Revisiting parton evolution and the large-x limit

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

Towards three-loop QCD corrections to the time-like splitting functions

We report on the status of a direct computation of the time-like splitting functions at next-to-next-to-leading order in QCD. Time-like splitting functions govern the collinear kinematics of inclusive hadron production and the evolution of the parton fragmentation distributions. Current knowledge about them at three loops has been inferred by means of crossing symmetry from their related space-like counterparts, which has left certain parts of the off-diagonal quark-gluon splitting function undetermined. This motivates an independent calculation from first principles. We review the tools and methods which are applied to attack the problem.Comment: 11 pages, 5 figures; presented at the Epiphany Conference 2015 (Cracow, Poland); additional files: MassFactorization.n

NNLO BFKL Pomeron eigenvalue in N=4 SYM

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.Comment: 6 pages; v2: typos fixed, references and supplementary Mathematica files adde

Heavy quark form factors in the large β0\beta_0 limit

Heavy quark form factors are calculated at $\beta_0 \alpha_s \sim 1$ to all orders in $\alpha_s$ at the first order in $1/\beta_0$. The $n_f^2 \alpha_s^3$ terms in the recent results [arXiv:1611.07535] for the vector form factors are confirmed, and $n_f^{L-1} \alpha_s^L$ terms for higher $L$ are predicted.Comment: v2: the section on inversion relations extended; v3: 3 refs added, discussion of the hypergeometric function expansion extended; v4: eq. (22) and fig. 5 correcte

Numerical Implementation of Harmonic Polylogarithms to Weight w = 8

We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9 \cdot 10^{-15}$ or better. Using algebraic and argument relations the numerical representation can be limited to the range $x \in [0, \sqrt{2}-1]$. We provide replacement files to map all harmonic polylogarithms to a basis and the usual range of arguments $x \in ]-\infty,+\infty[$ to the above interval analytically. We also briefly comment on a numerical implementation of real valued cyclotomic harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat