Quasi-two-body decays $B_c^{+}\to \ddot{I}{‡}_{c0,c1}[\ddot{I}(K^{\ast })\to ]\ddot{I}€\ddot{I}€(K\ddot{I}€)$ in the PQCD approach

Abstract

We study the quasi-two-body decays $B_c^{+}\to \ddot{I}{‡}_{c0,c1}[\ddot{I}(K^{\ast })\to ]\ddot{I}{€}^{+}\ddot{I}{€}^0(K^0\ddot{I}{€}^{+})$ in the perturbative QCD framework at leading order. The $\ddot{I}€\ddot{I}€$ and $K\ddot{I}€$ pairs are produced via the P-wave resonances $\ddot{I}(770)$, $\ddot{I}(1450)$, $\ddot{I}(1700)$, and $K^{\ast }(892)$, parametrized by the Gounaris-Sakurai and relativistic Breit-Wigner models. The dominant $\ddot{I}(770)$ channels yield $\mathcal{B}(B_c^{+}\to \ddot{I}{‡}_{c0}\ddot{I}{€}^{+}\ddot{I}{€}^0)=3.24\times 10^{-3}$ and $\mathcal{B}(B_c^{+}\to \ddot{I}{‡}_{c1}\ddot{I}{€}^{+}\ddot{I}{€}^0)=4.19\times 10^{-3}$, with constructive $\ddot{I}$ interference contributing $\sim 25\%$ of the total. The $K\ddot{I}€$ channels are Cabibbo-suppressed to $10^{-6}$. For $\ddot{I}{‡}_{c1}$ modes, $f_L\approx 94\%$ dominates and decreases with increasing resonance mass. The ratio $R_{\ddot{I}{‡}_{c1}/\ddot{I}{‡}_{c0}}^{\ddot{I}€\ddot{I}€}\approx 1.30$ contrasts with the two-body result $\sim 4.7$, showing that resonant $\ddot{I}$ production dramatically reshapes the relative yields of P-wave charmonia. The ratio $R_{K/\ddot{I}€}\approx 2\times 10^{-3}$ is consistent across $\ddot{I}{‡}_{c0}$ and $\ddot{I}{‡}_{c1}$.

17 pages, 1 figure