Heavy-quark condensate at zero and finite temperatures for various forms of the short-distance potential

Abstract

With the use of the world-line formalism, the heavy-quark condensate in the SU(N)-QCD is evaluated for the cases when the next-to-1/r term in the quark-antiquark potential at short distances is either quadratic, or linear. In the former case, which takes place in the stochastic vacuum model, the standard QCD-sum-rules result is reproduced. In the other case, the condensate turns out to be UV-finite only in less than four dimensions. This fact excludes a possibility to have, in four dimensions, the linear term in the potential, as well as short strings, at the distances smaller than the vacuum correlation length. The use of the world-line formalism enables one to generalize further both results for the condensate to the case of finite temperatures. A generalization of the QCD-sum-rules result to the case of an arbitrary number of space-time dimensions is also obtained and turns out to be UV-finite, provided this number is smaller than six.