Renormalon chain contributions to the non-singlet evolution kernels in [ϕ3]6 and QCD

The contributions to non-singlet evolution kernels P(z), for the DGLAP equation, and V(x,y), for the Brodsky–Lepage equation, are calculated for certain classes of diagrams including the renormalon chains. Closed expressions are obtained for the sums of contributions associated with these diagram classes. Calculations are performed in the [ϕ3]6 model and QCD in the MS scheme. The contribution of one of the classes of diagrams dominates for a large number of flavours Nf≫1. For the latter case, a simple solution to the Brodsky–Lepage evolution equation is obtained.