Studies of Unitarity at Small~$x$ Using the Dipole Formulation

Abstract

Mueller's dipole formulation of onium-onium scattering is used to study unitarity corrections to the BFKL power growth at high energies. After a short discussion of the spatial distribution of colour dipoles in a heavy quarkonium and the associated fluctuations, results are presented showing that the one and two-pomeron contributions to the total cross section are the same at a rapidity $Y\simeq 14$. Above this rapidity the large fluctuations in the onium wave function cause the multiple pomeron series to diverge. Resumming the series allows one to show that unitarity corrections set in gradually for the total cross section, which is dominated by rare, large, configurations of the onia. The elastic cross section comes mostly from much smaller impact parameters and has significant unitarity corrections starting at a rapidity $Y\simeq 8$.

30 pages LaTeX2e with 12 figures as appended as uuencoded eps. Uses epsfig. Postscript file for complete paper available from http://www.hep.phy.cam.ac.uk/theory/papers/index.html

References in corpus (3)

• Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes
• Unitarity and the BFKL Pomeron
• Multiplicity distribution of colour dipoles at small~$x$

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