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arXiv · 2404.09701

Four-loop splitting functions in QCD -- The quark-to-gluon case

G. Falcioni·F. Herzog·S. Moch·A. Pelloni·A. Vogt
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Abstract

We present the even-N moments N =< 20 of the fourth-order (N^3LO) contribution P_{gq}^(3)(x) to the quark-to-gluon splitting function in perturbative QCD. These moments, obtained by analytically computing off-shell operator matrix elements for a general gauge group, agree with all known results, in particular with the moments N =< 10 derived before from structure functions in deep-inelastic scattering. Using the new moments and the available endpoint constraints, we construct approximations for P_{gq}^(3)(x) which improve upon those obtained from the lowest five even moments. The remaining uncertainties of this function are now practically irrelevant at momentum fractions x > 0.1. The resulting errors of the convolution of P_{gq} at N^3LO with a typical quark distribution are small at x >~ 10^{-3} and exceed 1% only at x ~< 10^{-4} for a strong coupling alpha_s = 0.2. The present results for P_{gq}^(3)(x) should thus be sufficient for most collider-physics applications.

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G. Falcioni, F. Herzog, S. Moch, A. Pelloni, A. Vogt. 2024-04-15. Four-loop splitting functions in QCD -- The quark-to-gluon case. https://arxiv.org/abs/2404.09701

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