On the Summation of Non‐leading Logarithms in QCD

Abstract

AbstractExploiting the relations between the expansion coefficients of Green's functions and those of β and γ functions in massless QFT, the summation up to the n‐th non‐leading logarithms is reduced to the solution of a system of linear differential equations, which in general differ from renormalization group equations. Applying this procedure to the gluon propagator the leading log approximation is modified near the mass shell by a constant factor only. Furthermore for the gluon propagator exponentiation in terms of the running coupling constant is argued to be restricted to leading logarithms.