Abstract
In response to the growing need for theoretical tools that can be used in QCD to describe and understand the dynamics of gluons in hadrons in the Minkowski space–time, the renormalization group procedure for effective particles (RGPEP) is shown in the simplest available context of heavy quarkonia to exhibit a welcome degree of universality in the first approximation it yields once one assumes that beyond perturbation theory gluons obtain effective mass. Namely, in the second-order terms, the Coulomb potential with Breit–Fermi spin couplings in the effective quark–antiquark component of a heavy quarkonium, is corrected in one-flavor QCD by a spin-independent harmonic oscillator term that does not depend on the assumed effective gluon mass or the choice of the RGPEP generator. The new generator we use here is much simpler than the ones used before and has the advantage of being suitable for studies of the effective gluon dynamics at higher orders than the second and beyond the perturbative expansion.
Highlights
The growing need for understanding dynamics of gluons in QCD, comprehensively documented in [1], revives interest in Hamiltonian methods for describing heavy quarkonia in terms of wave functions in the Fock space of virtual quanta, where gluons are likely to behave in a relatively simple way because they are permanently coupled to the massive quarks that move slowly with respect to each other
This article presents a first step in a program of systematic studies of dynamics of scale-dependent gluons in heavy quarkonia, starting with the simplified case of canonical front form (FF) formulation of QCD with quarks of just one heavy flavor and assuming that the effective gluons which correspond to momentum scale of quark binding mechanism in quarkonia have mass
When the renormalization group procedure for effective particles (RGPEP) calculation of renormalized Hamiltonian Hs is extended to higher orders than second, and when the unknowns of the effective gluon mass are relegated to the Fock sectors with more than one gluon, the preliminary gluon-mass ansatz in the dynamics of QsQsGs component will be replaced by true QCD terms
Summary
The growing need for understanding dynamics of gluons in QCD, comprehensively documented in [1], revives interest in Hamiltonian methods for describing heavy quarkonia in terms of wave functions in the Fock space of virtual quanta, where gluons are likely to behave in a relatively simple way because they are permanently coupled to the massive quarks that move slowly with respect to each other. In the canonical formulation of QCD in the front form (FF) of dynamics in the Minkowski space-time [22], the need for understanding implications of an effective gluon mass is stressed in general in [23] and in the context of heavy quarkonia in [24, 25]. Scale-dependent Hamiltonian for quarkonium constituents in the Fock space using a new formulation of the renormalization group procedure for effective particles (RGPEP) in quantum field theory, see below. The new effective term respects rotational symmetry in the quark-antiquark relative three-momentum space, in which the eigenvalue problem for quarkonium two-body component resembles a non-relativistic Shrodinger equation with a potential, except that the eigenvalue is the quarkonium mass squared instead of its energy.
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