2020/05/31 by Victor Ananyev, Igor Danilkin, Marc Vanderhaeghen
Physics and Astronomy · #Atomic physics #Elementary particle #High-Energy Particle Collisions Research #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Quarkonium #Radiative transfer #Scattering #Spectrum (functional analysis) #Sum rule in quantum mechanics #hep-ph
paper · pdf · doi:10.1103/physrevd.102.096019
published as Phys. Rev. D 102, 096019 (2020) · 9 pages, 2 figures
arxiv created 2020/11/11 · openalex publication_date 2020/11/16 · arxiv updated 2020/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such a sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the transitions that are not known experimentally, we provide theoretical estimates within a potential model, and consider the spread between similar approaches in the literature as an estimate for the model error. For the \mathrm\ensuremathΥ(1S), \mathrm\ensuremathΥ(2S), and \mathrm\ensuremathΥ(3S) states we observe that, due to a cancellation between transitions involving \ensuremathχb0,\ensuremathχb1, and \ensuremathχb2 states, the sum rule is satisfied within experimental and theoretical error estimates. Having tested this sum rule for the low-lying bottomonium states, it may be used as a tool to investigate the nature of exotic states in the charmonium and bottomonium spectrum through the corresponding radiative transitions.