Renormalon chains contributions to the non-singlet evolutional kernels in QCD

Abstract

Contributions to QCD non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for a certain class of diagrams which include renormalon chains. Closed expressions are presented for the sums of these contributions that dominate for a large number of flavors $N_f \gg 1$. Calculations are performed in covariant $\xi$-gauge, in the \MSbar scheme. The assumption of "naive nonabelianization" approximation for kernel calculations is discussed. The partial solution to the Brodsky-Lepage evolution equation is obtained.