A multiloop improvement of non-singlet QCD evolution equations

An approach is elaborated for calculation of 'all loop' contributions to the non-singlet evolution kernels from the diagrams with renormalon chain insertions. Closed expressions are obtained for sums of contributions to kernels P(z) for the DGLAP equation and V(x, y) for the 'nonforward' ER-BL equation from these diagrams that dominate for a large value of b0, the first β-function coefficient. Calculations are performed in the covariant ξ-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter ξ = -3 generalizes the standard 'naive nonabelianization' approximation. The solutions are obtained to the ER-BL evolution equation (taken at the 'all loop' improved kernel), which are in form similar to one-loop solutions. A consequence for QCD descriptions of hard processes and the benefits and incompleteness of the approach are briefly discussed