Abstract
We obtain the renormalization group improved expressions of the Wilson coefficients associated to the ${\cal O}(1/m^3)$ spin-dependent heavy quark effective theory Lagrangian operators, with leading logarithmic approximation, in the case of zero light quarks. We have employed the Coulomb gauge.
Highlights
The expansion in inverse powers of the heavy quark mass is a useful tool for the study of hadrons containing heavy quarks
The Wilson coefficients of the heavy quark effective theory (HQET) Lagrangian enter into the Wilson coefficients of the operators of the pNRQCD Lagrangian [4,5], an effective field theory optimized for the description of heavy quarkonium systems near the threshold
The leading logarithmic (LL) running of the Wilson coefficients associated to the 1=m3 operators of the HQET Lagrangian without considering light fermion effects was first addressed in Refs. [15,16], where expressions for the anomalous dimension matrix and explicit expressions for the Wilson coefficients with single log accuracy are given
Summary
The expansion in inverse powers of the heavy quark mass is a useful tool for the study of hadrons containing heavy quarks. The Wilson coefficients we compute in this paper are necessary ingredients to obtain the pNRQCD Lagrangian with next-to-next-to-next-to-leading logarithmic (NNNLL) accuracy. It should be noted that the Wilson coefficients computed in this paper are not necessary to obtain the complete heavy quarkonium spectrum with NNNLL accuracy, nor the production and annihilation of heavy. The operator structure of the HQET Lagrangian, and the tree-level values of their Wilson coefficients, is known to Oð1=m3Þ in the case without massless quarks [10]. The Wilson coefficients with leading logarithmic (LL) accuracy were computed in Refs. We focus on spin-dependent operators and obtain the renormalization group improved Wilson coefficients of the HQET Lagrangian with LL accuracy to Oð1=m3Þ. In Appendix A we present some new Feynman rules needed for the computation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
