Running coupling and Borel singularities at small x

Details Running coupling and Borel singularities at small x Running coupling and Borel singularities at small x

1997-05-29

arxiv.org/abs/hep-ph/9705466v1

Nucl.Phys. B515 (1998) 249-268

Physics

High Energy Physics

High Energy Physics - Phenomenology

20 pages, Latex, 3 figures included

Scientific paper

10.1016/S0550-3213(97)00835-3

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 $b=1/ \beta_0$. 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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