The two-loop massless off-shell QCD operator matrix elements to finite terms

DOI10.1016/j.nuclphysb.2022.115794OpenAlexW4225147767MaRDI QIDQ2144901

Carsten Schneider, K. Schönwald, Johannes Blümlein, Peter Marquard

Publication date: 17 June 2022

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.03216

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Point estimation (62F10) Strong interaction, including quantum chromodynamics (81V05) Structure, classification theorems for modules and ideals in commutative rings (13C05) Polylogarithms and relations with (K)-theory (11G55)

Related Items (5)

Four-loop splitting functions in QCD -- the quark-quark case ⋮ Renormalization of twist-two operators in covariant gauge to three loops in QCD ⋮ The massless three-loop Wilson coefficients for the deep-inelastic structure functions \(F_2\), \(F_L\), \(xF_3\) and \(g_1\) ⋮ \(O(\alpha_s^2)\) polarized heavy flavor corrections to deep-inelastic scattering at \(Q^2 \gg m^2\) ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• FORM
• HarmonicSums
• EvaluateMultiSums
• LiteRed

Cites Work

• Unnamed Item
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• The complete \(O(\alpha_s^2)\) non-singlet heavy flavor corrections to the structure functions \(g_{1, 2}^{e p}(x, Q^2)\), \(F_{1, 2, L}^{e p}(x, Q^2)\), \(F_{1, 2, 3}^{\nu(\overline{\nu})}(x, Q^2)\) and the associated sum rules
• Calculating three loop ladder and \(V\)-topologies for massive operator matrix elements by computer algebra
• The \(O(\alpha_s^3)\) massive operator matrix elements of \(O(n_f)\) for the structure function \(F_{2}(x,Q^{2})\) and transversity
• Parameterized telescoping proves algebraic independence of sums
• Determining the closed forms of the anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
• Structural relations of harmonic sums and Mellin transforms up to weight \(w=5\)
• Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms
• Algebraic relations between harmonic sums and associated quantities.
• The three-loop splitting functions in QCD: the non-singlet case
• The three-loop splitting functions in QCD: the singlet case
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\) and transversity
• The three-loop splitting functions in QCD: the helicity-dependent case
• The 3-loop pure singlet heavy flavor contributions to the structure function \(F_2(x, Q^2)\) and the anomalous dimension
• The 3-loop non-singlet heavy flavor contributions to the structure function \(g_1(x, Q^2)\) at large momentum transfer
• Third-order QCD corrections to the charged-current structure function \(F_{3}\)
• Mellin moments of the \(O(\alpha_s^3)\) heavy flavor contributions to unpolarized deep-inelastic scattering at \(Q^{2}\gg m^{2}\) and anomalous dimensions
• Automated solution of first order factorizable systems of differential equations in one variable
• Automatic Feynman graph generation
• On rational and hypergeometric solutions of linear ordinary difference equations in \(\Pi\Sigma^\ast\)-field extensions
• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The polarized two-loop massive pure singlet Wilson coefficient for deep-inelastic scattering
• The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements
• The three-loop single mass polarized pure singlet operator matrix element
• The two-mass contribution to the three-loop polarized gluonic operator matrix element \(A_{gg, Q}^{(3)}\)
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• Computer algebra and polynomials. Applications of algebra and number theory
• The method of arbitrarily large moments to calculate single scale processes in quantum field theory
• The three-loop splitting functions \(P_{q g}^{(2)}\) and \(P_{g g}^{(2, \operatorname{N}_{\operatorname{F}})}\)
• The \(O({\alpha}_s^2)\) heavy quark corrections to charged current deep-inelastic scattering at large virtualities
• The transition matrix element \(A_{gq}(N)\) of the variable flavor number scheme at \(O({\alpha}_s^3)\)
• Symbolic summation assists combinatorics
• Ore Polynomials in Sage
• Harmonic sums and polylogarithms generated by cyclotomic polynomials
• Iterated binomial sums and their associated iterated integrals
• A Symbolic Summation Approach to Find Optimal Nested Sum Representations
• SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS
• Nielsen’s Generalized Polylogarithms
• Summation in Finite Terms
• HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS
• HARMONIC POLYLOGARITHMS
• Iterated elliptic and hypergeometric integrals for Feynman diagrams
• Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations
• Simplifying Multiple Sums in Difference Fields
• Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

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