Charm Dalitz Plot Analysis Formalism and Results.pdfVIP

a r X i v : h e p - e x / 0 4 1 0 0 1 4 v 3 1 9 D e c 2 0 0 4 – 1– CHARM DALITZ PLOT ANALYSIS FORMALISM AND RESULTS (EXPANDED RPP-2004 VERSION) Written November 2003 by D. Asner (University of Pittsburgh) Introduction: Charm meson decay dynamics have been stud- ied extensively over the last decade. Recent studies of multi- body decays of charm mesons probe a variety of physics includ- ing doubly-Cabibbo suppressed decays [1], searches for CP vi- olation [1,2,3], the properties of established light mesons [4,5,6] and the properties of ππ [1,6,7] and Kπ [8] S-wave states. Future studies could improve sensitivity to D0–D0 mixing [9]. Weak nonleptonic decays of charm mesons are expected to proceed dominantly through resonant two-body decays in several theoretical models [10]; see Ref. [11] for a review of res- onance phenomenology. These amplitudes are calculated with the Dalitz plot analysis technique [12], which uses the mininum number of independent observable quantities. For three-body final states when the parent particle is a scalar, the decay rate [13] is Γ = 1 (2π)3 32 √ s3 |M|2 dm212dm223, (1) where mij is the invariant mass of i ? j and the coefficient of the amplitude includes all kinematic factors. The scatter plot in m212 versus m 2 23 is called a Dalitz plot. If |M|2 is constant the allowed region of the plot will be populated uniformly with events. Any variation in |M|2 over the Dalitz plot is due to dynamical rather than kinematical effects. Formalism: The amplitude of the process, D → rc, r → ab, is given by Mr (L,mab, mbc) = ∑ λ 〈ab|rλ〉Tr (mab) 〈crλ|D〉 (2) = Z (L, ~p, ~q)BDL (|~p|)BrL (|~q|)Tr (mab) , where the sum is over the helicity states λ of the intermediate resonance particle r, a and b are the daughter particles of the resonance r, c is the spectator particle, L is the orbital angular momentum between r and c, ~p is the momentum of CITATION: S. Eidelman et al., Phys. Lett. B 592, 1 (2004) (URL: /) February 7, 2008 07:43 – 2– c in the r res