Phenomenological study of heavy hadron lifetimes

Abstract 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 τ(B +)/τ(B d 0 ) = 1.074 − 0.016 + 0.017 and τ(B s 0 )/τ(B d 0 ) = 0.9962 ± 0.0024 are in excellent agreement with experiment. Likewise, based on the quark model evaluation of baryon matrix elements, the resulting baryon lifetime ratios τ(Ξ b − )/τ(Λ b 0 ), τ(Ξ b − )/τ(Ξ b 0 ), τ(Ω b − )/τ(Ξ b − ) and the Λ b − B 0 lifetime ratio τ(Λ b 0 )/τ(B d 0 ) = 0.953 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 τ(Ξ c + )/τ(Λ c + ). However, the destructive 1/m c corrections to Γ(Ω c 0 ) are too large to justify the validity of the HQE, namely, the predicted Pauli interference and semileptonic rates for Ω c 0 become negative. Demanding these rates to be positive for a sensible HQE, we find the lifetime pattern τ(Ξ c + ) > τ(Ω c 0 ) > τ(Λ c + ) > τ(Ξ c 0 ), contrary to the current hierarchy τ(Ξ c + ) > τ(Λ c + ) > τ(Ξ c 0 ) > τ(Ω c 0 ). We conclude that the Ω c 0 , which is naively expected to be shortest-lived in the charmed baryon system owing to the large constructive Pauli interference, could live longer than the Λ c + due to the suppression from 1/m c corrections arising from dimension-7 four-quark operators. The new charmed baryon lifetime pattern needs to be tested in forthcoming experiments