Dalitz plot studies of D⁰ → K_S⁰π⁺π⁻ decays

¹ Division of Theoretical Physics, The Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Kraków, Poland
² ul. Bronowicka 85/26, 30-091 Kraków, Poland
³ Laboratoire de Physique Nucléaire et de Hautes Énergies, Groupe Théorie, Université Pierre et Marie Curie et Université Paris-Diderot, IN2P3 et CNRS, 4 place Jussieu, 75252 Paris, France

^a e-mail: Leonard.Lesniak@ifj.edu.pl

Abstract

The availaible data on the D⁰ → K_S⁰π⁺π⁻ decays are analysed in the framework of the quasi two-body QCD factorization approximation. The annihilation, via Wexchange, amplitudes are added to the weak-decay tree amplitudes. The doubly Cabibbo suppressed parts of the amplitudes are also considered. The strong interactions between the kaon-pion and pion-pion pairs in the S-, P- and D-final states are described in terms of the corresponding form factors. The kaon-pion or pion-pion scalar and vector form factors are constrained by other experimental data. Unitarity, analyticity and chiral symmetry are also used to obtain their functional forms. We go through a minimization procedure to reproduce the K_S⁰π⁻, K_S⁰π⁺ and π⁺ π^- effective mass projections of the Dalitz plot distributions. The large number (27) of non-zero amplitudes leads to a large number of parameters. The resulting model distributions and branching fractions are compared to the accurate Belle Collaboration data.