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Dynamical effects of gluon mass and small longitudinal momentum in heavy-quark bound states

Stanisław D. Głazek

  • Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

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Phys. Rev. D 114, 074058 – Published 27 October, 2026

DOI: https://doi.org/10.1103/1568-xmzd

Abstract

Precise derivation of the logarithmically scale-dependent Hamiltonian eigenstate picture for hadrons in the space of virtual quark and gluon states of the canonical front form of QCD requires addressing first the problem of divergences stronger than logarithmic and especially the small-p+ divergences in the dynamics of gluons. We propose to facilitate the regularization and cancellation of these divergences using a gluon mass parameter and an auxiliary color-octet scalar field corresponding to the longitudinally polarized gluons. The auxiliary field decouples from the hadronic constituent dynamics when the mass parameter tends to zero, as required in the gauge theory. The same method applies in the cancellation of the quadratic ultraviolet transverse divergences in the self-interactions. After explaining how the method works in the old-fashioned perturbative computations of the scattering amplitudes to all orders, we describe its application to computing the renormalized, scale-dependent Hamiltonian operator acting in the entire Fock space and to deriving its bound-state eigenvalue problems expressed in terms of the correspondingly scale-dependent creation and annihilation operators for effective quarks and gluons. Our detailed discussion focuses on the weak-coupling expansion of second order for the QCD Hamiltonian of effective heavy quarks and the corresponding eigenvalue problems for quarkonia. The results include the concept of confinement in an effective theory with the gluon mass parameter sent to zero and a heuristic scenario concerning extension of the Hamiltonian approach to the dynamics of light quarks.

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Phys. Rev. D 114, 074058– Published 27 October, 2026
  • Received 30 June 2026
  • Accepted 29 September 2026
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