19 research outputs found
Four-loop results on anomalous dimensions and splitting functions in QCD
We report on recent progress on the flavour non-singlet splitting functions
in perturbative QCD. The~exact four-loop (N^3LO) contribution to these
functions has been obtained in the planar limit of a large number of colours.
Phenomenologically sufficient approximate expressions have been obtained for
the parts not exactly known so far. Both cases include results for the
four-loop cusp and virtual anomalous dimensions which are relevant well beyond
the evolution of non-singlet quark distributions, for which an accuracy of
(well) below 1% has now been been reached.Comment: 11 pages, LaTeX (PoS style), 4 eps-figures. Contribution to the
proceedings of `RADCOR 2017', St. Gilgen (Austria), September 201
First Forcer results on deep-inelastic scattering and related quantities
We present results on the fourth-order splitting functions and coefficient
functions obtained using Forcer, a four-loop generalization of the Mincer
program for the parametric reduction of self-energy integrals. We have computed
the respective lowest three even-N and odd-N moments for the non-singlet
splitting functions and the non-singlet coefficient functions in
electromagnetic and nu+nu(bar) charged-current deep-inelastic scattering, and
the N=2 and N=4 results for the corresponding flavour-singlet quantities.
Enough moments have been obtained for an LLL-based determination of the
analytic N-dependence of the nf^3 and nf^2 parts, respectively, of the singlet
and non-singlet splitting functions. The large-N limit of the latter provides
the complete nf^2 contributions to the four-loop cusp anomalous dimension. Our
results also provide additional evidence of a non-vanishing contribution of
quartic group invariants to the cusp anomalous dimension.Comment: 11 pages, LaTeX (PoS style), 4 eps-figures. To appear in the
proceedings of `Loops & Legs 2016', Leipzig (Germany), April 201
Anomalous dimensions and splitting functions beyond the next-to-next-to-leading order
We report on recent progress on the splitting functions for the evolution of
parton distributions and related quantities, the (lightlike) cusp anomalous
dimensions, in perturbative QCD. New results are presented for the four-loop
(next-to-next-to-next-to-leading order, N^3LO) contributions to the
flavour-singlet splitting functions and the gluon cusp anomalous dimension. We
present first results, the moments N=2 and N=3, for the five-loop (N^4LO)
non-singlet splitting functions.Comment: 10 pages, LaTeX (PoS style), 3 eps-figures. Contribution to the
proceedings of `Loops & Legs 2018', St. Goar (Germany), April/May 201
Large-nf contributions to the four-loop splitting functions in QCD
We have computed the fourth-order nf^2 contributions to all three non-singlet
quark-quark splitting functions and their four nf^3 flavour-singlet
counterparts for the evolution of the parton distributions of hadrons in
perturbative QCD with nf effectively massless quark flavours. The analytic form
of these functions is presented in both Mellin N-space and momentum-fraction
x-space; the large-x and small-x limits are discussed. Our results agree with
all available predictions derived from lower-order information. The large-x
limit of the quark-quark cases provides the complete nf^2 part of the four-loop
cusp anomalous dimension which agrees with two recent partial computations.Comment: 29 pages, Latex, 8 figures. FORM files of the main results available
with the sourc
DIS coefficient functions at four loops in QCD and beyond
We report results for the lowest even- moments of the flavor-nonsinglet structure functions and in QCD at the fourth order in the perturbative expansion in the strong coupling constant .Our results are presented in numerical form and we compare them with theleading and subleading terms of the threshold expansion for large values of , which corresponds to the limit
Low moments of the four-loop splitting functions in QCD
We have computed the four lowest even-N moments of all four splitting functions for the evolution of flavour-singlet parton densities of hadrons at the fourth order in the strong coupling constant αs. The perturbative expansion of these moments, and hence of the splitting functions for momentum fractions x≳0.1, is found to be well behaved with relative αs-coefficients of order one and sub-percent effects on the scale derivatives of the quark and gluon distributions at αs≲0.2. More intricate computations, including other approaches such as the operator-product expansion, are required to cover the full x-range relevant to LHC analyses. Our results are presented analytically for a general gauge group for detailed checks and validations of such future calculations
Anomalous dimensions and splitting functions beyond the next-to-next-to-leading order
We report on recent progress on the splitting functions for the evolution of parton distributions and related quantities, the (lightlike) cusp anomalous dimensions, in perturbative QCD. New results are presented for the four-loop (next-to-next-to-next-to-leading order, NLO) contributions to the flavour-singlet splitting functions and the gluon cusp anomalous dimension. We present first results, the moments N=2 and N=3, for the five-loop (NLO) non-singlet splitting functions