Non-singlet coefficient functions for charged-current deep-inelastic scattering to the third order in QCD

Abstract

We have calculated the coefficient functions for the structure functions F 2 , F L and F 3 in ν −ν charged-current deep-inelastic scattering (DIS) at the third order in the strong coupling α 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 ν +ν charged-current DIS. The behaviour of all six third-order coefficient functions at small Bjorken-x is briefly discussed.

Towards the ${\mathrm{N^3LO}}$ evolution of parton distributions

“…We have checked that our non-singlet results up to N ≤ 4 agree with previously known results [32,33,34,35]. High-n f parts have simpler diagram structures and values up to N > 40 have been computed, which are enough to determine the complete n 2 f and n 3 f parts of the non-singlet splitting functions and n 3 f parts of the singlet contributions [18]. To obtain higher-N moments, we need to switch to the second method.…”

“…Recently, results for partonic cross sections even in the next order, N 3 LO, are starting to appear: Higgs boson production via the gluon fusion [12,13,14] and the vector-boson fusion [15] in proton-proton collisions. N 3 LO results are also available for inclusive lepton-hadron deep inelastic scattering (DIS) [16,17,18] and jet production in DIS [19]. However, such N 3 LO analyses in principle require the four-loop splitting, which are still missing.…”

Four-loop non-singlet splitting functions in the planar limit and beyond

“…They thus provide a major step towards the consistent application of QCD factorization to theoretical predictions for N 3 LO cross sections with initial (final) state hadrons, as already obtained in refs. [21][22][23][24]26], which requires hard partonic cross section and PDFs (FFs) at the same order in renormalization-group improved perturbation theory.…”

“…refs. [22][23][24], the most complicated parts (without a factor ζ n ) of the non-singlet anomalous dimensions at n loops read γ (n)…”

“…However, computations for a number key observables at hadron colliders have been performed even at next-to-next-to-next-to-leading order (N 3 LO), including the cross section for Higgs-boson production in gluon-gluon fusion [21] and structure functions in deep-inelastic scattering (DIS) [22][23][24][25]. The latter results have also found an application in predicting Higgs-boson production in vector-boson fusion at the LHC [26].…”