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

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

1996-08-22

arxiv.org/abs/hep-th/9608152v1

Phys.Rev. D55 (1997) 2486-2496

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 4 Postscript figures

Scientific paper

10.1103/PhysRevD.55.2486

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 Schr\"odinger 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.

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