We develop a model to study the \(D^0 \rightarrow K^- \pi ^+ \eta \) weak decay, starting with the color favored external emission and Cabibbo favored mode at the quark level. A less favored internal emission decay mode is also studied as a source of small corrections. Some pairs of quarks are allowed to hadronize producing two pseudoscalar mesons, which posteriorly are allowed to interact to finally provide the \(K^- \pi ^+ \eta \) state. The chiral unitary approach is used to take into account the final state interaction of pairs of mesons, which has as a consequence the production of the \(\kappa \) (\(K^*_0(700)\)) and the \(a_0(980)\) resonances, well visible in the invariant mass distributions. We also introduce the \(\bar{K}^{*0} \eta \) production in a phenomenological way and show that the s-wave pseudoscalar interaction together with this vector excitation mode are sufficient to provide a fair reproduction of the experimental data. The model provides the relative weight of the \(a_0(980)\) to the \(\kappa \) excitation, and their strength is clearly visible in the low energy part of the \(K \pi \) spectrum.

我们建立了一个模型来研究\（D ^ 0 \ rightarrow K ^-\ pi ^ + \ eta \）弱衰减，从夸克级的颜色偏向外部发射和Cabibbo偏向模式开始。还研究了较不受欢迎的内部发射衰减模式作为小校正的来源。允许某些夸克对强子进行强子化，从而产生两个伪标量子介子，随后允许它们相互作用以最终提供\（K ^-\ pi ^ + \ eta \）状态。手性unit合方法用于考虑介子对的最终状态相互作用，其结果是产生\（\ kappa \）（\（K ^ * _ 0（700）\））和\ （a_0（980）\）共振，在不变质量分布中很明显。我们还以现象学的方式介绍了\（\ bar {K} ^ {* 0} \ eta \）的产生，并证明了s波伪标量相互作用以及这种矢量激发模式足以提供实验的公平再现。数据。该模型提供了\（a_0（980）\）与\（\ kappa \）激发的相对权重，并且它们的强度在\（K \ pi \）光谱的低能量部分清晰可见。