Nonperturbative Power Corrections in $\bar\alpha_s(q^2)$ of Two-Loop Analytization Procedure

TL;DR

This paper applies an analytization procedure to the two-loop QCD coupling to remove unphysical singularities, deriving explicit nonperturbative power corrections and their coefficients in the infrared region.

Contribution

It introduces a method to incorporate nonperturbative power corrections into the two-loop QCD coupling using analytization, providing explicit formulas and coefficients.

Findings

Explicit nonperturbative contributions in the infrared are derived.

Power series of negative terms converge for $q^2 > \\Lambda^2$.

Different dependence on term numbers is observed in the series.

Abstract

The analytization procedure which allows one to remove nonphysical singularities of the QCD running coupling constant $\bar\alpha_s(q^2)$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop renormalization group equation. Non-leading at large momentum nonperturbative contributions in $\bar\alpha_s(q^2)$ are obtained in an explicit form. The coefficients of nonperturbative contributions expansions in inverse powers of the squared Euclidean momentum are calculated. For both cases considered there appear convergent at $q^2>\Lambda^2$ power series of negative terms with different dependence on term numbers.