Abstract
Aiming at relativistic description of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) is applied to baryons in QCD of heavy quarks. The baryon eigenvalue problem is posed using the Fock-space Hamiltonian operator obtained by solving the RGPEP equations up to second order in powers of the coupling constant. The eigenstate components that contain three quarks and two or more gluons are heuristically removed at the price of inserting a gluon-mass term in the component with one gluon. The resulting problem is reduced to the equivalent one for the component of three quarks and no gluons. Each of the three quark–quark interaction terms thus obtained consists of a spin-dependent Coulomb term and a spin-independent harmonic oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia masses most accurately. The resulting estimates for bbb and ccc states match estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc states are also estimated. The corresponding wave functions are invariant with respect to boosts. In the ccb states, charm quarks tend to form diquarks. The accuracy of our approximate Hamiltonian can be estimated through comparison by including components with two gluons within the same method.
Highlights
Quark model represented baryons as bound states of three quarks, e.g. see [1,2]
C (2018) 78:964 front form (FF) Hamiltonian of the theory using the concept of effective particles in the Fock space; we reduce the resulting heavy-baryon eigenvalue problem for low-mass eigenstates to the eigenvalue problem solely for their Fock component of three effective quarks, using a gluon mass ansatz to account for the Fock components with more effective gluons than one; and we draw a qualitative sketch of the estimated low-mass heavy baryons spectrum that follows from the dominant mechanism of binding, while spin and other relatively small corrections to the effects of dominant interactions require future more elaborate calculations of higherorder using the same method
We introduce the gluon mass in the effective QCD eigenvalue problem for heavy baryons within the same computational scheme that we previously applied to heavy quarkonia [3]
Summary
Quark model represented baryons as bound states of three quarks, e.g. see [1,2]. In QCD, baryons are instead superpositions of states of quanta of quark and gluon fields. The theoretical challenge our method addresses is how to represent states of heavy baryons in terms of the Fock-space wave-functions for quarks and gluons that are invariant with respect to Lorentz boosts. We use second-order perturbation theory to derive the resulting effective Hamiltonian for baryons that only acts in the component with three quarks. The parameters involved (the running coupling and the quark masses) are chosen using heavy quarkonia experimental data. In this way, our estimates for baryon masses contain no new parameters. 4. Details of the effective quark–quark interaction terms in ccc and bbb baryons, implied by the gluon mass, are described, including a comparison with the case of heavy quarkonia. “Appendix D” provides a detailed description of the baryon wave functions that are used in our estimates and “Appendix E” presents explicit formulas for the associated heavy-baryon masses
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