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arXiv · 2212.02162

Comments on 1+1d QCD with heavy adjoint quarks

Meseret Asrat
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Abstract

In this paper, we determine at weak coupling the non-relativistic $n$-body Schr\"{o}dinger equation that describes the low-lying color singlet bound states of two dimensional adjoint $QCD$ with heavy quarks. In the case of three adjoint quarks, we show that the three-body equation reduces equivalently to the Schr\"{o}dinger equation that describes a point electric dipole in an electric field in a plane angular sector. We conjecture that the three-body problem is solvable. The eigenstates are given in terms of the triconfluent Heun functions. Our conjecture implies that a bound state of three adjoint quarks is described by a particle confined in a two dimensional Cornell potential. We expect the $n$-parton problem also to be solvable in a similar fashion.

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Meseret Asrat. 2022-12-05. Comments on 1+1d QCD with heavy adjoint quarks. https://doi.org/10.1103/physrevd.107.106022

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