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  • Letter
  • Open Access

Meson states in the ‘t Hooft model: Hamiltonian approach

Andrei Smilga*

  • SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307, France

  • *Contact author: smilga@subatech.in2p3.fr
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Phys. Rev. D 114, L081702 – Published 20 October, 2026

DOI: https://doi.org/10.1103/n9c8-q7g3

Abstract

We point out that the masses of the highly excited bound quark-antiquark states in QCD2 in the infinite N limit may be determined in the framework of a simple quantum-mechanical model with the potential V(x)=σ|x|. In the ultrarelativistic case, the masses follow the pattern μn2=πg2N2n, which coincides with the law derived by ‘t Hooft by solving the Bethe-Salpeter equation. In the nonrelativistic case, the levels follow the asymptotics εn=μn−2m=Cn2/3, where the constant C can be determined by solving the ‘t Hooft equation or, alternatively, the nonrelativistic Schrödinger equation.

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References (11)

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Phys. Rev. D 114, L081702– Published 20 October, 2026
  • Received 25 July 2026
  • Accepted 30 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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