181 research outputs found
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 limit
Heavy quark form factors are calculated at to all
orders in at the first order in . The
terms in the recent results [arXiv:1611.07535] for the vector form factors are
confirmed, and terms for higher 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
or better. Using algebraic and argument relations the numerical representation
can be limited to the range . We provide replacement
files to map all harmonic polylogarithms to a basis and the usual range of
arguments 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
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