Additional results on the four-loop flavour-singlet splitting functions in QCD

2025/12/11 by G. Falcioni, Falcioni, G., Franz Herzog +7
Physics and Astronomy · #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #High-Energy Particle Collisions Research

paper · pdf · doi:10.48550/arxiv.2512.10783

Abstract

We have extended our previous computations, performed analytically for a general gauge group, of the even-N moments γ_{\rm ik} ⁽³⁾(N) of the four-loop flavour-singlet splitting functions P_{\rm ik} ⁽³⁾(x) to N = 22. The numerical QCD results perfectly agree with all predictions resulting from the approximations for P_{\rm ik} ⁽³⁾(x) that we obtained before from the moments N ≤ 20 and endpoint constraints, confirming their reliability for collider-physics applications. Due to the additional analytical constraints provided by our new N = 22 results, we are now closing in on determining the all-N forms of all non-rational (ζ-function) contributions to γ_{\rm ik} ⁽³⁾(N): only the n_f⁰ ζ₃ parts of the quark-to-gluon (gq) and the n_f¹ ζ₃ parts of the gluon-to-gluon (qg) cases still need to be completed. Finally we extend our approximations for all P_{\rm ik} ⁽³⁾(x) to n_f = 6 light flavours and update those for P_{\rm gq} ⁽³⁾(x) at lower n_f.

Citations

• Four-loop splitting functions in QCD -- The gluon-gluon case --
• Four-loop splitting functions in QCD -- The quark-to-gluon case
• The double fermionic contribution to the four-loop quark-to-gluon splitting function
• FORM version 4.2
• Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams
• New features of FORM

Related

• Additional moments and x-space approximations of four-loop splitting functions in QCD
• Four-loop splitting functions in QCD -- The quark-to-gluon case
• Flavour Non-Singlet Splitting Functions at Four Loops in QCD -- The Fermionic Contributions
• Four-loop splitting functions in QCD -- The gluon-gluon case --
• Four-loop results on anomalous dimensions and splitting functions in QCD