Comment on the Spin Splitting of the L1L \ge 1 Quarkonium Levels for a Class of Static Potentials

Nov, 1989
11 pages
Published in:
  • Phys.Rev.D 42 (1990) 166-170
Report number:
  • BI-TP-89-34

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Abstract: (APS)
Implications of a spin-dependent interaction generated by a static potential consisting of a vector [V(r)] and a scalar [S(r)] part are discussed for the mass splitting of the L≥1 levels of quarkonia. It is shown that when V(r) is a pure power law (∼rα, attractive for all r) and S(r) is arbitrary, a relation exists between the power α and the four masses for a given L≥1 for any quarkonium system. For various values of α chosen recently to predict the center of gravity of the four levels, we use this relation to predict the mass of the P11 cc¯ and bb¯ systems as well as the mass of the P03 level of the us¯ system. It is argued that an accurate measurement of the masses of the 1 P11(cc¯) and 1 P03(us¯) levels can already be decisive in ascertaining the viability of this class of static potentials for quarkonia.
  • charmonium
  • bottomonium
  • quarkonium: energy levels
  • dependence: spin
  • spin dependence
  • potential: scalar
  • potential: vector
  • quarkonium: mass spectrum
  • mass spectrum: quarkonium
  • hadron spectroscopy
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