The Polarized Transition Matrix Element $A_{gq}(N)$ of the Variable Flavor Number Scheme at $O({\alpha }_s^3)$

Abstract

We calculate the polarized massive operator matrix element $A_{gq}^{(3)}(N)$ to 3-loop order in Quantum Chromodynamics analytically at general values of the Mellin variable $N$ both in the single- and double-mass case in the Larin scheme. It is a transition function required in the variable flavor number scheme at $O({\alpha }_s^3)$. We also present the results in momentum fraction space.

arXiv comment26 pages Latex

References in corpus (77)

• Harmonic Polylogarithms
• The four-loop beta-function in Quantum Chromodynamics
• New features of FORM
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• The renormalization of the axial anomaly in dimensional regularization
• The three loop relation between the \bar {MS} and the pole quark masses
• Numerical evaluation of multiple polylogarithms
• Harmonic sums, Mellin transforms and Integrals
• Automatized analytic continuation of Mellin-Barnes integrals
• Reduze - Feynman Integral Reduction in C++
• Harmonic Sums and Mellin Transforms up to two-loop Order
• The Multiple Zeta Value Data Mine
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• Reduze 2 - Distributed Feynman Integral Reduction
• Charm electroproduction viewed in the variable-flavour number scheme versus fixed-order perturbation theory
• The Multithreaded version of FORM
• Quark mass relations to four-loop order
• Numerical Evaluation of Harmonic Polylogarithms
• The Calculation of the Two-Loop Spin Splitting Functions $P_{ij}^{(1)}(x)$
• 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
• 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
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• A Rederivation of the Spin-dependent Next-to-leading Order Splitting Functions
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• The three loop on-shell renormalization of QCD and QED
• The spin-dependent two-loop splitting functions
• Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• The Three-Loop Splitting Functions in QCD: The Helicity-Dependent Case
• A Refined Difference Field Theory for Symbolic Summation
• Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
• On the Behaviour of Non--Singlet Structure Functions at Small $x$
• 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
• 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 Gluonic Operator Matrix Elements at O(α_s^2) for DIS Heavy Flavor Production
• On the Twist 2 and Twist 3 Contributions to the Spin-dependent Electroweak Structure Functions
• The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
• The Evolution of Unpolarized Singlet Structure Functions at Small x
• 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)
• Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable
• Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction
• 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 $Q^2\gg m^2$
• The Singlet Contribution to the Structure Function $g_1(x,Q^2)$ at Small $x$
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• The $O({\alpha }_s^3{n}_f{T}_F^2{C}_{A,F})$} Contributions to the Gluonic Massive Operator Matrix Elements
• Workshop on Precision Measurements of alphas
• The $O({\alpha }_s^2)$ Heavy Quark Corrections to Charged Current Deep-Inelastic Scattering at large Virtualities
• The O(α_s^3 T_F^2) Contributions to the Gluonic Operator Matrix Element
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• The Polarized Three-Loop Anomalous Dimensions from On-Shell Massive Operator Matrix Elements
• Two-loop operator matrix elements calculated up to finite terms for polarized deep inelastic lepton-hadron scattering
• Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• The 3-Loop Non-Singlet Heavy Flavor Contributions to the Structure Function g_1(x,Q^2) at Large Momentum Transfer
• $O({\alpha }_s^2)$ and $O({\alpha }_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2\gg m^2$
• The O(α_s^3) Heavy Flavor Contributions to the Charged Current Structure Function xF_3(x,Q^2) at Large Momentum Transfer
• The three-loop single mass polarized pure singlet operator matrix element
• The two-mass contribution to the three-loop pure singlet operator matrix element
• Exact mass dependent two--loop ${\bar{\alpha }}_s(Q^2)$ in the background MOM renormalization scheme
• The Variable Flavor Number Scheme at Next-to-Leading Order
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• The three-loop polarized pure singlet operator matrix element with two different masses
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• Less Singular Terms and Small x Evolution in a Soluble Model
• The Asymptotic 3-Loop Heavy Flavor Corrections to the Charged Current Structure Functions $F_L^{W^{+}-W^{-}}(x,Q^2)$ and $F_2^{W^{+}-W^{-}}(x,Q^2)$

Cited by in corpus (12)

• The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements
• The massless three-loop Wilson coefficients for the deep-inelastic structure functions $F_2,F_L,x{F}_3$ and $g_1$
• The Logarithmic Contributions to the Polarized and Operator Matrix Elements in Deeply Inelastic Scattering
• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• $O({\alpha }_s^2$) Polarized Heavy Flavor Corrections}to Deep-Inelastic Scattering at $Q^2\gg m^2$
• Yadism: Yet Another Deep-Inelastic Scattering Module
• The inverse Mellin transform via analytic continuation
• The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
• Benchmark of deep-inelastic-scattering structure functions at $\mathcal{O}({\alpha }_s^3)$
• General mass variable flavor number scheme for $Z$ boson production in association with a heavy quark at hadron colliders
• Toward Precision Helicity PDFs from Global DIS and SIDIS Fits with Projected EIC Measurements