Color-allowed Bottom Baryon to $s$-wave and $p$-wave Charmed Baryon non-leptonic Decays

Abstract

We study color allowed bottom baryon to $s$-wave and $p$-wave charmed baryon non-leptonic decays in this work. The charmed baryons include spin-1/2 and spin-3/2 states. Explicitly, we consider ${\Lambda }_b\to {\Lambda }_c^{(\ast ,\ast \ast )}{M}^{-}$, ${\Xi }_b\to {\Xi }_c^{(\ast \ast )}{M}^{-}$ and ${\Omega }_b\to {\Omega }_c^{(\ast ,\ast \ast )}{M}^{-}$ decays with $M=\pi ,K,\rho ,K^{\ast },a_1,D,D_s,D^{\ast },D_s^{\ast }$, ${\Lambda }_c^{(\ast ,\ast \ast )}={\Lambda }_c,{\Lambda }_c(2595),{\Lambda }_c(2625),{\Lambda }_c(2765),{\Lambda }_c(2940)$, ${\Xi }_c^{(\ast \ast )}={\Xi }_c,{\Xi }_c(2815),{\Xi }_c(2790)$ and ${\Omega }_c^{(\ast ,\ast \ast )}={\Omega }_c,{\Omega }_c(2770),{\Omega }_c(3050),{\Omega }_c(3090),{\Omega }_c(3120)$. There are six types of transitions, namely, (i) ${\mathcal{B}}_b({\bar{3}}_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c({\bar{3}}_{\mathbf{f}},1/2^{+})$, (ii) ${\mathcal{B}}_b(6_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c(6_{\mathbf{f}},1/2^{+})$, (iii) ${\mathcal{B}}_b(6_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c(6_{\mathbf{f}},3/2^{+})$, (iv) ${\mathcal{B}}_b(6_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c(6_{\mathbf{f}},3/2^{-})$, (v) ${\mathcal{B}}_b({\bar{3}}_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c({\bar{3}}_{\mathbf{f}},1/2^{-})$, and (vi) ${\mathcal{B}}_b({\bar{3}}_{\mathbf{f}},1/2^{+})$ to ${\mathcal{B}}_c({\bar{3}}_{\mathbf{f}},3/2^{-})$ transitions. Types (i) to (iii) involve spin 1/2 and 3/2 $s$-wave charmed baryons, while types (iv) to (vi) involve spin 1/2 and 3/2 $p$-wave charmed baryons. The transition form factors are calculated in the light-front quark model approach. All of the form factors in the $1/2\to 1/2$ and $1/2\to 3/2$ transitions are extracted, and they are found to reasonably satisfy the relations obtained in the heavy quark limit, as we are using heavy but finite $m_b$ and $m_c$. Using naïve factorization, decay rates and up-down asymmetries of the above modes are predicted and can be checked experimentally. The study on these decay modes may shed light on the quantum numbers of ${\Lambda }_c(2765)$, ${\Lambda }_c(2940)$ ${\Omega }_c(3050)$, ${\Omega }_c(3090)$ and ${\Omega }_c(3120)$.

Comments: To appear in Phys. Rev. D, 45 pages, 15 tables, 6 figures