Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-11-19
J.Exp.Theor.Phys. 93 (2001) 1-23; Zh.Eksp.Teor.Fiz. 120N1 (2001) 5-30
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, PDF
Scientific paper
10.1134/1.1391515
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for estimating errors is developed, and an optimization procedure is described. Application of the algorithm to the $\phi^4$ theory gives a behavior $\beta(g)\approx 7.4 g^{0.96}$ at large $g$ for its Gell-Mann -- Low function. The fact that the exponent is close to unity can be interpreted as a manifestation of the logarithmic branching of the type $\beta(g)\sim g (\ln g)^{-\gamma}$ (with $\gamma\approx 0.14$), which is confirmed by independent evidence. In any case, the $\phi^4$ theory is internally consistent. The procedure of summing perturbartive series with arbitrary values of expansion parameter is discussed.
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