Renormalon chains contributions to the non-singlet evolutional kernels in ${\varphi }_6^3$ and QCD

Abstract

The contributions to non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for certain classes of diagrams which include the renormalon chains. Closed expressions are obtained for the sums of contributions associated with these diagram classes. Calculations are performed in the $[{\varphi }^3{]}_6$ model and QCD in the \MSbar scheme. The contribution for one of the classes of diagrams dominates for a number of flavors $N_f\gg 1$. For the latter case, a simple solution to the Brodsky-Lepage evolution equation is obtained.

11 pages, LATEX, 1 Table, 2 figures are enclosed as ps-file, the text style and figures are corrected following to Phys. Lett. B version of this paper

References in corpus (1)

• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit

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