We have computed the first 30 even-N moments for the double fermionic (nf^2) part of the quark-to-gluon splitting function P_{gq} at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. From these results we have determined the all-N form, and hence the exact x-space expression, using systems of Diophantine equations for its coefficients. The dominant and subdominant leading small-x nf^2 contributions to P_{gq}^(3)(x) are of the form 1/x ln x and ln^4 x, respectively; the leading large-x term is ln^4 (1-x). The coefficient of the first of these is new, the other two agree with results obtained before and thus provide checks of our results.
Cite
@article{arxiv.2310.01245,
title = {The double fermionic contribution to the four-loop quark-to-gluon splitting function},
author = {G. Falcioni and F. Herzog and S. Moch and J. Vermaseren and A. Vogt},
journal= {arXiv preprint arXiv:2310.01245},
year = {2023}
}
Comments
10 pages, LaTex, 1 eps-based figure. Analytical results in ancillary FORM files