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arXiv · hep-ph/9705466

Running coupling and Borel singularities at small x

K. D. Anderson·D. A. Ross·M. G. Sotiropoulos
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Abstract

Starting from the dipole representation of small-$x$ evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel $(b)$ space. We show that the Borel image of the dipole density is analytic in the neighbourhood of $b=0$ and that it is equal to the BFKL solution at $b=0$. We study the Borel singularity structure of the dipole cascade emanating from a virtual photon at small $x$ and find a branch cut on the positive $b$-semiaxis starting at $b=1/ β_0$. This indicates the presence of $1/Q^2$ power corrections to the small-$x$ structure functions. Finally we present numerical results in the context of D.I.S.

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K. D. Anderson, D. A. Ross, M. G. Sotiropoulos. 1997-05-29. Running coupling and Borel singularities at small x. https://doi.org/10.1016/s0550-3213(97)00835-3

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