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Approximate three-quark Hamiltonian in heavy flavor QCD

17 May 2018, 11:05
Auditorium (Jefferson Lab - CEBAF Center)


Jefferson Lab - CEBAF Center



Mr Kamil Serafin (University of Warsaw)


Hamiltonian for baryons in heavy-flavor QCD is approximately evaluated using the renormalization group procedure for effective particles (RGPEP). The calculation yields Hamiltonian terms up to second order in the strong coupling constant. The renormalized Hamiltonian eigenvalue problem is reduced to the Fock sector of only three quarks using assumption that effective gluons develop a mass. The resulting effective three-quark interaction Hamiltonian consists of the Coulomb and harmonic oscillator terms. The oscillator terms depend on the coupling constant, quark masses and the RGPEP scale, but they do not depend on the gluon mass ansatz. Masses of ground and excited states of triply heavy baryons are estimated by evaluating expectation values of the Coulomb terms in the harmonic oscillator three-quark eigenstates. This very crude approximation produces spectra that are in qualitative and in many cases also in quantitative agreement with quark model predictions and lattice QCD calculations, especially for bbb and ccc systems. In ccb systems, the cc pair forms a tight diquark circling around the quark b. Our results for baryons are obtained with no free parameters, except the renormalization scale for ccb and cbb systems, because the coupling constant and quark masses are fixed in the same theory by comparison with the known spectra of heavy quarkonia. These results suggest that heavy-flavor QCD is suitable for realistic studies of the dynamics of gluons in the presence of stable color sources using the front form of Hamiltonian dynamics. The RGPEP that we use here in second order, can be extended to fourth order and inclusion of nonperturbative solutions to the evolution equation for effective particles. These extensions are needed to verify our gluon mass ansatz in theory.

Primary author

Mr Kamil Serafin (University of Warsaw)


Dr Jai More (Indian Institute of Technology Bombay) Dr Maria Gomez-Rocha (University of Graz) Stanislaw Glazek (University of Warsaw)

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