Bethe-Salpeter study of radially excited vector quarkonia

Abstract

We solve the Bethe-Salpeter equation (BSE) for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found 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 a method which is enable to provide solution of full four dimensional BSE for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale $\mu \simeq 350MeV$ appears to be relatively larger then the one defined in various potential models $\mu \simeq 150MeV$.

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References in corpus (8)

• Pinch Technique: Theory and Applications
• Higher Charmonia and X,Y,Z states with Screened Potential
• Restoration of chiral and $U(1{)}_A$ symmetries in excited hadrons
• Experimental indication on chiral symmetry restoration in meson spectrum
• Matrix algorithms for solving (in)homogeneous bound state equations
• Heavy meson interquark potential
• Rho-Like Mesons from Analysis of the Pion-Pion Scattering
• Bethe-Salpeter Equations with Instantaneous Confinement: Establishing Stability of Bound States

Cited by in corpus (12)

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• Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
• $B_c$ meson spectroscopy motivated by general features of pNRQCD
• Revisiting the $P$-wave charmonium radiative decays $h_c\to \gamma {\eta }^{(\prime )}$ with relativistic corrections
• Radiative decays of heavy-light quarkonia through $M1$, and $E1$ transitions in the framework of Bethe-Salpeter equation
• $E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation
• The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
• Confinement of Fermions in Tachyon Matter at Finite Temperature
• Excited charmonium states from Bethe-Salpeter equation
• Spin splitting spectroscopy of heavy quark anti quark systems