### 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 α_{s}, the minimum occurring formally at log(1/x)∼1/α_{s}. We calculate the properties of the dip, including corrections of relative order α_{s}, and discuss how this expansion in powers of α_{s}, which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of α_{s}. Finally, we note that the dip position, as a function of α_{s}, provides a lower bound in x below which the NNLO fixed-order expansion of the splitting function breaks down and the resummation of small-x terms is mandatory.

Original language | English (US) |
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Pages (from-to) | 87-94 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 587 |

Issue number | 1-2 |

DOIs | |

State | Published - May 6 2004 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*587*(1-2), 87-94. https://doi.org/10.1016/j.physletb.2004.02.054