Abstract
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-plot 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.
Highlights
B+ → π+K0, B+ → π0K+, Bd0 → π−K+ and Bd0 → π0K0
Assuming flavor SU(3) symmetry, the amplitudes can be written in terms of eight theoretical parameters: the magnitudes of the diagrams Pt′c, T ′, C′, Pu′ c, three relative strong phases, and the weak phase γ. (The value of the weak phase β is taken from the measurement of indirect CP violation in Bd0(t) → J/ΨKS [7].) With more observables than theoretical parameters, one can perform a fit to extract γ
The main purpose of the present paper is to note that the method of ref. [9] can be applied to charmless B → P P P decays (P is a pseudoscalar meson) whose amplitudes are related by U spin
Summary
Consider the decay B → P1P2P3, in which each pseudoscalar Pi has momenta pi. The B → P1P2P3 Dalitz plot is a measure of the decay rate as a function of two Mandelstam variables. Note that reversing the direction of the three momenta does not affect the Mandelstam variables, since sij = (pi + pj)2 = (pi + pj)2 = sij. In this case the difference between f and farises from an exchange of the indices 2 and 3. At different points in the analysis we consider the direct CP asymmetry. Things are similar for the indirect CP asymmetry, which arises because both B0 and B0 can decay to the same final state. One indirect asymmetry involves the interference of the amplitudes for B0 → f and B0 → f , while the other involves the interference of A(B0 → f) and A(B0 → f)
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