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 MSlike 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. PACS: 12.38.Cy, 12.38.-t, 13.60.Hb