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Open-flavor threshold effects on quarkonium spectrum in the Born-Oppenheimer effective field theory

Nora Brambilla1,2,3,*, Abhishek Mohapatra1,4,†, Tommaso Scirpa1,‡, and Antonio Vairo1,§

  • *Contact author: nora.brambilla@tum.de
  • †Contact author: abhishek.mohapatra@tum.de
  • ‡Contact author: tommaso.scirpa@tum.de
  • §Contact author: antonio.vairo@tum.de
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Phys. Rev. D 114, 054049 – Published 24 September, 2026

DOI: https://doi.org/10.1103/1jng-m25w

Abstract

The impact of open-flavor thresholds on the quarkonium spectrum has been a subject of study since the introduction of the Cornell potential and has been quantified through various phenomenological approaches, most notably the P03 model. We revisit this problem using the Born-Oppenheimer effective field theory (BOEFT), an effective field theory systematically derived from QCD by exploiting hierarchies of energy scales and symmetries. Within the BOEFT, open-flavor threshold effects emerge from the mixing between quarkonium and tetraquark static potentials sharing the same Born-Oppenheimer quantum numbers. The shapes of the static potentials are constrained by lattice QCD calculations. Furthermore, we account for the distinctive behavior of the BOEFT tetraquark static potentials at short and large distances: at short distances they are repulsive, reflecting the color-octet configuration of the heavy quark-antiquark pair, while at large distances they asymptotically approach heavy-light meson-antimeson thresholds. To quantify threshold effects on the quarkonium spectrum below threshold, we solve a set of coupled Schrödinger equations dictated by the BOEFT, whose only free parameter, the adjoint meson mass, is fixed to the mass of the χc1(3872) state. These coupled equations are solved both in the spin-isospin averaged threshold limit and, for the first time, including the spin splittings of the physical thresholds. We validate our results by computing the same threshold effects as self-energy corrections to the quarkonium propagator. We compare our predictions with existing experimental data and previous literature. Finally, we provide a field-theoretical interpretation of the pair-creation constant γ appearing in the P03 model.

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Phys. Rev. D 114, 054049– Published 24 September, 2026
  • Received 24 April 2026
  • Accepted 21 August 2026
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