All-loops calculation of the structure function for x → 0 in perturbative QCD

• Published in: Nuclear physics. B Vol. 361; no. 3; pp. 645 - 672
• Main Authors: Catani, S., Fiorani, F., Marchesini, G., Oriani, G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 09.09.1991; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics; Theory of quantized fields; Perturbation theory; Structure function; Quantum chromodynamic; Approximation; Recurrence formula; Elementary particle; Evolution equation; Factorization; Inelastic scattering; Gluon; Particle scattering; Quantum field theory; Feynman diagram
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(91)90598-R

We study in perturbative QCD the initial-state radiation associated to hadron processes in the semi-hard region of small x ( x is the Bjorken variable). A recent analysis of the exclusive multi-gluon distributions to double (infrared and collinear) logarithmic accuracy is extended to the case of inclusive distributions, which we evaluate to single (infrared) logarithmic accuracy. Thus the resulting x → 0 structure function or N → 1 gluon anomalous dimension is computed to all-loops accuracy. For the inclusive distributions we are able to perform a calculation to such an accuracy by extensively using cancellations which originate from coherence of QCD radiation and the infrared regularity of real-virtual singularities. We find that the x → 0 structure function satisfies the Lipatov equation. With the present study we therefore provide a new derivation of the Lipatov result in the context of hard collisions together with a fully exclusive description. We discuss the structure of the Lipatov equation in relation with the x → 0 exclusive distributions previously obtained and with the Altarelli-Parisi equation valid for finite values of x.