The Three-Loop Splitting Functions in QCD: The Non-Singlet Case

By Sven-Olaf Moch, Jos Vermaseren, A. Vogt. 2004

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We compute the next-to-next-to-leading order (NNLO) contr ibutions to the three splitting functions governing the evolution of unpolarized non-singlet combin ations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fr actionsx do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factorddabc entering at three loops for the first time. We investigate the siz of the corrections and the stability of the NNLO evolution under variation of th e renormalization scale. Except for very smallx the corrections are found to be rather small even for large va lues of the strong coupling constant, in principle facilitating a perturbative evolut ion into the sub-GeV regime.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8d3dede01e53deb9c16882197cbcb6aca0444348

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Citations in the corpus

Calculation of the quark and gluon form factors to three loops in QCD (2010, background): “Casimir scaling has been verified to three loops [29, 30], but it is an open question whether it holds at four loops and beyond [41].”
Four loop twist two, BFKL, wrapping and strings (2008, methodology): “up to 3 loops [29] and using the maximum transcendentality conjecture [30] the corresponding answer in N = 4 SYM has been extracted [31, 32, 33].”
Transverse-momentum resummation: Higgs boson production at the Tevatron and the LHC (2011, methodology): “[35] were obtained by using the A(3) value from threshold resummation [72]).”
A facility to search for hidden particles at the CERN SPS: the SHiP physics case (2015, background): “The exact quark mass dependence for charm quark production in charged current DIS to NNLO is not available at present, though, it could, in principle, be extracted from Ref.”
Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (2011, neutral): “[47]), MSTW, and HERAPDF [48] are available with NNLO evolution [244, 245].”
Transcendentality and crossing (2006, background): “The conjecture was based on an intriguing transcendentality principle, which allowed us to extract the answer from a hard QCD computation [11].”
The quark beam function at NNLL (2010, background): “[49] to obtain γ J at three loops from the known three-loop result for γ f [29].”
Planar N = 4 gauge theory and the Hubbard model (2005, background): “Again, the construction seems compelling as it may be shown that (1) the Bethe ansatz correctly diagonalizes to three loops twist-two operators [33] whose dimensions are known form the work of [37, 38], (2) it also diagonalizes a twist-three operator to two loops which was confirmed using field theo”
The quark form factor at higher orders (2005, methodology): “[17, 18], the calculation has been performed via forward Compton amplitu des and the optical theorem.”
Two-loop soft corrections and resummation of the thrust distribution in the dijet region (2011, methodology): “J H E P 0 8 ( 2 0 1 1 ) 0 1 0 the two-loop value of Γsoft computed above and the three-loop splitting functions [97, 98].”
Introduction to Soft-Collinear Effective Theory (2014, background): “The coefficients for the cusp anomalous dimension are [111]”
A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions (2006, background): “In recent years severe efforts have been made to compute the NNLO corrections to the parton distribution functions [7] and important basic processes, such as vector boson production [8, 9, 10, 11, 12] and Higgs production [9, 13, 14, 15, 16] in hadron collisions 2”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, neutral): “First, we recall the expressions up to three loops [2, 30]:”
Model independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL (2012, background): “(4) we get the following relation, dD dlnμ = Γcusp , (8) where the cusp anomalous dimension Γcusp is known at three-loops [28].”