Revisiting parton evolution and the large-x limit

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.Comment: 6 pages, v2 corrects misprints and contains an additional referenc

Timelike structure functions and hadron multiplicities

“…Two of them have been the most successfull. The first one is due to Dokshitzer, Marchesini and Salam [22] who developed a formalism trying to rescue (at least at the formal level) the GribovLipatov relation at higher orders. The approach of Ref.…”

“…The approach of Ref. [22] shaded light on many theoretical aspects revealing (using their words) "intrinsic beauty of the perturbative quark-gluon dynamics" [23]. The second one is based on the fact that the "timelike" and the "spacelike" splitting functions can be related by the analytic continuation of the scaling variable x → 1/x with x representing the fraction of the parton longitudinal momentum.…”

A complete basis of helicity operators for subleading factorization

“…The description of observables with more complicated dynamics typically relies on factorization theorems and much less is known about the structure of power corrections in these cases. Power corrections have been considered for Drell-Yan [11][12][13][14][15] at O(Λ 2 QCD /Q 2 ), for inclusive B decays in the endpoint region at O((1−z) 0 , (Λ QCD /m b ) 1,2 ) [16][17][18][19][20][21][22][23][24], for exclusive B decays at O(Λ QCD /m b ) [25][26][27][28][29][30][31][32][33], for event shapes τ in e + e − , ep, and pp collisions at O(Λ k QCD /(Qτ ) k ) [13,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], and at O((1 − z) 0 ) for threshold resummation [49][50][51][52][53][54][55][56]…”

Twist 3 of the sector of SYM and reciprocity respecting evolution

“…Here we employ the definition of the anomalous dimension which is more familiar to the integrable community 1 ; within this convention the scaling violation rate is given by the expression ÐÒ É ¾ ÐÒ AE´É ¾ µ ¾ ´AEµ In the context of the QCD parton picture, the notion of the RR evolution kernel È emerges as a result of the reformulation of space-like (DIS, "S") and time-like parton multiplication processes ( · , "T") in terms of a unified evolution equation [16,17]. This equation is constructed on a basis of the parton fluctuation time ordering.…”