Renormalon chains contributions to the non-singlet evolutional kernels in QCD

Abstract

Contributions to QCD non-singlet evolution kernels $P(z)$ for the DGLAP equation and $V(x,y)$ for the Brodsky-Lepage evolution equation are calculated for a certain class of diagrams which include renormalon chains. Closed expressions are presented for the sums of these contributions that dominate for a large number of flavors $N_f\gg 1$. Calculations are performed in covariant $\xi$-gauge, in the \MSbar scheme. The assumption of "naive nonabelianization" approximation for kernel calculations is discussed. The partial solution to the Brodsky-Lepage evolution equation is obtained.

9 pages, LATEX, 1 Table, 1 figure is included into the tex-file, 1 figure is added as ps-file. References added, minor corrections in style, to be published in Physics Letters B

References in corpus (3)

• Predictions from conformal algebra for the deeply virtual Compton scattering
• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit
• Renormalon chains contributions to the non-singlet evolutional kernels in ${\varphi }_6^3$ and QCD

Cited by in corpus (13)

• Renormalons
• Transition form factors of the pion in light-cone QCD sum rules with next-to-next-to-leading order contributions
• Renormalons and multiloop estimates in scalar correlators, Higgs decay and quark-mass sum rules
• Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion
• Comparison of the Gottfried and Adler sum rules within the large-Nc expansion
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The gluon content of the $\eta$ and ${\eta }^{\prime }$ mesons and the $\eta \gamma$, ${\eta }^{\prime }\gamma$ electromagnetic transition form factors
• IR-Improved DGLAP Theory: Kernels, Parton Distributions, Reduced Cross Sections
• IR-Improved DGLAP Theory
• A multiloop improvement of non-singlet QCD evolution equations
• The analytical $\mathcal{O}(a_s^4)$ expression for the polarized Bjorken sum rule in the miniMOM scheme and the consequences for the generalized Crewther relation
• Correlators of vector, tensor, and scalar composite vertices of order $O({\alpha }_s^2{\beta }_0)$
• Convergence and Gauge Dependence Properties of the Resummed One-loop Quark-Quark Scattering Amplitude in Perturbative QCD