# Revisiting parton evolution and the large-x limit

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Yuri Dokshitzer, Jul 13, 2015 Available from:-
- "The reciprocity-respecting splitting function P(x) [73] [74], related to P(M ) through a Mellin transformation, should satisfy the Gribov-Lipatov relation [76] P(x) = − x P 1 x (2.14) at all orders of perturbation theory. "

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**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. -
- "It is however known that also logarithms accompanied by subleading powers of the threshold variable, most notably those with m = 0, which we call next-to-leading power (NLP) threshold logarithms, can give numerically significant contributions [11]. In recent years, a number of studies have appeared [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] developing our understanding of certain classes of NLP threshold logarithms. A full-fledged resummation formalism for NLP logarithms is however still not available. "

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**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 -
- "For the reconstruction of the general expression for the anomalous dimension of the twist-2 operators, coming from the ABA one can used results for the definite values of M . For the full anomalous dimension besides analytical properties we can used a generalized Gribov-Lipatov relation [71] [72] and looking for the reciprocityrespecting function, instead of the anomalous dimension, which is related to each other through: "

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**ABSTRACT:**Using known all-loop results from the BFKL and generalized double-logarithmic equations and large spin limit we have computed the five-loop anomalous dimension of twist-2 operators without consideration of any wrapping effects. One part of the anomalous dimension was calculated in a usual way with the help of Asymptotic Bethe Ansatz. The rest part, related with the wrapping effects, was reconstructed from known constraints with the help of methods from the numbers theory.Journal of High Energy Physics 11/2013; 2014(6). DOI:10.1007/JHEP06(2014)108 · 6.22 Impact Factor