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How Chiral Symmetry Breaking Affects the Spectrum of the Light-Heavy Mesons in the 't Hooft Model

We find the spectrum and wave functions of the heavy-light mesons in $(1 + 1)$-dimensional QCD in the 't Hooft limit, both in the rest frame, using the Coulomb (axial) gauge, and on the light cone. Our emphasis is on the effects of chiral symmetry breaking on the spectrum. While dynamical equations in both cases look different, the results for the spectrum are identical. The chiral symmetry breaking is clearly seen from the gap and Bethe--Salpeter equations in the laboratory frame. At the same time, while vacuum is trivial on the light cone (no chiral condensate), the effects of the spontaneous breaking of the chiral symmetry manifest themselves in the same way, as it follows from the coincidence of the spectra obtained from the laboratory-frame Bethe--Salpeter equation on the one hand, and the light-cone 't Hooft-type equation on the other.