Charmless Charmless B B VPVP Decays using Decays using Flavor SU(3) SymmetryFlavor SU(3) Symmetry

hep-ph/0307395hep-ph/0307395C.-W. Chiang, M. Gronau, Z. Luo, J. Rosner, DSC.-W. Chiang, M. Gronau, Z. Luo, J. Rosner, DS

Denis SuprunUniversity of Chicago

Denis Suprun hep-ph/0307395 2

ApproachApproach Take all available information on charmless B decays to a VP final state

and fit it with a simple model of interference between appropriate tree and penguin diagrams

Extract magnitudes and relative phases of tree and penguin amplitudes Predict amplitudes and CP asymmetries for observed and as-yet-unseen

modes

Different from CKM Fitter: We do not fit with Wolfenstein parameters λ, and . Instead, we take the CKM Fitter preferred values for λ and sin(2β) and fit for γ only

Conservative statistical errors (take account of the scaling factor S) Considerable sensitivity to γ if the results are taken at face value. The

magnitude of theoretical uncertainties is not yet clear

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Charmless Charmless BB decays decays Relatively rare decays with branching ratios of the order 10-5

Wealth of new increasingly precise measurements Many of them involve interference of a tree and a penguin

amplitude with a weak phase γ between them Nonzero (mod π) strong phases are required for CP Violation

Are well suited to constrain γ determine the magnitude of penguin contributions get some information on strong phases

CKM Fitter

results

012)(

5

Dominant types of amplitudesDominant types of amplitudes

Tree (T) Color-suppressed (C) EW penguin (PEW)Penguin (P)

Color-suppressed EW penguin ( )

Neglect

Exchange (E) Annihilation (A)Penguin

annihilation (PA)Singlet

penguin (S) CEWP

Hierarchy

:0S

CEW

EW

PPAO

PAEO

PCO

T

,:)(

,,:)(

,:)(

:1

3

2

:1S

AEO

PAPCO

PTO

P

CEW

EW

,:)(

,,:)(

,:)(

:1

3

2

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AssumptionsAssumptions Take account of tree, color-suppressed, penguin, and singlet-penguin

diagrams and EW penguin contributions to color-suppressed and singlet-penguin diagrams

Ignore OZI suppressed QCD piece of singlet-penguin. Also neglect annihilation, exchange, penguin annihilation diagrams and color-suppressed EW penguin contributions to tree and penguin diagrams

The only deviation from SU(3) is through decay constants in tree diagrams SU(3) is implied when we assume

the same phases for t and t

that QCD and EW penguins P and P and color-suppressed amplitudes C and C are related to each other as the ratio of the involved CKM parameters

that a penguin in which a gluon couples to has the same amplitude as those that couple to and

ssuu dd

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Examples of Examples of B B VPVP decays decays ρ+π-: -(tP+pP); -(|tP|ei(γ+δp)+|pP|), CP-conjugate: -(|tP|ei(-γ+δp)+|pP|)

ρ-π+: -(tV+pV); |tV|ei(γ+δv+φ)+|pV|eiφ, CP-conjugate: |tV|ei(-γ+δv+φ)+|pV|eiφ

ρ-K+: -(tV+pV ); |tV|ei(γ+δv+φ)-|p

V|eiφ, CP-conjugate: |tV|ei(-γ+δv+φ)-|pV|eiφ

No CP asymmetry when strong phases are negligible. Large ACP(ρ-π+)=-0.54±0.19 drives non-zero δv and leads to predictions of

significant CP asymmetries in other δv modes, e.g., in ρ0π+ and ωK+

ACP(ρ+π-)=-0.16±0.15 as well as ACP in other δp modes are about 1σ away from 0. Predictions: CP asymmetries in all δp modes are small

QCD factorization predicts Arg(tP/tV)0. SS and ΔS (time-dependent ρ±π analysis) help to determine Arg(tP/tV)

The only deviation from SU(3) is through decay constants in tree diagrams:

f

f

t

t K

P

P *

f

f

t

t K

V

V

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Electroweak penguinsElectroweak penguins

K*0π+: pP Br. ratio: (9.0±1.4) 10-6

K+: pP - P

EW,P/3 Br. ratio: (9.0±0.9) 10-6

Expect very small EW penguin PEW,P

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Data and Fit ParametersData and Fit Parameters 34 data points:

branching ratios and CP asymmetries in strangeness-preserving ρπ, ρη, ρη, ωπ decays (ΔS=0) strangeness-changing K*π, K*η, K*η, ρK, ωK, K decays (ΔS=1)

time-dependent parameters in ρ±π and KS decays

12 fit parameters: weak phase γ amplitudes: tP , tV , CP , CV , P

P , PV , P

EW,P , PEW,V

strong phases: δV , δP , φ

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χχ22 plot plot Three minima of aboutequal depth: γ=26o, 63o, 162o

Ambiguity can not be resolved from the BVP data alone.

Appeal to experiment:CKM Fitter: 39o<γ<80o

Appeal to theory:Minima at 26o and 162o feature large strong phases leading to Arg(tP/tV)=-(87±10)o and (38±12)o,

respectively.Arg(tP/tV)=-(20±10)o at γ=63o

γ=(63±6)o

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Phase diagram for Phase diagram for γ=63γ=63oo minimumminimum

Expect no CP asymmetry in interference between tree tP

and penguin diagrams and noticeable CP asymmetry in interference between tree tV

and penguins

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PredictionsPredictions Largest predicted CP asymmetries:

ACP(ρ0π+)=-0.16±0.04 ACP(ρ0K+)=0.21±0.10

ACP(ρ-π+)=-0.13±0.06 ACP(ρ-K+)=0.16±0.07

ACP(ωK+)=0.19±0.08

As yet unseen modes to be observed soon (in 10-6):

Predicted br. ratio: Current UL BaBar error in 2004B(K*+π0)=15.0±3.1 <31 2.19B(ρ0K0)=7.2±2.0 <12.4 1.48B(ρ+K0)=12.6±1.6 <48 1.73

ρ+K0 is a pure pV penguin and its measurement is

particularly important

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500 fb500 fb-1 -1 samplesample Unseen modes that may be observed with a 500 fb-1 sample:

B(K*0π0)=0.8±0.8 Expected BaBar error: 0.2

B(K*0η)=3.0±0.8 Expected BaBar error : 0.83

B( K+)=0.50±0.05 Expected BaBar error : 0.12

B( K*+)=0.66±0.08 Expected BaBar error : 0.14

B( K0)=0.46±0.04 Expected BaBar error : 0.12

B( K*0)=0.61±0.08 Expected BaBar error : 0.13 These modes will not be observed:

B(K*+η)=2.8±0.8 Expected BaBar error : 1.56

Modes (ρ0,ω)(π0,η,η) contain pP+ pV as a main contribution. These two penguins cancel each other and the branching ratios are predicted at the level below 10-6.

Modes (π+,π0,η,η) are pure PEW,P and are way below 10-6.

0*K0K0*K

0K

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Comments on SU(3) Comments on SU(3) In August I saw new and more precise measurements shifting

closer to our predictions. Despite smaller errors the quality of the fit improved. Probably, we can not yet see significant SU(3) breaking effects in the current B VP data. I expect that the predictions of this method will remain reliable through Summer of 2004.

Checks of γ sensitivity to some SU(3) breaking effects: Strict SU(3) (ratios of decay constants are set to 1): γ=62o

2 additional SU(3) breaking parameters: amplitudes for penguins in which a gluon couples to : γ=62oss