Abstract
In this work, we evaluate the lifetimes of the doubly charmed baryons Ξcc+, Ξcc++ and Ωcc+. We carefully calculate the non-spectator contributions at the quark level, where the Cabibbo-suppressed diagrams are also included. The hadronic matrix elements are evaluated in the simple non-relativistic harmonic oscillator model. Our numerical results are generally consistent with that obtained by other authors who used the diquark model. However, all the theoretical predictions on the lifetimes are one order larger than the upper limit set by the recent SELEX measurement. This discrepancy would be clarified by the future experiment. If more accurate experiment still confirms the value of the SELEX collaboration, there must be some unknown mechanism to be explored.