Heavy quark expansion for heavy hadron lifetimes: completing the 1 / m b 3 $$ 1/{m}_b^3 $$ corrections
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Springer
Received: May 20, 2020 Accepted: July 16, 2020 Published: August 19, 2020
Th. Mannel, D. Moreno and A.A. Pivovarov Theoretische Physik 1, Naturwiss. techn. Fakult¨ at, Universit¨ at Siegen, D-57068 Siegen, Germany
E-mail: [email protected], [email protected], [email protected] 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 . Keywords: Effective Field Theories, Heavy Quark Physics, Perturbative QCD ArXiv ePrint: 2004.09485
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)089
JHEP08(2020)089
Heavy quark expansion for heavy hadron lifetimes: completing the 1/m3b corrections
Contents 1
2 Synopsis on the status of bottom-hadron lifetimes
2
3 Outline of the calculation (q) 3.1 Matching of four-fermion operators: computation of C4Fi 3.1.1 The channel b → c¯ ud 3.1.2 The channel b → c¯ cs 3.2 Matching of two-fermion operators: computation of Ci
3 5 5 6 7
4 Results for the Wilson coefficients at order 1/m3Q 4.1 Comment on the basis of four-quark operators 4.2 Numerical analysis
8 12 14
5 Discussion and conclusions
16
A Some technical results A.1 The decay b → c¯ cs A.2 The computation of the decay b → c¯ cs in a scheme with a hard IR regularization
17 17
1
19
Introduction
Inclusive weak decays of hadrons with a single heavy quark Q have been intensively studied over the last decades [1–3]. The most inclusive quantity is the lifetime of the ground state heavy hadrons which is determined by their weak decay [4–6]. The theoretical method is the heavy quark expansion (HQE) [7–9], which is a combined expansion in the strong coupling αs (mQ ) [10] and inverse powers of the heavy quark mass [11]. The leading term of this expansion is free of any hadronic parameter and is given by the decay rate of the “free” heavy quark. The corrections to this statement appear only at order 1/m2Q and are given in terms of the residual kinetic energy µ2π and the chromomagnetic moment µ2G which are both of order Λ2QCD . Consequently these corrections should be at the level of a few percent, since the leading order result implies that all lifetimes of hadrons with a single heavy quark Q should be identical up to corrections of order Λ2QCD /m2Q . In the early days of the HQE this was taken as an embarrassment, since the lifetimes of the bottom hadrons had not been measured yet, and the lifetimes between charmed hadrons differ by factors of two to five, which is related to the fact that the c-quark is too light for the HQE to be a good approximation for these observables [12].
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JHEP08(2020)089
1 Introduction
2
Synopsis on the status of bottom-hadron lifetimes
The measurements of lifetimes and lifetime rations for bottom hadrons have become very precise of the last decades. The current (2019) experimental a
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