Quasi-two-body decays $B_c^+ \to χ_{c0,c1} [ρ(K^*) \to] ππ(Kπ)$ in the PQCD approach

We study the quasi-two-body decays $B_c^+ \to χ_{c0,c1} [ρ(K^*) \to] π^+π^0(K^0π^+)$ in the perturbative QCD framework at leading order. The $ππ$ and $Kπ$ pairs are produced via the P-wave resonances $ρ(770)$, $ρ(1450)$, $ρ(1700)$, and $K^*(892)$, parametrized by the Gounaris-Sakurai and relativisti