Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-12-08
Physics
High Energy Physics
High Energy Physics - Phenomenology
7p,1f
Scientific paper
We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by effective one gluon exchange. Within the model we reasonably reproduce known radial excitation of charmonium. Using free charm quark propagators we observe that $J/\Psi$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. We develop numerical method which succesfully overcome obstacles related with threshold singularity and we discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. Comparing with the model quantum mechanical limit then the Bethe-Salpeter string breaking scale $\mu\simeq 350MeV$ (identified with screening mass) appears to be relatively larger then the one defined in potential model $\mu\simeq 150MeV$.
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