Asymptotic Behavior of Renormalization Constants in Higher Orders of the Perturbation Expansion for the (4−∈)-Dimensionally Regularized O(n)-Symmetric φ4 Theory

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Higher-order asymptotic expansions for renormalization constants and critical exponents of the O(n)-symmetric φ4 theory are found based on the instanton approach in the minimal subtraction scheme for the (4−∈)-dimensional regularization. The exactly known expansion terms differ substantially from their asymptotic values. We find expressions that improve the asymptotic expansions for unknown expansion terms of the renormalization constants.