A Phenomenological Analysis of Heavy Hadron Lifetimes

A phenomenological analysis of lifetimes of bottom and charmed hadrons within the framework of the heavy quark expansion is performed. The baryon matrix element is evaluated using the bag model and the nonrelativistic quark model. We find that bottom-baryon lifetimes follow the pattern τ(Ωb) ' τ(Ξ − b ) > τ(Λb) ' τ(Ξ 0 b). However, neither the lifetime ratio τ(Λb)/τ(Bd) nor the absolute decay rates of the Λb baryon and B mesons can be explained. One way of solving both difficulties is to allow the presence of linear 1/mQ corrections by scaling the inclusive nonleptonic width with the fifth power of the hadron mass mHQ rather than the heavy quark mass mQ. The hierarchy of bottom baryon lifetimes is dramatically modified to τ(Λb) > τ(Ξ − b ) > τ(Ξ 0 b) > τ(Ωb): The longest-lived Ωb among bottom baryons in the OPE prescription now becomes shortest-lived. The replacement ofmQ by mHQ in nonleptonic widths is natural and justified in the PQCD-based factorization approach formulated in terms of hadron-level kinematics. For inclusive charmed baryon decays, we argue that since the heavy quark expansion does not converge, local duality cannot be tested in this case. We show that while the ansatz of substituting the heavy quark mass by the hadron mass provides a much better description of the charmed-baryon lifetime ratios, it appears unnatural and unpredictive for describing the absolute inclusive decay rates of charmed baryons, contrary to the bottom case. PACS numbers: 12.39.Hg, 12.39.Jh, 13.20.He, 13.30-a