PNNL

Abstract

Weak nonleptonic decays of D and B mesons are expected to proceed dominantly through resonant two-body decays [1]; see Ref. [2] for a review of resonance phenomenology. The amplitudes are typically calculated with the Dalitz-plot analysis technique [3], which uses the minimum number of independent observable quantities. For three-body decays of a spin-0 particle to all pseudo-scalar final states, D or B ? abc, the decay rate [4] is r = 1 (2p)3 32vs3 |M|2 dm2 ab dm2bc , (1) where mij is the invariant mass of particles i and j. The coefficient of the amplitude includes all kinematic factors, and |M|2 contains the dynamics. The scatter plot in m2 ab versus m2bc is the Dalitz plot. If |M|2 is constant, the kinematically allowed region of the plot will be populated uniformly with events. Any variation in the population over the Dalitz plot is due to dynamical rather than kinematical effects. It is straightforward to extend the formalism beyond three-body final states. For N-body final states with only spin-0 particles, phase space has dimension 3N - 7. Other decays of interest include one vector particle or a fermion/anti-fermion pair (e.g., B ? D*pp, B ? *cpp, B ? Kll) in the final state. For the first case, phase space has dimension 3N - 5, and for the latter two the dimension is 3N - 4.