Abstract
We complete the calculation of the contributions from the dimension six operators in the heavy quark expansion for the total lifetime of heavy hadrons. We give the leading order expressions for the Wilson coefficients of the Darwin term ρD and the spin-orbit term ρLS.
Highlights
Since the methods have been refined and the HQE makes quite precise predictions for the lifetime pattern of bottom hadrons and qualitatively describes the pattern of charmed hadrons
Assuming SU(2)flavour symmetry for the light quarks the lifetime differences between the three ground state mesons are driven by the terms of 1/m3Q and higher, in particular by the four-quark operators appearing at tree level, which involve light quarks of a particular flavour
The current (2019) experimental averages obtained by the Heavy Flavor Averaging Group (HFLAV) of the b-hadron lifetime ratios are [14]
Summary
The measurements of lifetimes and lifetime rations for bottom hadrons have become very precise of the last decades. For semi-leptonic decays the current precision is NNLO-QCD [27,28,29,30,31,32,33,34,35,36]. The contribution from the first power correction due to the dimension five kinetic and chromomagnetic operators is already known at LO-QCD for both semi-leptonic and non-leptonic decays [37,38,39,40]. For semi-leptonic decays NLO-QCD corrections are know as well [41,42,43]. The contribution from the second power correction due to the dimension six Darwin and spin-orbit operators is known at LO-QCD [44] and NLO-QCD [45] only for the semi-leptonic case. The contribution from dimension six four-quark operators is known at NLO-QCD [6, 46, 47]
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