Revisiting parton evolution and the large-x limit

University of Milan, Milano, Lombardy, Italy
Physics Letters B (Impact Factor: 6.02). 12/2005; 634(5-6):504-507. DOI: 10.1016/j.physletb.2006.02.023
Source: arXiv

ABSTRACT This remark is part of an ongoing project to simplify the structure of the multi-loop anomalous dimensions for parton distributions and fragmentation functions. It answers the call for a “structural explanation” of a “very suggestive” relation found by Moch, Vermaseren and Vogt in the context of the x→1 behaviour of three-loop DIS anomalous dimensions. It also highlights further structure that remains to be fully explained.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the "radiative jet function", responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We perform a case study of the behavior of gluon radiation beyond the soft approximation, using as an example the Drell-Yan production cross section at NNLO. We draw a careful distinction between the eikonal expansion, which is in powers of the soft gluon energies, and the expansion in powers of the threshold variable $1 - z$, which involves important hard-collinear effects. Focusing on the contribution to the NNLO Drell-Yan K-factor arising from real-virtual interference, we use the method of regions to classify all relevant contributions up to next-to-leading power in the threshold expansion. With this method, we reproduce the exact two-loop result to the required accuracy, including $z$-independent non-logarithmic contributions, and we precisely identify the origin of the soft-collinear interference which breaks simple soft-gluon factorization at next-to-eikonal level. Our results pave the way for the development of a general factorisation formula for next-to-leading-power threshold logarithms, and clarify the nature of loop corrections to a set of recently proposed next-to-soft theorems.
    Physics Letters B 10/2014; 742. DOI:10.1016/j.physletb.2015.02.008 · 6.02 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We compute the general form of the six-loop anomalous dimension of twist-two operators with arbitrary spin in planar N=4 SYM theory. First we find the contribution from the asymptotic Bethe ansatz. Then we reconstruct the wrapping terms from the first 35 even spin values of the full six-loop anomalous dimension computed using the quantum spectral curve approach. The obtained anomalous dimension satisfies all known constraints coming from the BFKL equation, the generalised double-logarithmic equation, and the small spin expansion.

Full-text (2 Sources)

Available from
May 31, 2014