A multiloop improvement of non-singlet QCD evolution equations

TL;DR

This paper develops a comprehensive method to calculate all-loop contributions to non-singlet QCD evolution equations, improving the precision of theoretical predictions for hard scattering processes.

Contribution

It introduces a multiloop approach for non-singlet QCD evolution kernels, providing closed-form expressions and an improved solution method that accounts for dominant diagrams at large $b_0$.

Findings

Derived closed expressions for evolution kernels $P(z)$ and $V(x,y)$.

Established a special gauge choice $\xi=-3$ for generalized approximation.

Obtained solutions similar to one-loop solutions with all-loop kernels.

Abstract

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 $b_0$, the first $\beta$-function coefficient. Calculations are performed in the covariant $\xi$-gauge in a MS-like scheme. It is established that a special choice of the gauge parameter $\xi=-3$ 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.