Masses of the physical mesons from an effective QCD--Hamiltonian

Abstract

The front form Hamiltonian for quantum chromodynamics, reduced to an effective Hamiltonian acting only in the $q\bar{q}$ space, is solved approximately. After coordinate transformation to usual momentum space and Fourier transformation to configuration space a second order differential equation is derived. This retarded Schrödinger equation is solved by variational methods and semi-analytical expressions for the masses of all 30 pseudoscalar and vector mesons are derived. In view of the direct relation to quantum chromdynamics without free parameter, the agreement with experiment is remarkable, but the approximation scheme is not adequate for the mesons with one up or down quark. The crucial point is the use of a running coupling constant ${\alpha }_s(Q^2)$, in a manner similar but not equal to the one of Richardson in the equal usual-time quantization. Its value is fixed at the Z mass and the 5 flavor quark masses are determined by a fit to the vector meson quarkonia.

arXiv comment18 pages, 4 Postscript figures

References in corpus (8)

• Heavy Quark Symmetry
• Nonperturbative Light-Front QCD
• Hadron Masses from the Valence Approximation to Lattice QCD
• Wavefunction-Independent Relations between the Nucleon Axial-Coupling g_A and the Nucleon Magnetic Moments
• Glueball spectrum in a (1+1)-dimensional model for QCD
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Cited by in corpus (7)

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• Variational Analysis of Mass Spectra and Decay Constants for Ground State Pseudoscalar and Vector Mesons in Light-Front Quark Model
• Nonperturbative renormalization and the electron's anomalous moment in large-alpha QED
• Application of Pauli-Villars Regularization and Discretized Light-Cone Quantization to a (3+1)-Dimensional Model
• The charmonium and bottomonium mass spectroscopy with a simple approximaton of the kinetic term
• Succesful renormalization of a QCD-inspired Hamiltonian