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arXiv · hep-ph/9910389

A multiloop improvement of non-singlet QCD evolution equations

S. V. Mikhailov
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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 $β$-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.

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S. V. Mikhailov. 2000-03-20. A multiloop improvement of non-singlet QCD evolution equations. https://doi.org/10.1103/physrevd.62.034002

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