



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



Double Cabibbo (Too)Large/Imaginary

tbtdVV

btdt VV

cbcdVV

ubudVV

x ~ 0.22

tbtsVV

btst VV

cbcsVV ubusVV

“Typical” CKM Matrix

b s b d



Intriguing “Prediction”: AJ/K + 0 ?

_c

cJ/

Ku u

Bsb t, t’

• B J/K+ dominated by color suppressed b ccs (a2) - Inclusion of SM3 Penguin does not alter Weak Phase ~ 0• The amplitude above likely has Strong PhaseStrong 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 PhaseWeak Phase ee

ii sbsb

- Factorized amplitude : J/spits off from virtual Z ➯ ° Likely Retained

Expt

Making of DCPV !InterferenceInterference

WSH, Nagashima, Soddu, hep-ph/0605080



Another hint: Low SJ/K ?

0.685 ± 0.0320.685 ± 0.032 HFAG 0.790 ± 0.031 UTfit

CKMfit0.752 0.0570.035

vs.

indirect Belle/BaBar

PDG ’06

AJ/K + 0 ?

PDG ’05

similar to S

°



PDG ’06

• AJ/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 AJ/K + Measurement

Sign flip



b s CPV Phenomena Is Current NP Frontier

• Sf in b sqq

• AK+- AK+0 Puzzle • Sf in b scc ?

Two Hints

Can All 3 Arise from PEW w/ 4th Generation ?Seemingly Yes.

Three ?

Check AJ/K +

V. Conclusion

Best Bets may be sin2sin2 BBss < 0< 0 and AAJ/J/KK ++ 0 0

Model-indep. treatmennt: Sinha, Basuda, WSH, hep-ph/0605194


fourth generation manifestations in b decays

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