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Exact solution of the’ t Hooft equation in the limit of heavy quarks with unequal masses

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Abstract

We consider the’ t Hooft equation for bound states in the two-dimensional quantum chromodynamics in the limit of an infinite number of colors. In the case of quarks with unequal masses tending to infinity, we obtain an approximation to the low-energy part of the spectrum and the corresponding wave functions. We show that as in the case of equal masses, the’ t Hooft equation in the first approximation reduces to the Schrödinger equation with a linear potential, i.e., to the equation for a particle in a “triangular” potential well. We also discuss the possibility of obtaining corrections to this approximation.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    R. A. Zubov, S. A. Paston & E. V. Prokhvatilov

Authors
  1. R. A. Zubov
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  2. S. A. Paston
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  3. E. V. Prokhvatilov
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Correspondence to R. A. Zubov or S. A. Paston.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 3, pp. 449–455, September, 2015.

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Zubov, R.A., Paston, S.A. & Prokhvatilov, E.V. Exact solution of the’ t Hooft equation in the limit of heavy quarks with unequal masses. Theor Math Phys 184, 1281–1286 (2015). https://doi.org/10.1007/s11232-015-0335-6

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