# Renormalized quark-antiquark Hamiltonian induced by a gluon mass ansatz in heavy-flavor QCD

## TL;DR

This paper develops a renormalized quark-antiquark Hamiltonian in heavy-flavor QCD using a simplified RGPEP approach, revealing a universal harmonic oscillator correction to the Coulomb potential that is independent of the effective gluon mass.

## Contribution

It introduces a simpler RGPEP generator that allows for higher-order and nonperturbative studies of gluon dynamics in heavy quarkonia.

## Key findings

- Coulomb potential is corrected by a spin-independent harmonic oscillator term.
- The correction is universal and independent of the effective gluon mass.
- The new generator simplifies higher-order calculations.

## 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.