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We develop a model to study the $D^0 \to K^- \pi^+ \eta$ weak decay, startingwith the color favored external emission and Cabibbo favored mode at the quarklevel. A less favored internal emission decay mode is also studied as a sourceof small corrections. Some pairs of quarks are allowed to hadronize producingtwo pseudoscalar mesons, which posteriorly are allowed to interact to finallyprovide the $K^- \pi^+ \eta$ state. The chiral unitary approach is used to takeinto account the final state interaction of pairs of mesons, which has as aconsequence the production of the $\kappa$ ($K^*_0(700)$) and the $a_0(980)$resonances, very well visible in the invariant mass distributions. We alsointroduce the $\bar{K}^{*0} \eta$ production in a phenomenological way and showthat the $s$-wave pseudoscalar interaction together with this vector excitationmode are sufficient to provide a fair reproduction of the experimental data.The agreement with the data, in particular the relative weight of the$a_0(980)$ to the $\kappa$ excitation, provides extra support to the pictureused, in which these two resonances are a consequence of the interaction ofpseudoscalar mesons and not ordinary $q \bar{q}$ mesons.

Theoretical study of the $D^0 \to K^- \pi^+ \eta$ reaction