CKM Constraints from Charmless B Decays:
Winter 2003

  • Experimental inputs

  • In the (rhobar,etabar) plane for the four theoretical frameworks defined above. The prediction from the standard CKM fit which includes the WA of sin2beta/phi1 is overlaid on each of the four plots.

    • Confidence levels in the large (rhobar,etabar) plane obtained from the isospin analysis, for BABAR (top) and Belle (bottom) results.

    Confidence levels in the large (rhobar,etabar) plane obtained from unbroken SU(3) symetry, for BABAR (top) and Belle (bottom) results. P is evaluated with the upper bound |P|=|P(B0 -> K+pi-)|.

    Confidence levels in the large (rhobar,etabar) plane obtained from broken SU(3) symetry, for BABAR (top) and Belle (bottom) results. P is evaluated with |P|=fpi/fK.|P(B+ -> K0pi+)|, taking into account other small correction factors.

    Confidence levels in the large (rhobar,etabar) plane obtained using QCD FA. The upper plot is obtained with Cpipi and Spipi from BABAR. Strong constraints are obtained with QCD FA. The comparison of the allowed regions obtained here (phases and magnitude of the tree and penguin amplitudes are predicted and their uncertainties are small with respect to the experimental errors) shows that the experimental accuracy is already competitive with the constraint from the standard CKM fit for BABAR's results.

    The two plots below use Belle's values. Whereas these measurements by themselves are not in disagreement with the Standard Model for unconstrained P/T, when analyzed within QCD FA, they lead to a conflict. The bottom plot represents a zoom to low CL values to quantify the disagreement with the standard fit.




  • In the (Spipi,Cpipi) plane
    •

    Predictions for Spipi and Cpipi within the four frameworks. The input values for rhobar and etabar are taken from the standard CKM fit. The relative large uncertainty of the QCD FA in Spipi is due to the weak sin2alpha/phi2 constraint of the standard CKM fit. For comparison, the 1 sigma and 2 sigma contours for the experimental results from BABAR, Belle and their average are overlaid.

  • In the (|P/T|,delta) plane
    •

    Constraints on the penguin-to-tree ratio and their relative strong phase delta. The shaded (coloured) region gives the CL obtained from a fit corresponding to the SU(2) approach.

    The CKM phase is constrained by means of the standard CKM fit. The extended contour indicates the 5% CL limit when only using Spipi and Cpipi. Also shown are the 5% CL contours corresonding to the three other approaches.

    The upper plot is obtained with the BABAR's results. The BABAR measurements prefer low values for |P/T| and set no constraint on the strong phase since there is no compelling indication for direct CP violation. The middle plot is obtained with Belle's measurements and the bottom one with both combined. In the two last cases, in contrast with the first one, a large negative phase is prefered together with large values of |P/T|.




  • The angle alpha/phi2

    • Confidence levels for alpha/phi2 within the four frameworks. The CP and BRs experimental results in B --> h+h- decays are used from BABAR (top) and from Belle (bottom). The radius (rhobar^2 + etabar^2)^(1/2) has been confined using in addition |Vub|. The prediction from the standard CKM fit which includes the WA of sin2beta/phi1 is overlaid (dashed lines, hatched area). Significant constraints (up to the four-fold ambiguity) are obtained once the penguin-to-tree ratio is determined (the last two frameworks). Consistency with the Standard Model are observed for all cases. Comparable uncertainties are obtained for standard CKM fit and QCD FA.

  • The angle alpha/phi2 minus alpha/phi2 effective
    •

    Residual (alpha/phi2 - alpha/phi2_eff) for the present (ICHEP'02) central values and errors as well as projected luminosities of BABAR, Belle and future B-factories (always keeping the central values unchanged). Note that due to finite binning only, the central peaks do not reach until CL=1. The full isospin analysis is employed, i.e., we assume the flavours of B0(B0bar) --> pi0pi0 are tagged. Moreover, we assume that direct CPV is absent (lambda_{pi0pi0}=1) leading to the symmetric solutions shown in the figure. When the flavour information for B0 --> pi0pi0 is missing (as currently the case), only the outer borders of the curves can be obtained from the isospin analysis while the inner structure remains unresolved because the strong phase of the tree amplitude is unconstrained. The inner structure reveals the remnants of the eight-fold ambiguity in the range alpha/phi2 in {0,2pi}. For this setup of central values, only luminosities of the order of 10/ab allow to separate the mirror solutions.

  • The BR(B0 --> pi0pi0)

    • Constraints on the branching fraction B0 --> pi0pi0 obtained from the measurements of B0 --> pi+pi-, B+ --> pi+pi0, B- --> pi-pi0 and Cpipi using the isospin relations (preprint). Given by the hatched area is the prediction from QCD FA: larger BR(B0 --> pi0pi0) require larger values of the unitarity triangle angle alpha/phi2. The upper plot uses Cpipi from BABAR, the lower plot uses Cpipi from Belle. The vertical arrow indicates the experimental upper limit at 90% CL found by BABAR. The horizontal arrows indicate the zone for which the CL is equal or better than 10%.