55 research outputs found
A calculation of the three-loop helicity-dependent splitting functions in QCD
We have calculated the complete matrix of three-loop helicity-difference
(`polarized') splitting functions Delta P_ik^(2), i,k = q,g, in massless
perturbative QCD. In this note we briefly discuss some properties of the
polarized splitting functions and our non-standard determination of the
hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The
resulting next-to-next-to-leading order (NNLO) corrections to the evolution of
polarized parton distributions are illustrated and found to be small even at
rather large values of the strong coupling constant alpha_s.Comment: 10 pages, LaTeX (PoS style), 4 eps-figures. Proceedings of `Loops &
Legs 2014', Weimar (Germany), April/May 201
The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
We present the next-to-next-to-leading order (NNLO) contributions to the main
splitting functions for the evolution of longitudinally polarized parton
densities of hadrons in perturbative QCD. The quark-quark and gluon-quark
splitting functions have been obtained by extending our previous all Mellin-N
calculations to the structure function g_1 in electromagnetic deep-inelastic
scattering (DIS). Their quark-gluon and gluon-gluon counterparts have been
derived using third-order fixed-N calculations of structure functions in
graviton-exchange DIS, relations to the unpolarized case and mathematical tools
for systems of Diophantine equations. The NNLO corrections to the splitting
functions are small outside the region of small momentum fractions x where they
exhibit a large double-logarithmic enhancement, yet the corrections to the
evolution of the parton densities can be unproblematic down to at least x about
10^{-4}.Comment: 52 pages, Latex, 10 figures. FORM and Fortran files of the main
results available with the sourc
The Quark Form Factor at Higher Orders
We study the electromagnetic on-shell form factor of quarks in massless
perturbative QCD. We derive the complete pole part in dimensional
regularization at three loops, and extend the resummation of the form factor to
the next-to-next-to-leading contributions. These results are employed to
evaluate the infrared finite absolute ratio of the time-like and space-like
form factors up to the fourth order in the strong coupling constant. Besides
for the pole structure of higher-loop QCD amplitudes, our new contributions to
the form factor are also relevant for the high-energy limit of massive gauge
theories like QED. The highest-transcendentality component of our results
confirms a result recently obtained in N=4 Super-Yang-Mills theory.Comment: 16 pages, 1 figure, Late
First results for three-loop deep-inelastic structure functions in QCD
As a first step towards the complete calculation of deep-inelastic scattering
at third order of massless perturbative QCD, we have computed the fermionic
(nf) contributions to the flavour non-singlet structure functions in
unpolarized electromagnetic scattering. We briefly discuss the approach chosen
for this calculation, the problems we encountered and the status of the
project. We show the results for the corresponding anomalous dimension in both
Mellin-N and Bjorken-x. Together with the nf part of A_3, our calculation
facilitates the complete determination of the threshold-resummation
coefficients B_2 and D_2^DIS. The latter quantity vanishes in the MSbar scheme.Comment: 5 pages, LaTeX. Talk given at RADCOR02, Kloster Ban
On gamma_5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution
We discuss the prescription for the Dirac matrix gamma_5 in dimensional
regularization used in most second- and third-order QCD calculations of
collider cross sections. We provide an alternative implementation of this
approach that avoids the use of an explicit form of gamma_5 and of its (anti-)
commutation relations in the most important case of no more than one gamma_5 in
each fermion trace. This treatment is checked by computing the third-order
corrections to the structure functions F_2 and g_1 in charged-current
deep-inelastic scattering with axial-vector couplings to the W-bosons. We
derive the so far unknown third-order helicity-difference splitting function
Delta P_ns^(2)s that contributes to the next-to-next-to-leading order (NNLO)
evolution of the polarized valence quark distribution of the nucleon. This
function is negligible at momentum fractions x >~ 0.3 but relevant at x << 1.Comment: 11 pages, Latex, 2 figures. FORM and Fortran files of the main
results available with the sourc
Non-singlet coefficient functions for charged-current deep-inelastic scattering to the third order in QCD
We have calculated the coefficient functions for the structure functions F_2,
F_L and F_3 in nu-nubar charged-current deep-inelastic scattering (DIS) at the
third order in the strong coupling alpha_s, thus completing the description of
unpolarized inclusive W^(+-) exchange DIS to this order of massless
perturbative QCD. In this brief note, our new results are presented in terms of
compact approximate expressions that are sufficiently accurate for
phenomenological analyses. For the benefit of such analyses we also collect, in
a unified notation, the corresponding lower-order contributions and the flavour
non-singlet coefficient functions for nu+nubar charged-current DIS. The
behaviour of all six third-order coefficient functions at small Bjorken-x is
briefly discussed.Comment: 6 pages, LaTeX (PoS style), 1 eps-figure. Fortran files of the main
results available with the source. To appear in the proceedings of `DIS
2016', DESY, Hamburg (Germany), April 201
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
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
Resummed small-x and first-moment evolution of fragmentation functions in perturbative QCD
We study the splitting functions for the evolution of fragmentation
distributions and the coefficient functions for single-hadron production in
semi-inclusive electron-positron annihilation in massless perturbative QCD for
small values of the momentum fraction and scaling variable x, where their
fixed-order approximations are completely destabilized by huge double
logarithms of the form alpha_s^n 1/x ln^(2n-a) x. Complete analytic all-order
expressions in Mellin-N space are presented for the resummation of these terms
at the next-to-next-to-leading logarithmic accuracy. The poles for the first
moments, related to the evolution of hadron multiplicities, and the small-x
instabilities of the next-to-leading order splitting and coefficient functions
are removed by this resummation, which leads to an oscillatory small-x
behaviour and functions that can be used at N=1 and down to extremely small
values of x. First steps are presented towards extending these results to the
higher accuracy required for an all-x combination with the state-of-the-art
next-to-next-to-leading order large-x results.Comment: 21 pages, LaTeX, 4 figures (.eps). FORM file of main results included
in sourc
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