Approximate Hamiltonian for baryons in heavy-flavor QCD

TL;DR

This paper develops an approximate Hamiltonian for heavy-flavor baryons in QCD using RGPEP, leading to predictions consistent with lattice QCD and quark models, and introduces a simplified, boost-invariant wave function approach.

Contribution

It presents a novel application of RGPEP to derive an effective Hamiltonian for heavy baryons, incorporating a gluon-mass term and simplifying the Fock space to improve tractability.

Findings

Accurate estimates for bbb and ccc baryon masses match lattice QCD and quark model results.

Wave functions are boost-invariant, facilitating relativistic descriptions.

Charm quarks tend to form diquarks in ccb states.

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.