Large-order asymptotic terms in perturbation theory: The first (4-ε)-expansion correction to renormalization constants in the O(n)-symmetric theory

We investigate large-order asymptotic terms in the perturbation theory for the O(n) symmetric φ4 (4-ε)-model in the minimal subtraction scheme. Taking the specificity of the (4-ε)-minimal-subtraction scheme into account, we calculate corrections to the asymptotic formula for the expansion coefficients of the renormalization constant Zg and the critical index η. The resulting corrections essentially improve the asymptotic description of the results in loop calculations.