Exact $m_{quark}\neq 0$ Condensates in $QCD_{1+1}(N_C\rightarrow \infty)$

Details Exact $m_{quark}\neq 0$ Condensates in $QCD_{1+1}(N_C\rightarrow \infty)$ Exact $m_{quark}\neq 0$ Condensates in $QCD_{1+1}(N_C\rightarrow \infty)$

1994-09-15

arxiv.org/abs/hep-ph/9409333v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

5 pages, 1 postscript figure (available by email from the author), LATEX

Scientific paper

In the limit of an infinite number of colors, we derive an analytic expression for the quark condensate in $QCD_{1+1}$ as a function of the quark mass and the gauge coupling constant. For zero quark mass, a nonvanishing quark condensate is obtained. Nevertheless, we prove that there is no phase transition as a function of the quark mass. It is furthermore shown that the expansion of $\langle 0 | \overline{\psi}\psi |0\rangle$ in the gauge coupling has zero radius of convergence but that the perturbation series is Borel summable with finite radius of convergence. The nonanalytic behavior $\langle 0 | \overline{\psi}\psi |0\rangle \stackrel{m_q\rightarrow0}{\sim} - N_C \sqrt{G^2}$ can only be obtained by summing the perturbation series to infinite order.

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