Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1995-10-22
Phys.Rev. D53 (1996) 5821-5833
Physics
High Energy Physics
High Energy Physics - Phenomenology
latex, 26 pages. A final version to appear in Phys. Rev.D
Scientific paper
10.1103/PhysRevD.53.5821
We discuss two dimensional $QCD (N_c\to\infty)$ with fermions in the fundamental as well as adjoint representation. We find factorial growth $\sim (g^2N_c\pi)^{2k}\frac{(2k)!(-1)^{k-1}}{(2 \pi)^{2k}}$ in the coefficients of the large order perturbative expansion. We argue that this behavior is related to classical solutions of the theory, instantons, thus it has nonperturbative origin. Phenomenologically such a growth is related to highly excited states in the spectrum. We also analyze the heavy-light quark system $Q\bar{q}$ within operator product expansion (which it turns out to be an asymptotic series). Some vacuum condensates $\la\bar{q}(x_{\mu}D_{\mu})^{2n}q\ra\sim (x^2)^n\cdot n!$ which are responsible for this factorial growth are also discussed. We formulate some general puzzles which are not specific for 2D physics, but are inevitable features of any asymptotic expansion. We resolve these apparent puzzles within $QCD_2$ and we speculate that analogous puzzles might occur in real 4-dimensional QCD as well.
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