Phenomenological Study of Heavy Hadron Lifetimes

The lifetimes of bottom and charmed hadrons are analyzed within the framework of the heavy quark expansion (HQE). Lifetime differences arise from the spectator effects such as weak $W$-annihilation and Pauli interference. Spectator effects originating from dimension-7 four-quark operators are derived. Hadronic matrix elements of four-quark operators are parameterized in a model-independent way. Using the dimension-6 bag parameters recently determined from HQET sum rules and the vacuum insertion approximation for meson matrix elements of dimension-7 operators, the calculated $B$ meson lifetime ratios $\tau(B^+)/\tau(B^0_d)=1.074$ and $\tau(B^0_s)/\tau(B^0_d)=0.996$ are in excellent agreement with experiment. Likewise, based on the quark model evaluation of baryon matrix elements, the resulting baryon lifetime ratios $\tau(\Xi_b^-)/\tau(\Lambda_b^0)$, $\tau(\Xi_b^-)/\tau(\Xi_b^0)$, $\tau(\Omega_b^-)/\tau(\Xi_b^-)$ and the $\Lambda_b-B^0$ lifetime ratio $\tau(\Lambda_b^0)/\tau(B^0_d)=0.955$ also agree well with the data. Contrary to the bottom hadron sector where the HQE in $1/m_b$ works well, the HQE to $1/m_c^3$ fails to give a satisfactory description of the lifetimes of both charmed mesons and charmed baryons. This calls for the subleading $1/m_Q$ corrections to spectator effects. The relevant dimension-7 spectator effects are in the right direction for explaining the large lifetime ratio of $\tau(\Xi_c^+)/\tau(\Lambda_c^+)$.