The two-mass contribution to the three-loop pure singlet operator matrix element

2017/11/17 by Jakob Ablinger, J. Ablinger, J. Blümlein +6 · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chemistry #Combinatorics #Element (criminal law) #Iterated function #Loop (graph theory) #Mass matrix #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Operator (biology) #Order (exchange) #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Singlet state #hep-ph #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2017.12.018

28 papges Latex, 3 figures

arxiv created 2017/11/17 · openalex created_date 2017/12/04 · openalex publication_date 2017/12/28 · arxiv updated 2018/02/01 · openalex updated_date 2026/08/06

Abstract

We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function F2(x,Q2) at O(αs3) as well as for the matching relations in the variable flavor number scheme and the heavy quark distribution functions at the same order. The result for the operator matrix element is given in terms of generalized iterated integrals that include square root letters in the alphabet, depending also on the mass ratio through the main argument. Numerical results are presented.

Citations

• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• Two-loop massive operator matrix elements for unpolarized heavy flavor production to O(ϵ)
• Automatized analytic continuation of Mellin–Barnes integrals
• Mellin moments of the O(αs3) heavy flavor contributions to unpolarized deep-inelastic scattering at Q2≫m2 and anomalous dimensions
• Two-loop massive operator matrix elements and unpolarized heavy flavor production at asymptotic values Q2≫m2
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• Harmonic Polylogarithms
• Big-Bang Nucleosynthesis

Cited by

• The three-loop polarized pure singlet operator matrix element with two different masses
• Analytic computing methods for precision calculations in quantum field theory