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

Abstract

We have computed the even-$N$ moments $N\le 20$ of the pure-singlet quark splitting function $P_{\mathrm{ps}}$ at the fourth order of perturbative QCD via the anomalous dimensions of off-shell flavour-singlet operator matrix elements. Our results, derived analytically for a general gauge group, agree with all results obtained for this function so far, in particular with the lowest six even moments obtained via physical cross sections. Using these results and all available endpoint constraints, we construct approximations for $P_{\mathrm{ps}}$ at four loops that should be sufficient for most collider-physics applications. Together with the known results for the non-singlet splitting function $P_{\mathrm{ns}}^{+}$ at this order, this effectively completes the quark-quark contribution for the evolution of parton distribution at N${}^3$LO accuracy. Our new results thus provide a major step towards fully consistent N${}^3$LO calculations at the LHC and the reduction of the residual uncertainty in the parton evolution to the percent level.

arXiv comment17 pages latex, 2 figures, 2 ancillary files (FORM file with results and FORTRAN subroutine)

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Cited by in corpus (13)

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• Scaling violation in power corrections to energy correlators from the light-ray OPE
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
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• Combining QED and Approximate N${}^3$LO QCD Corrections in a Global PDF Fit: MSHT20qed_an3lo PDFs
• An FONLL prescription with coexisting flavor number PDFs
• disorder: Deep inelastic scattering at high orders
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• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• Constraints for twist-two alien operators in QCD
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
• Parton distribution functions and strong coupling constant: MSHT