The double fermionic contribution to the four-loop quark-to-gluon splitting function

2023/10/02 by Falcioni, G., Herzog, F., Moch, S. +2 · 9 citations
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2310.01245

Abstract

We have computed the first 30 even-N moments for the double fermionic (nf²) 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 nf² contributions to P_gq^(3)(x) are of the form 1/x ln x and ln⁴ x, respectively; the leading large-x term is ln⁴ (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.

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