U-spin Symmetry in Charmless B Decays

We prove a general theorem about equal CP rate differences within pairs of U-spin related charmless B and Bs decays. Six pairs of decays into two pseudoscalar mesons are identified where such relations hold. Ratios of corresponding rate differences and certain ratios of rates measure U-spin breaking. These processes provide useful information on the weak phase γ = ArgV ∗ ub. Applications of U-spin symmetry to other decays are discussed. Applying flavor symmetries of strong interactions to B decays into two light pseudoscalar mesons (B → PP ) may provide useful information about phases of the CabibboKobayashi-Maskawa (CKM) matrix. Using isospin symmetry, the three B → ππ decays, B → ππ, ππ and B → ππ, were shown [1] to determine quite precisely the weak phase α = Arg(−V ∗ tbVtd/V ∗ ubVud) (at least in principle, albeit a potential difficulty in measuring B → ππ). Within the approximation of flavor SU(3) symmetry, various aspects of B → Kπ decays were studied [2] to learn the weak phase γ = Arg(−V ∗ ubVud/V ∗ cbVcd). An accurate determination of γ requires the knowledge of SU(3) breaking and rescattering effects which modify some of the amplitudes. Recently the important role of two Bs decay processes, Bs → KK and Bs → Kπ, was demonstarted in this framework [3, 4]. Here one makes explicit use only of a discrete U-spin symmetry transformation interchanging d and s quarks [6]. The purpose of this Letter is to reconsider more generally the implications of Uspin symmetry in charmless B decays [7]. First, we will look at a very general case of charmless B and Bs decays, comparing decays from and into any U-spin related states. We will prove as a general theorem that pairs of U-spin related processes involve CP rate differences which are equal in magnitude and are oppoisite in sign. This property applies not only to two-body and quasi-two-body decays, but in fact to any pair of Uspin related processes. Then, by focusing on B → PP , we will find altogether twelve Permanent Address: Physics Department, Technion – Israel Institute of Technology, 32000 Haifa, Israel.