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

TL;DR

This paper calculates higher charmonium state masses using a relativistic string Hamiltonian, establishing linear Regge trajectories with larger slopes than light mesons, and compares results with recent experimental data.

Contribution

It introduces new linear Regge trajectories for higher $ ext{psi}(nS)$ and $ ext{psi}(nD)$ states based on relativistic string Hamiltonian calculations.

Findings

Calculated masses of higher charmonium states with ~50 MeV accuracy.

Established linear Regge trajectories with larger slopes for higher excitations.

Compared theoretical masses with recent experimental enhancements in $e^+e^-$ collisions.

Abstract

The masses of $\psi((n+1) {}^3S_1)$ and $\psi(n {}^3D_1)$ 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\geq 4) $ and $M^2(nD)=(4.54^2+ 2.88 (n-3))$ GeV$^2$ ($n\geq 3$) 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.