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Meson scattering and tetraquarks in two-dimensional QCD

Hagop Sazdjian*

  • *Contact author: hagop.sazdjian@ijclab.in2p3.fr
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Phys. Rev. D 112, 054029 – Published 17 September, 2025

DOI: https://doi.org/10.1103/fnk2-jj72

Abstract

Two-quark–two-antiquark systems with four different quark flavors are considered in the framework of two-dimensional QCD, in the light-cone gauge, at leading orders of the 1/Nc expansion. Introducing basis functions with color-singlet mesonic clusters, integral equations are established for the Green’s functions and the related scattering amplitudes involved in the sectors of the direct and quark-exchange channels. The problem of infrared divergences is dealt with via a systematic use of an infrared regulator cutoff introduced in the gluon propagator. It is shown that the on-mass shell scattering amplitudes are free of infrared divergences up to order 1/Nc2. In the limit of vanishing of the infrared cutoff, they can be represented by effective four-meson contact-type interaction terms with unitarity loops, calculable in terms of the meson wave functions and propagators. The results, obtained at order 1/Nc2, are summed with the constraint of unitarization. The unitarized scattering amplitudes are continued in the total mass-squared variable below the two-meson thresholds, leading to a tetraquark bound state equation, which generally has one solution. Spectroscopic applications of the above results are sketched and discussed.

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Phys. Rev. D 112, 054029– Published 17 September, 2025
  • Received 30 April 2025
  • Accepted 20 August 2025
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