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Nonrelativistic meson masses from the Curci-Ferrari model

Anaclara Alvez1, Nahuel Barrios2, Florencia Benítez2, Sofía Bortagaray3, and Marcela Peláez2

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Phys. Rev. D 114, 076014 – Published 8 October, 2026

DOI: https://doi.org/10.1103/5hhz-dgnb

Abstract

We study the mass spectrum of nonrelativistic mesons composed of charm and bottom quarks within the framework of the Curci-Ferrari model in the Landau gauge, deriving the Hamiltonian from the scattering amplitude of a single massive gluon exchange. We solve the Schrödinger equation for the dominant terms of the Hamiltonian, which include the kinetic energy and a Yukawa-type potential, together with a confining Cornell potential. Other corrections to the energy, such as the spin-dependent terms, are introduced perturbatively. We perform two types of fits to the experimental/lattice data. In the first, we fit the charmonium and bottomonium spectra independently. In the second, we fit all three spectra simultaneously, making use of the one-loop running of the gauge coupling and the gluon mass. Both fits provide a reasonable description of the available data within the present model uncertainties and the latter, being more constrained, favors a nonvanishing gluon mass.

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Phys. Rev. D 114, 076014– Published 8 October, 2026
  • Received 24 September 2025
  • Accepted 10 August 2026
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