### 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) |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### 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

}

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*, vol. 587, no. 1-2, pp. 87-94. https://doi.org/10.1016/j.physletb.2004.02.054

**The gluon splitting function at moderately small x.** / Ciafaloni, M.; Colferai, D.; Salam, G. P.; Staśto, A. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The gluon splitting function at moderately small x

AU - Ciafaloni, M.

AU - Colferai, D.

AU - Salam, G. P.

AU - Staśto, A. M.

PY - 2004/5/6

Y1 - 2004/5/6

N2 - 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 Pgg splitting function for sufficiently small αs, the minimum occurring formally at log(1/x)∼1/αs. We calculate the properties of the dip, including corrections of relative order αs, and discuss how this expansion in powers of αs, which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of αs. Finally, we note that the dip position, as a function of αs, 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.

AB - 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 Pgg splitting function for sufficiently small αs, the minimum occurring formally at log(1/x)∼1/αs. We calculate the properties of the dip, including corrections of relative order αs, and discuss how this expansion in powers of αs, which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of αs. Finally, we note that the dip position, as a function of αs, 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=1842738679&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2004.02.054

DO - 10.1016/j.physletb.2004.02.054

M3 - Article

AN - SCOPUS:1842738679

VL - 587

SP - 87

EP - 94

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

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

SN - 0370-2693

IS - 1-2

ER -