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(Bd0) = 1.074− 0.016+ 0.017 and τ(Bs0)/τ(Bd0) = 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(Ξb−)/τ(Λb0), τ(Ξb−)/τ(Ξb0), τ(Ωb−)/τ(Ξb−) and the Λb − B0 lifetime ratio τ(Λb0)/τ(Bd0) = 0.953 also agree well with the data. Contrary to the bottom hadron sector where the HQE in 1/mb works well, the HQE to 1/mc3 fails to give a satisfactory description of the lifetimes of both charmed mesons and charmed baryons. This calls for the subleading 1/mQ corrections to spectator effects. The relevant dimension-7 spectator effects are in the right direction for explaining the large lifetime ratio of τ(Ξc+)/τ(Λc+). However, the destructive 1/mc corrections to Γ(Ωc0) are too large to justify the validity of the HQE, namely, the predicted Pauli interference and semileptonic rates for Ωc0 become negative. Demanding these rates to be positive for a sensible HQE, we find the lifetime pattern τ(Ξc+) > τ(Ωc0) > τ(Λc+) > τ(Ξc0), contrary to the current hierarchy τ(Ξc+) > τ(Λc+) > τ(Ξc0) > τ(Ωc0). We conclude that the Ωc0, 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 Λc+ due to the suppression from 1/mc corrections arising from dimension-7 four-quark operators. The new charmed baryon lifetime pattern needs to be tested in forthcoming experiments.
Highlights
The lifetimes of bottom and charmed hadrons are analyzed within the framework of the heavy quark expansion (HQE)
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 (Bd0) = 1.074+−00..001176 and τ (Bs0)/τ (Bd0) = 0.9962 ± 0.0024 are in excellent agreement with experiment
We conclude that the Ω0c, 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/mc corrections arising from dimension-7 four-quark operators
Summary
We write down the general expressions for the inclusive decay widths of heavy hadrons and leave the evaluation of the relevant hadronic matrix elements to the section. It is known that the inclusive decay rate is governed by the imaginary part of an effective nonlocal forward transition operator T. When the energy released in the decay is large enough, the nonlocal effective action can be recast as an infinite series of local operators with coefficients containing inverse powers of the heavy quark mass mQ. Under this heavy quark expansion, the inclusive nonleptonic decay rate of a singly heavy hadron HQ containing a heavy quark Q is given by [1,2,3,4].
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