Some years ago, a method was proposed for measuring the CP-violating phase gamma using pairs of two-body decays that are related by U-spin reflection (d <-> s). In this paper we adapt this method to charmless B -> PPP decays. Time-dependent Dalitz-pl
ot analyses of these three-body decays are required for the measurement of the mixing-induced CP asymmetries. However, isobar analyses of the decay amplitudes are not necessary. A potential advantage of using three-body decays is that the effects of U-spin breaking may be reduced by averaging over the Dalitz plot. This can be tested independently using the measurements of direct CP asymmetries and branching ratios in three-body charged B decays.
In the scenario with four quark generations, we perform a fit using flavor-physics data and determine the allowed values -- preferred central values and errors -- of all of the elements of the 4X4 quark mixing matrix. In addition to the direct measur
ements of some of the elements, we include in the fit the present measurements of several flavor-changing observables in the K and B systems that have small hadronic uncertainties, and also consider the constraints from the vertex corrections to Z -> b bbar. The values taken for the masses of the fourth-generation quarks are consistent with the measurements of the oblique parameters and perturbativity of the Yukawa couplings. We find that |{tilde V}_{tb}| >= 0.98 at 3sigma, so that a fourth generation cannot account for any large deviation of |{tilde V}_{tb}| from unity. The fit also indicates that all the new-physics parameters are consistent with zero, and the mixing of the fourth generation with the other three is constrained to be very small: we obtain |{tilde V}_{ub}| < 0.06, |{tilde V}_{cb}| < 0.027, and |{tilde V}_{tb}| < 0.31 at 3sigma. Still, this does allow for the possibility of new-physics signals in Bd, Bs and rare K decays.
