Non Abelian $q\bar{q}$ contributions to small-$x$ anomalous dimensions
G. Camici, M. Ciafaloni
TL;DR
This work investigates non-abelian qbarq contributions to small-x anomalous dimensions within the k-factorization and BFKL frameworks, addressing both heavy flavour production and the NL gluon kernel. It derives closed-form NL resummation formulas for these contributions and combines them with virtual corrections in the Q0-scheme to obtain the complete qbarq effect on the gluon anomalous dimension. The results show that, while qbarq NL effects are significant for heavy flavour production, they largely cancel in the gluon eigenvalue gamma+ due to abelian/non-abelian interplay, with sizable NL scaling violations remaining in gamma_qg. These findings have implications for reducing factorization-scheme dependence and motivate measurements of observables like F_L to better constrain gluon densities and NL dynamics at small x.
Abstract
By using $\k$-factorization, we derive resummation formulas for the non-abelian $q\bar{q}$ contributions to both heavy flavour production by gluon fusion, and to the next-to-leading BFKL kernel. By combining this result with previous ones by Fadin et al. on the virtual terms, we also compute in closed form the complete $q\bar{q}$ contribution to the gluon anomalous dimension in the $Q_0$-scheme. We find that $q\bar{q}$ resummation effects are important for heavy flavour production, but are instead small in the anomalous dimension eigenvalues, because of a cancellation between abelian and non abelian contributions.