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Renormalisation group improved small-x Green's function

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arxiv hep-ph/0307188 v1 pith:EI5ODJOY submitted 2003-07-15 hep-ph

M. Ciafaloni , D. Colferai , G. P. Salam , A. M. Stasto This is my paper · ORCID
classification hep-ph
keywords functionsmall-xexponentgreenpomeronresummedsplittingalpha
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We investigate the basic features of the gluon density predicted by a renormalisation group improved small-x equation which incorporates both the gluon splitting function at leading collinear level and the exact BFKL kernel at next-to-leading level. We provide resummed results for the Green's function and its hard Pomeron exponent $\omega_s(\alpha_s)$, and for the splitting function and its critical exponent $\omega_c(\alpha_s)$. We find that non-linear resummation effects considerably extend the validity of the hard Pomeron regime by decreasing diffusion corrections to the Green's function exponent and by slowing down the drift towards the non-perturbative Pomeron regime. As in previous analyses, the resummed exponents are reduced to phenomenologically interesting values. Furthermore, significant preasymptotic effects are observed. In particular, the resummed splitting function departs from the DGLAP result in the moderate small-x region, showing a shallow dip followed by the expected power increase in the very small-x region. Finally, we outline the extension of the resummation procedure to include the photon impact factors.

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Cited by 4 Pith papers

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  1. New results on small-x resummation for splitting functions

    hep-ph 2026-03 conditional novelty 8.0 of 10

    A closed-form all-order expression for the qg anomalous dimension, plus new all-order results for the LL gluon anomalous dimension and the finite qg/gg Green functions, derived and implemented in HELL 4.0.

  2. Running coupling effects in the anti-collinear resummation in high energy evolution

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  4. QCD-Gravity double copy in Regge asymptotics: from $2\rightarrow n$ amplitudes to radiation in shockwave collisions

    hep-th 2025-07 accept novelty 3.0 of 10

    A lecture-note synthesis showing that the same Lipatov vertices and reggeized propagators govern multi-particle production in QCD and gravity, with double-copy, Weinberg soft, and shockwave limits all connected in one...

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