Charmless B  VP Decays using Flavor SU(3) Symmetry hep-ph/ C.-W. Chiang, M. Gronau, Z. Luo, J. Rosner, DS Denis Suprun University of Chicago

Denis Suprun hep-ph/ Approach 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

Denis Suprun hep-ph/ Charmless B decays Relatively rare decays with branching ratios of the order 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

5 Dominant types of amplitudes Tree (T) Color-suppressed (C)EW penguin (P EW )Penguin (P) Color-suppressed EW penguin ( ) Neglect Exchange (E)Annihilation (A) Penguin annihilation (PA) Singlet penguin (S) Hierarchy

Denis Suprun hep-ph/ Assumptions 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

Denis Suprun hep-ph/ Examples of B  VP decays ρ + π - : -(t P +p P ); -(|t P |e i(γ+δp) +|p P |), CP-conjugate: -(|t P |e i(-γ+δp) +|p P |) ρ - π + : -(t V +p V ); |t V |e i(γ+δv+φ) +|p V |e iφ, CP-conjugate: |t V |e i(-γ+δv+φ) +|p V |e iφ ρ - K +: -(t  V +p  V ); |t  V |e i(γ+δv+φ) -|p  V |e iφ, CP-conjugate: |t  V |e i(-γ+δv+φ) -|p  V |e iφ No CP asymmetry when strong phases are negligible.  Large A CP (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 ρ 0 π + and ωK +  A CP (ρ + π - )=-0.16±0.15 as well as A CP in other δp modes are about 1σ away from 0. Predictions: CP asymmetries in all δp modes are small S QCD factorization predicts Arg(t P /t V )  0. S and ΔS (time-dependent ρ ± π analysis) help to determine Arg(t P /t V ) The only deviation from SU(3) is through decay constants in tree diagrams:

Denis Suprun hep-ph/ Electroweak penguins K *0 π + : p  P Br. ratio: ( 9.0±1.4)  K + : p  P - P EW,P /3 Br. ratio: ( 9.0±0.9)  Expect very small EW penguin P EW,P

Denis Suprun hep-ph/ Data 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  K S decays 12 fit parameters:  weak phase γ  amplitudes: t P, t V, C P, C V, P P, P V, P EW,P, P EW,V  strong phases: δ V, δ P, φ

Denis Suprun hep-ph/ χ 2 plot Three minima of about equal depth: γ=26 o, 63 o, 162 o Ambiguity can not be resolved from the B  VP data alone. Appeal to experiment: CKM Fitter: 39 o <γ<80 o Appeal to theory: Minima at 26 o and 162 o feature large strong phases leading to Arg(t P /t V )=-(87±10) o and (38±12) o, respectively. Arg(t P /t V )=-(20±10) o at γ=63 o γ=(63±6) o

Denis Suprun hep-ph/ Phase diagram for γ=63 o minimum Expect no CP asymmetry in interference between tree t P and penguin diagrams and noticeable CP asymmetry in interference between tree t V and penguins

Denis Suprun hep-ph/ Predictions Largest predicted CP asymmetries: A CP (ρ 0 π + )=-0.16±0.04A CP (ρ 0 K + )=0.21±0.10 A CP (ρ - π + )=-0.13±0.06A CP (ρ - K + )=0.16±0.07 A CP (ωK + )=0.19±0.08 As yet unseen modes to be observed soon (in ): Predicted br. ratio: Current UL BaBar error in 2004 B(K *+ π 0 )=15.0±3.1 < B(ρ 0 K 0 )=7.2±2.0 < B(ρ + K 0 )=12.6±1.6 < ρ + K 0 is a pure p V penguin and its measurement is particularly important

Denis Suprun hep-ph/ fb -1 sample Unseen modes that may be observed with a 500 fb -1 sample: B(K *0 π 0 )=0.8±0.8 Expected BaBar error: 0.2 B(K *0 η)=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( K 0 )=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 (ρ 0,ω)(π 0,η,η  ) contain p P + p V as a main contribution. These two penguins cancel each other and the branching ratios are predicted at the level below Modes  (π +,π 0,η,η  ) are pure P EW,P and are way below

Denis Suprun hep-ph/ 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 Checks of γ sensitivity to some SU(3) breaking effects:  Strict SU(3) (ratios of decay constants are set to 1): γ=62 o  2 additional SU(3) breaking parameters: amplitudes for penguins in which a gluon couples to : γ=62 o