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The gluon splitting function at moderately small x

Marcello Ciafaloni·Dimitri Colferai·Gavin P. Salam·Anna M. Stasto
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Abstract

It is widely believed that at small x, the BFKL resummed gluon splitting function should grow as a power of 1/x. But in several recent calculations it has been found to decrease for moderately small-x before eventually rising. We show that this `dip' structure is a rigorous feature of the P_gg splitting function for sufficiently small alpha_s, the minimum occurring formally at ln 1/x of order 1/sqrt(alpha_s). We calculate the properties of the dip, including corrections of relative order sqrt(alpha_s), and discuss how this expansion in powers of sqrt(alpha_s), which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of alpha_s. Finally, we note that the dip position, as a function of alpha_s, provides a lower bound in x below which the NNLO fixed-order expansion of the splitting function breaksdown and the resummation of small-x terms is mandatory.

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Marcello Ciafaloni, Dimitri Colferai, Gavin P. Salam, Anna M. Stasto. 2004-05-03. The gluon splitting function at moderately small x. https://doi.org/10.1016/j.physletb.2004.02.054

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