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_d⁰) = 1.074_− 0.016^+ 0.017 and τ(B_s⁰)/τ(B_d⁰) = 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_b⁰), τ(Ξ_b⁻)/τ(Ξ_b⁰), τ(Ω_b⁻)/τ(Ξ_b⁻) and the Λ_b − B⁰ lifetime ratio τ(Λ_b⁰)/τ(B_d⁰) = 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_c³ 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_c⁰) are too large to justify the validity of the HQE, namely, the predicted Pauli interference and semileptonic rates for Ω_c⁰ become negative. Demanding these rates to be positive for a sensible HQE, we find the lifetime pattern τ(Ξ_c⁺) > τ(Ω_c⁰) > τ(Λ_c⁺) > τ(Ξ_c⁰), contrary to the current hierarchy τ(Ξ_c⁺) > τ(Λ_c⁺) > τ(Ξ_c⁰) > τ(Ω_c⁰). We conclude that the Ω_c⁰, 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.