The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element

Abstract

The $O({\alpha }_s^3{T}_F^2{C}_F(C_A))$ contributions to the transition matrix element $A_{gg,Q}$ relevant for the variable flavor number scheme at 3--loop order are calculated. The corresponding graphs contain two massive fermion lines of equal mass leading to terms given by inverse binomially weighted sums beyond the usual harmonic sums. In $x$-space two root-valued letters contribute in the iterated integrals in addition to those forming the harmonic polylogarithms. We outline technical details needed in the calculation of graphs of this type, which are as well of importance in the case of two different internal massive lines.

arXiv comment39 papges LATEX, 8 Figures

References in corpus (65)

• Harmonic Polylogarithms
• Differential Equations for Two-Loop Four-Point Functions
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Harmonic sums, Mellin transforms and Integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Reduze - Feynman Integral Reduction in C++
• Group theory factors for Feynman diagrams
• Harmonic Sums and Mellin Transforms up to two-loop Order
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Reduze 2 - Distributed Feynman Integral Reduction
• Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
• The ABM parton distributions tuned to LHC data
• The Multithreaded version of FORM
• Massive Feynman diagrams and inverse binomial sums
• Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
• MATAD: a program package for the computation of MAssive TADpoles
• Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Rates for Inclusive Deep-Inelastic Electroproduction of Charm Quarks at HERA
• The massless higher-loop two-point function
• Numerical Evaluation of Two-Dimensional Harmonic Polylogarithms
• 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
• Analytic two-loop results for selfenergy- and vertex-type diagrams with one non-zero mass
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• A Refined Difference Field Theory for Symbolic Summation
• Expansion around half-integer values, binomial sums and inverse binomial sums
• Computer Algebra Algorithms for Special Functions in Particle Physics
• Analytic Continuation of Mellin Transforms up to two-loop Order
• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• The Theory of Deeply Inelastic Scattering
• The Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production
• The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• The Transition Matrix Element A_{gq}(N) of the Variable Flavor Number Scheme at O(α_s^3)
• The Strange Sea Density and Charm Production in Deep Inelastic Charged Current Processes
• Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Single-scale diagrams and multiple binomial sums
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements
• Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
• $O({\alpha }_s^2)$ corrections to polarized heavy flavour production at $Q^2\gg m^2$
• Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• Order α_s^2 Contributions to charm production in charged-current deep-inelastic lepton-hadron scattering
• The $O({\alpha }_s^3{n}_f{T}_F^2{C}_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements
• A Symbolic Summation Approach to Feynman Integral Calculus
• Workshop on Precision Measurements of alphas
• The $O({\alpha }_s^2)$ Heavy Quark Corrections to Charged Current Deep-Inelastic Scattering at large Virtualities
• Two-loop QED Operator Matrix Elements with Massive External Fermion Lines
• The Quark and Gluon Structure of the Proton
• Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations
• $O({\alpha }_s)$ Heavy Flavor Corrections to Charged Current Deep-Inelastic Scattering in Mellin Space
• $O({\alpha }_s^2)$ and $O({\alpha }_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2\gg m^2$
• 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines
• Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• New Heavy Flavor Contributions to the DIS Structure Function $F_2(x,Q^2)$ at $O(α_s^3)
• Logarithmic $O({\alpha }_s^3)$ contributions to the DIS Heavy Flavor Wilson Coefficients at $Q^2\gg m^2$

Cited by in corpus (40)

• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Evidence for intrinsic charm quarks in the proton
• Snowmass 2021 whitepaper: Proton structure at the precision frontier
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• Iterated Binomial Sums and their Associated Iterated Integrals
• Resummation and Matching of $b$-quark Mass Effects in $b\bar{b}H$ Production
• The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$
• The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,N_F)}$
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• EKO: Evolution Kernel Operators
• The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• The three-loop single mass polarized pure singlet operator matrix element
• The two-mass contribution to the three-loop pure singlet operator matrix element
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• Heavy-flavor parton distributions without heavy-flavor matching prescriptions
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• The Two-mass Contribution to the Three-Loop Polarized Operator Matrix Element $A_{gg,Q}^{(3)}$
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations
• The inverse Mellin transform via analytic continuation
• An FONLL prescription with coexisting flavor number PDFs
• Exact N${}^3$LO results for $q{q}^{\prime }\to H+X$
• A toolbox to solve coupled systems of differential and difference equations
• Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering
• Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• 3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering
• Unitarity methods for Mellin moments of Drell-Yan cross sections
• 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines
• Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
• 3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$
• Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package
• Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering
• 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering