Lifetimes of Doubly Charmed Baryons

Abstract

The lifetimes of doubly charmed hadrons are analyzed within the framework of the heavy quark expansion (HQE). Lifetime differences arise from spectator effects such as $W$-exchange and Pauli interference. The $\Xi_{cc}^{++}$ baryon is longest-lived in the doubly charmed baryon system owing to the destructive Pauli interference absent in the $\Xi_{cc}^+$ and $\Omega_{cc}^+$. In the presence of dimension-7 contributions, its lifetime is reduced from $\sim5.2\times 10^{-13}s$ to $\sim3.0\times 10^{-13}s$. The $\Xi_{cc}^{+}$ baryon has the shortest lifetime of order $0.45\times 10^{-13}s$ due to a large contribution from the $W$-exchange box diagram. It is difficult to make a precise quantitative statement on the lifetime of $\Omega_{cc}^+$. Contrary to $\Xi_{cc}$ baryons, $\tau(\Omega_{cc}^+)$ becomes longer in the presence of dimension-7 effects and the Pauli interference $\Gamma^{\rm int}_+$ even becomes negative. This implies that the subleading corrections are too large to justify the validity of the HQE. Demanding the rate $\Gamma^{\rm int}_+$ to be positive for a sensible HQE, we conjecture that the $\Omega_c^0$ lifetime lies in the range of $(0.75\sim 1.80)\times 10^{-13}s$. The lifetime hierarchy pattern is $\tau(\Xi_{cc}^{++})>\tau(\Omega_{cc}^+)>\tau(\Xi_{cc}^+)$ and the lifetime ratio $\tau(\Xi_{cc}^{++})/\tau(\Xi_{cc}^+)$ is predicted to be of order 6.7.