2017/11/27 by Pablo G. Ortega, Ortega, Pablo G., Vicent Mateu +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1711.09998
openalex publication_date 2017/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The non-perturbative nature of QCD at hadronic scales implied the development of phenomenological approaches such as quark models or, more recently, computer-based calculations using Lattice QCD. However, the unique properties of heavy quarkonium systems allow an entire calculation in terms of non-relativistic perturbative QCD. In this work, the bottomonium spectrum, up to n = 3, and the ground state charmonium states, are analyzed in the framework of Non-Relativistic Quantum Chromodynamics at N3LO. For bottomonium, finite charm quark mass effects in the QCD potential and the MS-pole mass relation are incorporated to the highest known order, O(ε3) in the Υ-scheme counting. The bottom quark pole mass is expressed in terms of the MSR mass, a low-scale short-distance mass which cancels the u = 1/2 renormalon of the static potential. We study the n_ℓ = 3 and n_ℓ = 4 schemes, finding a negligible difference between the two if finite mc effects are smoothly incorporated in the MSR mass definition. We find that bottomonium n=3 states are not well behaved within perturbative NRQCD. Hence, fitting to the n=1,2 b b states we obtain mb(mb) = 4.216± 0.039 GeV. Similarly, from the lowest lying charmonium states we find mc(mc)=1.273 ± 0.054 GeV.