Radial Regge trajectories for higher $\psi (nS)$ and $\psi (nD)$ states

Abstract

The masses of $\psi ((n+1){}^3{S}_1)$ and $\psi (n{}^3{D}_1)$ are calculated using the relativistic string Hamiltonian with "linear+gluon-exchange" potential. They occur in the range 4.5-5.8 GeV, in particular, $M(3D)=4.54$ GeV, $M(5S)=4.79$ GeV, $M(4D)=4.85$ GeV are calculated with accuracy $\sim 50$ MeV. Linear Regge trajectories: $M^2(nS)=M^2(\psi (4.42))+2.91$ GeV${}^2(n-4)$ $(n\ge 4)$ and $M^2(nD)=(4.54^2+2.88(n-3))$ GeV${}^2$ ($n\ge 3$) are obtained only for higher charmonium excitations. They have slopes two times larger than those of light mesons and give good description of calculated masses. These masses are compared with enhancements in some recent $e^{+}{e}^{-}$ experiments.

LaTeX, 15 pages.References and short comments added. Invited paper to the special issue of Yadernaya Fizika, dedicated to the centennial anniversary of the birthday of A.B.Migdal

References in corpus (7)

• The Exotic XYZ Charmonium-like Mesons
• Observation of a near-threshold enhancement in the e+e- -->Lambda_c+Lambda_c- cross section using initial-state radiation
• Decay channels and charmonium mass-shifts
• The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $1^{--}$ states
• Systematics of heavy quarkonia from Regge trajectories on $(n,M^2)$ and $(M^2,J)$ planes
• Spin-dependent interactions in quarkonia
• Di-electron and two-photon widths in charmonium

Cited by in corpus (5)

• Spectroscopy and Regge trajectories of heavy quarkonia and B_c mesons
• Radial and orbital Regge trajectories in heavy quarkonia
• The $c\bar{c}$ interaction above threshold and the radiative decay $X(3872)\to J/\psi \gamma$
• Theory of hadron decay into baryon-antibaryon final state
• Microscopic study of the string breaking in QCD